1,1,113,0,0.310618," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 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)} C a - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a}{480 \, d}"," ",0,"-1/480*(160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a)/d","A",0
2,1,90,0,0.509908," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a + 96 \, A a \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a + 96*A*a*sin(d*x + c))/d","A",0
3,1,67,0,0.774315," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 12 \, A a \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a + 12*A*a*sin(d*x + c))/d","A",0
4,1,63,0,0.985330," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 4 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, C a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a + 4*A*a*log(sec(d*x + c) + tan(d*x + c)) + 4*C*a*sin(d*x + c))/d","A",0
5,1,59,0,0.625108," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C a + A a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a \sin\left(d x + c\right) + 2 \, A a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a + A*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a*sin(d*x + c) + 2*A*a*tan(d*x + c))/d","A",0
6,1,95,0,0.323356," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C a - A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*a - A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a*tan(d*x + c))/d","A",0
7,1,107,0,0.625061," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a - 3 \, A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a - 3*A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a*tan(d*x + c))/d","A",0
8,1,152,0,0.447351," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a - 3 \, A a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a - 3*A*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*C*a*tan(d*x + c))/d","A",0
9,1,204,0,0.646961," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 128 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{2} + 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2}}{960 \, d}"," ",0,"-1/960*(640*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 - 128*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^2 + 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^2 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2)/d","A",0
10,1,156,0,0.320771," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 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)} C a^{2} + 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 240 \, A a^{2} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(80*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 - 16*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^2 + 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 - 240*A*a^2*sin(d*x + c))/d","A",0
11,1,132,0,0.707509," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 96 \, {\left(d x + c\right)} A a^{2} - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a^{2} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 192 \, A a^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 96*(d*x + c)*A*a^2 - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 192*A*a^2*sin(d*x + c))/d","A",0
12,1,107,0,0.504085," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a^{2} - 2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 6 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 6 \, A a^{2} \sin\left(d x + c\right) + 6 \, C a^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(12*(d*x + c)*A*a^2 - 2*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 6*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 6*A*a^2*sin(d*x + c) + 6*C*a^2*sin(d*x + c))/d","A",0
13,1,101,0,0.372162," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 4 \, {\left(d x + c\right)} C a^{2} + 4 \, A a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, C a^{2} \sin\left(d x + c\right) + 4 \, A a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 4*(d*x + c)*C*a^2 + 4*A*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*C*a^2*sin(d*x + c) + 4*A*a^2*tan(d*x + c))/d","A",0
14,1,142,0,0.593040," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{8 \, {\left(d x + c\right)} C a^{2} - A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{2} \sin\left(d x + c\right) + 8 \, A a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(8*(d*x + c)*C*a^2 - A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*A*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*a^2*sin(d*x + c) + 8*A*a^2*tan(d*x + c))/d","A",0
15,1,138,0,0.482067," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 6 \, {\left(d x + c\right)} C a^{2} - 3 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A a^{2} \tan\left(d x + c\right) + 6 \, C 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*a^2 + 6*(d*x + c)*C*a^2 - 3*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*A*a^2*tan(d*x + c) + 6*C*a^2*tan(d*x + c))/d","A",0
16,1,234,0,0.423965," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} - 3 \, A a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 96 \, C a^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 - 3*A*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 96*C*a^2*tan(d*x + c))/d","A",0
17,1,218,0,0.329713," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{2} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 15 \, A a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, C a^{2} \tan\left(d x + c\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*a^2 + 40*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 40*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 15*A*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*C*a^2*tan(d*x + c))/d","A",0
18,1,284,0,0.414124," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{448 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} - 6720 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} + 630 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 192 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} C a^{3} + 1344 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{3} - 105 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3}}{6720 \, d}"," ",0,"1/6720*(448*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 - 6720*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 + 630*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 + 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 192*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*C*a^3 + 1344*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^3 - 105*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^3 + 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3)/d","A",0
19,1,239,0,0.396141," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A 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)} C 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)} C a^{3} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 960 \, A a^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(960*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 - 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*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))*C*a^3 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 960*A*a^3*sin(d*x + c))/d","A",0
20,1,190,0,0.683275," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 480 \, {\left(d x + c\right)} A a^{3} - 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)} C a^{3} + 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 1440 \, A a^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"-1/480*(160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 480*(d*x + c)*A*a^3 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^3 + 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 1440*A*a^3*sin(d*x + c))/d","A",0
21,1,163,0,0.596587," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{8 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 96 \, {\left(d x + c\right)} A a^{3} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a^{3} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 32 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 96 \, A a^{3} \sin\left(d x + c\right) + 32 \, C a^{3} \sin\left(d x + c\right)}{32 \, d}"," ",0,"1/32*(8*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 + 96*(d*x + c)*A*a^3 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 32*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 96*A*a^3*sin(d*x + c) + 32*C*a^3*sin(d*x + c))/d","A",0
22,1,137,0,0.503063," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{36 \, {\left(d x + c\right)} A a^{3} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 12 \, {\left(d x + c\right)} C a^{3} + 18 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{3} \sin\left(d x + c\right) + 36 \, C a^{3} \sin\left(d x + c\right) + 12 \, A a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(36*(d*x + c)*A*a^3 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 12*(d*x + c)*C*a^3 + 18*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^3*sin(d*x + c) + 36*C*a^3*sin(d*x + c) + 12*A*a^3*tan(d*x + c))/d","A",0
23,1,175,0,0.374343," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a^{3} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 12 \, {\left(d x + c\right)} C a^{3} - A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a^{3} \sin\left(d x + c\right) + 12 \, A a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a^3 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 12*(d*x + c)*C*a^3 - A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a^3*sin(d*x + c) + 12*A*a^3*tan(d*x + c))/d","A",0
24,1,177,0,0.691175," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 36 \, {\left(d x + c\right)} C a^{3} - 9 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a^{3} \sin\left(d x + c\right) + 36 \, A a^{3} \tan\left(d x + c\right) + 12 \, C 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*a^3 + 36*(d*x + c)*C*a^3 - 9*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a^3*sin(d*x + c) + 36*A*a^3*tan(d*x + c) + 12*C*a^3*tan(d*x + c))/d","A",0
25,1,257,0,0.678118," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 16 \, {\left(d x + c\right)} C a^{3} - A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 16 \, A a^{3} \tan\left(d x + c\right) + 48 \, C 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*a^3 + 16*(d*x + c)*C*a^3 - A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 4*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 16*A*a^3*tan(d*x + c) + 48*C*a^3*tan(d*x + c))/d","A",0
26,1,292,0,0.345486," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 45 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 720 \, C a^{3} \tan\left(d x + c\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*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 45*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 720*C*a^3*tan(d*x + c))/d","A",0
27,1,382,0,0.337329," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\frac{96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{3} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 5 \, A a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, C a^{3} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^3 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 5*A*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 90*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 360*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*C*a^3*tan(d*x + c))/d","A",0
28,1,393,0,0.334623," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{28672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 143360 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} + 20160 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 26880 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 12288 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} C a^{4} + 28672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{4} - 35 \, {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 840 \, d x - 840 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 3360 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 3360 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4}}{107520 \, d}"," ",0,"1/107520*(28672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 560*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 - 143360*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 + 20160*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 26880*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 12288*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*C*a^4 + 28672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 - 35*(128*sin(2*d*x + 2*c)^3 - 840*d*x - 840*c - 3*sin(8*d*x + 8*c) - 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*C*a^4 - 3360*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^4 + 3360*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4)/d","A",0
29,1,319,0,0.351584," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{112 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 3360 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} + 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 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)} C 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)} C a^{4} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 560 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 1680 \, A a^{4} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(112*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 3360*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 + 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 48*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*C*a^4 + 672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 - 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^4 - 560*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 + 1680*A*a^4*sin(d*x + c))/d","A",0
30,1,273,0,0.389832," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 1440 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 960 \, {\left(d x + c\right)} A 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)} C 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)} C a^{4} + 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a^{4} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 3840 \, A a^{4} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 - 1440*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 960*(d*x + c)*A*a^4 - 256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*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))*C*a^4 + 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 - 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 3840*A*a^4*sin(d*x + c))/d","A",0
31,1,222,0,0.334937," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","-\frac{40 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 480 \, {\left(d x + c\right)} A a^{4} - 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)} C a^{4} + 240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 120 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 720 \, A a^{4} \sin\left(d x + c\right) - 120 \, C a^{4} \sin\left(d x + c\right)}{120 \, d}"," ",0,"-1/120*(40*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 480*(d*x + c)*A*a^4 - 8*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 + 240*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 120*A*a^4*log(sec(d*x + c) + tan(d*x + c)) - 720*A*a^4*sin(d*x + c) - 120*C*a^4*sin(d*x + c))/d","A",0
32,1,194,0,0.335852," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 576 \, {\left(d x + c\right)} A a^{4} - 128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a^{4} + 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 96 \, {\left(d x + c\right)} C a^{4} + 192 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 384 \, A a^{4} \sin\left(d x + c\right) + 384 \, C a^{4} \sin\left(d x + c\right) + 96 \, A a^{4} \tan\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 576*(d*x + c)*A*a^4 - 128*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 + 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 96*(d*x + c)*C*a^4 + 192*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 384*A*a^4*sin(d*x + c) + 384*C*a^4*sin(d*x + c) + 96*A*a^4*tan(d*x + c))/d","A",0
33,1,211,0,0.334075," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{48 \, {\left(d x + c\right)} A a^{4} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 12 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 48 \, {\left(d x + c\right)} C a^{4} - 3 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{4} \sin\left(d x + c\right) + 72 \, C a^{4} \sin\left(d x + c\right) + 48 \, A a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(48*(d*x + c)*A*a^4 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 12*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 48*(d*x + c)*C*a^4 - 3*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 36*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^4*sin(d*x + c) + 72*C*a^4*sin(d*x + c) + 48*A*a^4*tan(d*x + c))/d","A",0
34,1,211,0,0.341529," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 12 \, {\left(d x + c\right)} A a^{4} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 72 \, {\left(d x + c\right)} C a^{4} - 12 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a^{4} \sin\left(d x + c\right) + 72 \, A a^{4} \tan\left(d x + c\right) + 12 \, C a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 12*(d*x + c)*A*a^4 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 72*(d*x + c)*C*a^4 - 12*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*C*a^4*sin(d*x + c) + 72*A*a^4*tan(d*x + c) + 12*C*a^4*tan(d*x + c))/d","A",0
35,1,296,0,0.337512," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 192 \, {\left(d x + c\right)} C a^{4} - 3 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a^{4} \sin\left(d x + c\right) + 192 \, A a^{4} \tan\left(d x + c\right) + 192 \, C a^{4} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(64*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 192*(d*x + c)*C*a^4 - 3*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 72*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 144*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*C*a^4*sin(d*x + c) + 192*A*a^4*tan(d*x + c) + 192*C*a^4*tan(d*x + c))/d","A",0
36,1,315,0,0.648602," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{4} + 120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 20 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} + 60 \, {\left(d x + c\right)} C a^{4} - 15 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 60 \, A a^{4} \tan\left(d x + c\right) + 360 \, C 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*a^4 + 120*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 20*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 + 60*(d*x + c)*C*a^4 - 15*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 60*A*a^4*tan(d*x + c) + 360*C*a^4*tan(d*x + c))/d","A",0
37,1,456,0,0.506790," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,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 a^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 5 \, A 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 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)} - 30 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 720 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 1920 \, C a^{4} \tan\left(d x + c\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*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 5*A*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*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)) - 30*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 720*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 1920*C*a^4*tan(d*x + c))/d","B",0
38,1,462,0,0.395239," ","integrate((a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""maxima"")","\frac{24 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} A a^{4} + 336 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{4} + 280 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 56 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 1680 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 35 \, A a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 840 \, C a^{4} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(24*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*A*a^4 + 336*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^4 + 280*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 56*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 1680*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 35*A*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 210*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 210*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 840*C*a^4*tan(d*x + c))/d","A",0
39,1,351,0,0.753093," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{109 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{115 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{12 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 12 \, A {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{12 \, d}"," ",0,"-1/12*(C*((21*sin(d*x + c)/(cos(d*x + c) + 1) + 109*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 115*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 12*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 12*A*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
40,1,269,0,0.642849," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, A {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{3 \, d}"," ",0,"1/3*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*A*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
41,1,184,0,0.440488," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - A {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(C*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))) - A*(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
42,1,117,0,0.647158," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - \frac{A \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - A*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
43,1,125,0,0.419905," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + A {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"(C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + A*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
44,1,144,0,0.373693," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - \frac{C \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(A*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - C*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
45,1,239,0,0.345472," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 2 \, C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{2 \, d}"," ",0,"-1/2*(A*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 2*C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
46,1,325,0,0.421723," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{A {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 6 \, C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(A*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a - 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 6*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 6*C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
47,1,415,0,0.453237," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{93 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{341 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{395 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{195 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{2 \, {\left(\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{165 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + 2 \, A {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{12 \, d}"," ",0,"-1/12*(C*((93*sin(d*x + c)/(cos(d*x + c) + 1) + 341*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 395*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 195*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^2 + 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 2*(33*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 165*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + 2*A*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","B",0
48,1,325,0,0.421782," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{60 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + A {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(C*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 60*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + A*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
49,1,236,0,0.453347," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"-1/6*(C*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + A*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","A",0
50,1,165,0,0.415663," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{A {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(C*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 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))) + A*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
51,1,119,0,0.500450," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - \frac{A {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - A*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
52,1,146,0,0.365902," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(A*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 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) - C*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
53,1,191,0,0.415810," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{A {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(A*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 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))) + C*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
54,1,288,0,0.343102," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{A {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} + C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"-1/6*(A*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 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) + C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2))/d","B",0
55,1,379,0,0.337303," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{A {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} + C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(A*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 - 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 30*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 30*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) + C*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
56,1,365,0,0.431792," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{C {\left(\frac{20 \, {\left(\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{76 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{51 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{735 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{50 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{1380 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + 3 \, A {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(C*(20*(33*sin(d*x + c)/(cos(d*x + c) + 1) + 76*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 51*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3 + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (735*sin(d*x + c)/(cos(d*x + c) + 1) - 50*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 1380*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + 3*A*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","A",0
57,1,276,0,0.454541," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(C*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + A*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","A",0
58,1,205,0,1.143421," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + \frac{A {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(3*C*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + A*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
59,1,140,0,0.507223," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - \frac{3 \, A {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(C*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - 3*A*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
60,1,134,0,0.347338," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{A {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(A*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + C*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
61,1,167,0,0.342659," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - \frac{3 \, C {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(A*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - 3*C*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
62,1,233,0,0.397979," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, A {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(3*A*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 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) + C*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
63,1,330,0,0.350939," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(A*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 - 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 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) + C*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","A",0
64,1,421,0,0.329904," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{A {\left(\frac{20 \, {\left(\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{76 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{51 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3} - \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{735 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{50 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{690 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{690 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + 3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(A*(20*(33*sin(d*x + c)/(cos(d*x + c) + 1) - 76*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 51*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3 - 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (735*sin(d*x + c)/(cos(d*x + c) + 1) + 50*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 690*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 690*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) + 3*C*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 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
65,1,318,0,0.420701," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, C {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} + \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{5880 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + 5 \, A {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"-1/840*(3*C*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) + 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 + 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) - 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 5880*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + 5*A*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4))/d","A",0
66,1,246,0,0.417868," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{C {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} + \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + \frac{3 \, A {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(C*(1680*sin(d*x + c)/((a^4 + a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) - 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + 3*A*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
67,1,201,0,0.420802," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, C {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} - \frac{A {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"-1/840*(5*C*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) - A*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
68,1,175,0,0.330591," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{A {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{3 \, C {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(A*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + 3*C*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
69,1,175,0,0.331912," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{C {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{3 \, A {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(C*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + 3*A*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
70,1,228,0,0.337141," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, A {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - \frac{C {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"-1/840*(5*A*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 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) - C*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
71,1,274,0,0.348106," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{A {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + \frac{3 \, C {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(A*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + 3*C*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
72,1,372,0,0.357196," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, A {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} - \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + 5 \, C {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"-1/840*(3*A*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 - 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) + 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + 5*C*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4))/d","A",0
73,1,461,0,0.354194," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{A {\left(\frac{560 \, {\left(\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{62 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{39 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{4} - \frac{3 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{21945 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2065 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{231 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{18480 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{18480 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + C {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"1/840*(A*(560*(27*sin(d*x + c)/(cos(d*x + c) + 1) - 62*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 39*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^4 - 3*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (21945*sin(d*x + c)/(cos(d*x + c) + 1) + 2065*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 231*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 18480*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 18480*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + C*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 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
74,1,160,0,0.582233," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{396 \, {\left(5 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 35 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 105 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 5 \, {\left(63 \, \sqrt{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 77 \, \sqrt{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 495 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 693 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2310 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6930 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{55440 \, d}"," ",0,"1/55440*(396*(5*sqrt(2)*sin(7/2*d*x + 7/2*c) + 7*sqrt(2)*sin(5/2*d*x + 5/2*c) + 35*sqrt(2)*sin(3/2*d*x + 3/2*c) + 105*sqrt(2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 5*(63*sqrt(2)*sin(11/2*d*x + 11/2*c) + 77*sqrt(2)*sin(9/2*d*x + 9/2*c) + 495*sqrt(2)*sin(7/2*d*x + 7/2*c) + 693*sqrt(2)*sin(5/2*d*x + 5/2*c) + 2310*sqrt(2)*sin(3/2*d*x + 3/2*c) + 6930*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
75,1,131,0,0.575562," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{84 \, {\left(3 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + {\left(35 \, \sqrt{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 252 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 420 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 1890 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(84*(3*sqrt(2)*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*sin(3/2*d*x + 3/2*c) + 30*sqrt(2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + (35*sqrt(2)*sin(9/2*d*x + 9/2*c) + 45*sqrt(2)*sin(7/2*d*x + 7/2*c) + 252*sqrt(2)*sin(5/2*d*x + 5/2*c) + 420*sqrt(2)*sin(3/2*d*x + 3/2*c) + 1890*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
76,1,103,0,0.542617," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{140 \, {\left(\sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 3 \, {\left(5 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 35 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 105 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{420 \, d}"," ",0,"1/420*(140*(sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 3*(5*sqrt(2)*sin(7/2*d*x + 7/2*c) + 7*sqrt(2)*sin(5/2*d*x + 5/2*c) + 35*sqrt(2)*sin(3/2*d*x + 3/2*c) + 105*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
77,1,72,0,0.574271," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{60 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(3 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{30 \, d}"," ",0,"1/30*(60*sqrt(2)*A*sqrt(a)*sin(1/2*d*x + 1/2*c) + (3*sqrt(2)*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*sin(3/2*d*x + 3/2*c) + 30*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
78,1,37,0,0.513959," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(\sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{3 \, d}"," ",0,"1/3*(sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a)/d","A",0
79,1,731,0,0.629771," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{8 \, \sqrt{2} C \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{4 \, d}"," ",0,"1/4*(8*sqrt(2)*C*sqrt(a)*sin(1/2*d*x + 1/2*c) - (4*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 4*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
80,1,2643,0,4.327532," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(3 \, {\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)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 12 \, {\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)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\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)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, {\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)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 24 \, \sqrt{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 8 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(6 \, {\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)} \cos\left(2 \, d x + 2 \, c\right) + 6 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 6 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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) - 4 \, {\left(2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(3 \, {\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)} \sin\left(2 \, d x + 2 \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 12 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 4 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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)} A \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*(3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(4*d*x + 4*c)^2 + 12*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(2*d*x + 2*c)^2 + 3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(4*d*x + 4*c)^2 + 12*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(2*d*x + 2*c)^2 - 24*sqrt(2)*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) - 8*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 2*(6*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(2*d*x + 2*c) + 6*sqrt(2)*sin(7/2*d*x + 7/2*c) + 2*sqrt(2)*sin(5/2*d*x + 5/2*c) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) - 6*sqrt(2)*sin(1/2*d*x + 1/2*c) + 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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) - 4*(2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*sin(1/2*d*x + 1/2*c) - 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*(3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(2*d*x + 2*c) - 3*sqrt(2)*cos(7/2*d*x + 7/2*c) - sqrt(2)*cos(5/2*d*x + 5/2*c) + sqrt(2)*cos(3/2*d*x + 3/2*c) + 3*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c) + 12*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*d*x + 7/2*c) + 4*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 8*(sqrt(2)*cos(3/2*d*x + 3/2*c) + 3*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*sin(1/2*d*x + 1/2*c) + 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*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
81,1,3088,0,0.888573," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(120 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 8 \, {\left(15 \, \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 50 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 42 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 360 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 1200 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 24 \, {\left(42 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 15 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 15 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 120 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 8 \, {\left(15 \, \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 50 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 42 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3 \, \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)\right)} \sin\left(6 \, d x + 6 \, c\right) - 120 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 400 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 24 \, {\left(42 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3 \, \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)\right)} \sin\left(4 \, d x + 4 \, c\right) - 336 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 24 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 1008 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 72 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 120 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 120 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 120 \, {\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)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 40 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} A \sqrt{a}}{\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}} + \frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"-1/96*((120*(sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 3*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) - 8*(15*sin(11/2*d*x + 11/2*c) + 50*sin(9/2*d*x + 9/2*c) + 42*sin(7/2*d*x + 7/2*c) + 3*sin(5/2*d*x + 5/2*c) - 5*sin(3/2*d*x + 3/2*c))*cos(6*d*x + 6*c) + 360*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) + 1200*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) - 24*(42*sin(7/2*d*x + 7/2*c) + 3*sin(5/2*d*x + 5/2*c) - 5*sin(3/2*d*x + 3/2*c))*cos(4*d*x + 4*c) - 15*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 15*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 120*(cos(6*d*x + 6*c) + 3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*sin(13/2*d*x + 13/2*c) + 8*(15*cos(11/2*d*x + 11/2*c) + 50*cos(9/2*d*x + 9/2*c) + 42*cos(7/2*d*x + 7/2*c) + 3*cos(5/2*d*x + 5/2*c) - 5*cos(3/2*d*x + 3/2*c))*sin(6*d*x + 6*c) - 120*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*sin(11/2*d*x + 11/2*c) - 400*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*sin(9/2*d*x + 9/2*c) + 24*(42*cos(7/2*d*x + 7/2*c) + 3*cos(5/2*d*x + 5/2*c) - 5*cos(3/2*d*x + 3/2*c))*sin(4*d*x + 4*c) - 336*(3*cos(2*d*x + 2*c) + 1)*sin(7/2*d*x + 7/2*c) - 24*(3*cos(2*d*x + 2*c) + 1)*sin(5/2*d*x + 5/2*c) + 1008*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 72*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 120*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) + 120*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 120*(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)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 40*sin(3/2*d*x + 3/2*c))*A*sqrt(a)/(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)) + 24*(4*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 4*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
82,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^5*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,1,170,0,1.485254," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{44 \, {\left(15 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 175 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 735 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 7 \, {\left(15 \, \sqrt{2} a \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, \sqrt{2} a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 165 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 429 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 990 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3630 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{18480 \, d}"," ",0,"1/18480*(44*(15*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 63*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 175*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 735*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 7*(15*sqrt(2)*a*sin(11/2*d*x + 11/2*c) + 55*sqrt(2)*a*sin(9/2*d*x + 9/2*c) + 165*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 429*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 990*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 3630*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
84,1,138,0,0.772877," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{252 \, {\left(\sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + {\left(35 \, \sqrt{2} a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 378 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 1050 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3780 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(252*(sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 20*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + (35*sqrt(2)*a*sin(9/2*d*x + 9/2*c) + 135*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 378*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 1050*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 3780*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
85,1,108,0,0.804940," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{140 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + {\left(15 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 175 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 735 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{420 \, d}"," ",0,"1/420*(140*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + (15*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 63*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 175*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 735*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
86,1,54,0,0.643895," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{{\left(\sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{10 \, d}"," ",0,"1/10*(sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 20*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a)/d","A",0
87,1,1354,0,1.114518," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a} - \frac{3 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 6 \, \sqrt{2} a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 2 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 6 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{12 \, d}"," ",0,"1/12*(4*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a) - 3*(2*sqrt(2)*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 6*sqrt(2)*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 5*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 2*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/2*d*x + 7/2*c) - 6*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/2*d*x + 5/2*c) + 2*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
88,1,2025,0,1.056239," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","-\frac{{\left(12 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 48 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 48 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 160 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 168 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 72 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 24 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 12 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 48 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 4 \, {\left(12 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 20 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 3 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 7 \, {\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 12 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 48 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 4 \, {\left(12 \, a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 9 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 80 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 84 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 24 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + 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) + 56 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{16 \, {\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)} d}"," ",0,"-1/16*(12*a*cos(4*d*x + 4*c)^2*sin(3/2*d*x + 3/2*c) + 48*a*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 12*a*sin(4*d*x + 4*c)^2*sin(3/2*d*x + 3/2*c) + 48*a*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 160*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 168*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 72*a*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 24*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 4*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) + 12*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) + 48*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) + 4*(12*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 20*a*sin(7/2*d*x + 7/2*c) - 21*a*sin(5/2*d*x + 5/2*c) - 3*a*sin(3/2*d*x + 3/2*c))*cos(4*d*x + 4*c) - 7*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(13/2*d*x + 13/2*c) - 12*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(11/2*d*x + 11/2*c) - 48*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(9/2*d*x + 9/2*c) + 4*(12*a*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 20*a*cos(7/2*d*x + 7/2*c) + 21*a*cos(5/2*d*x + 5/2*c) + 9*a*cos(3/2*d*x + 3/2*c))*sin(4*d*x + 4*c) - 80*(2*a*cos(2*d*x + 2*c) + a)*sin(7/2*d*x + 7/2*c) - 84*(2*a*cos(2*d*x + 2*c) + a)*sin(5/2*d*x + 5/2*c) - 24*a*sin(3/2*d*x + 3/2*c) - 4*(a*cos(4*d*x + 4*c)^2 + 4*a*cos(2*d*x + 2*c)^2 + a*sin(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*sin(2*d*x + 2*c)^2 + 2*(2*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 56*(a*cos(4*d*x + 4*c)^2 + 4*a*cos(2*d*x + 2*c)^2 + a*sin(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*sin(2*d*x + 2*c)^2 + 2*(2*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/((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))*d)","B",0
89,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,1,6985,0,1.948353," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","-\frac{\frac{{\left(140 \, a \cos\left(8 \, d x + 8 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2240 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5040 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2240 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 140 \, a \sin\left(8 \, d x + 8 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2240 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5040 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 2240 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 4064 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 336 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 240 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 1360 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 36 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 4 \, a \sin\left(6 \, d x + 6 \, c\right) + 6 \, a \sin\left(4 \, d x + 4 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{21}{2} \, d x + \frac{21}{2} \, c\right) + 140 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 4 \, a \sin\left(6 \, d x + 6 \, c\right) + 6 \, a \sin\left(4 \, d x + 4 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{19}{2} \, d x + \frac{19}{2} \, c\right) + 456 \, {\left(a \sin\left(8 \, d x + 8 \, c\right) + 4 \, a \sin\left(6 \, d x + 6 \, c\right) + 6 \, a \sin\left(4 \, d x + 4 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{17}{2} \, d x + \frac{17}{2} \, c\right) + 4 \, {\left(280 \, a \cos\left(6 \, d x + 6 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 420 \, a \cos\left(4 \, d x + 4 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 280 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 290 \, a \sin\left(\frac{15}{2} \, d x + \frac{15}{2} \, c\right) - 596 \, a \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 780 \, a \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 750 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 254 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 85 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(8 \, d x + 8 \, c\right) + 2320 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{2} \, d x + \frac{15}{2} \, c\right) + 4768 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 16 \, {\left(420 \, a \cos\left(4 \, d x + 4 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 280 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 780 \, a \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 750 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 254 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 85 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 6240 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 6000 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 24 \, {\left(280 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 254 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 85 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 75 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, \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(2 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \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(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, \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(6 \, d x + 6 \, c\right) + \sqrt{2} 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) + 75 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, \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(2 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \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(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, \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(6 \, d x + 6 \, c\right) + \sqrt{2} 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) - 75 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, \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(2 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \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(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, \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(6 \, d x + 6 \, c\right) + \sqrt{2} 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) + 75 \, {\left(\sqrt{2} a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right)^{2} + 8 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(4 \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, \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(2 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 3 \, \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(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, \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(6 \, d x + 6 \, c\right) + \sqrt{2} 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) + 36 \, {\left(a \cos\left(8 \, d x + 8 \, c\right) + 4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{21}{2} \, d x + \frac{21}{2} \, c\right) - 140 \, {\left(a \cos\left(8 \, d x + 8 \, c\right) + 4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{19}{2} \, d x + \frac{19}{2} \, c\right) - 456 \, {\left(a \cos\left(8 \, d x + 8 \, c\right) + 4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{17}{2} \, d x + \frac{17}{2} \, c\right) + 4 \, {\left(280 \, a \sin\left(6 \, d x + 6 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 420 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 280 \, a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 290 \, a \cos\left(\frac{15}{2} \, d x + \frac{15}{2} \, c\right) + 596 \, a \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 780 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 750 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 254 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 15 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) - 1160 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{15}{2} \, d x + \frac{15}{2} \, c\right) - 2384 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 16 \, {\left(420 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 280 \, a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 780 \, a \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 750 \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 254 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 15 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - 3120 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 3000 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 24 \, {\left(280 \, a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 254 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 15 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 1016 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 84 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 200 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 36 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \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) + 600 \, {\left(a \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, a \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, a \cos\left(6 \, d x + 6 \, c\right) + 6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, a \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(2 \, a \sin\left(6 \, d x + 6 \, c\right) + 3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + a\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{\sqrt{2} \cos\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)^{2} + 16 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 36 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(4 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(8 \, d x + 8 \, c\right) + 8 \, {\left(6 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 12 \, {\left(4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(8 \, d x + 8 \, c\right) + 16 \, {\left(3 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 8 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}} + \frac{16 \, {\left(12 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 48 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 48 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 160 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 168 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 72 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 24 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 12 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 48 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 4 \, {\left(12 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 20 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 3 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 7 \, {\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 12 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 48 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 4 \, {\left(12 \, a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 9 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 80 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 84 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 24 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + 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) + 56 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} C \sqrt{a}}{\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}}}{256 \, d}"," ",0,"-1/256*((140*a*cos(8*d*x + 8*c)^2*sin(3/2*d*x + 3/2*c) + 2240*a*cos(6*d*x + 6*c)^2*sin(3/2*d*x + 3/2*c) + 5040*a*cos(4*d*x + 4*c)^2*sin(3/2*d*x + 3/2*c) + 2240*a*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 140*a*sin(8*d*x + 8*c)^2*sin(3/2*d*x + 3/2*c) + 2240*a*sin(6*d*x + 6*c)^2*sin(3/2*d*x + 3/2*c) + 5040*a*sin(4*d*x + 4*c)^2*sin(3/2*d*x + 3/2*c) + 2240*a*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 4064*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 336*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 240*a*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) + 1360*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 36*(a*sin(8*d*x + 8*c) + 4*a*sin(6*d*x + 6*c) + 6*a*sin(4*d*x + 4*c) + 4*a*sin(2*d*x + 2*c))*cos(21/2*d*x + 21/2*c) + 140*(a*sin(8*d*x + 8*c) + 4*a*sin(6*d*x + 6*c) + 6*a*sin(4*d*x + 4*c) + 4*a*sin(2*d*x + 2*c))*cos(19/2*d*x + 19/2*c) + 456*(a*sin(8*d*x + 8*c) + 4*a*sin(6*d*x + 6*c) + 6*a*sin(4*d*x + 4*c) + 4*a*sin(2*d*x + 2*c))*cos(17/2*d*x + 17/2*c) + 4*(280*a*cos(6*d*x + 6*c)*sin(3/2*d*x + 3/2*c) + 420*a*cos(4*d*x + 4*c)*sin(3/2*d*x + 3/2*c) + 280*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 290*a*sin(15/2*d*x + 15/2*c) - 596*a*sin(13/2*d*x + 13/2*c) - 780*a*sin(11/2*d*x + 11/2*c) - 750*a*sin(9/2*d*x + 9/2*c) - 254*a*sin(7/2*d*x + 7/2*c) - 21*a*sin(5/2*d*x + 5/2*c) + 85*a*sin(3/2*d*x + 3/2*c))*cos(8*d*x + 8*c) + 2320*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(15/2*d*x + 15/2*c) + 4768*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) + 16*(420*a*cos(4*d*x + 4*c)*sin(3/2*d*x + 3/2*c) + 280*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 780*a*sin(11/2*d*x + 11/2*c) - 750*a*sin(9/2*d*x + 9/2*c) - 254*a*sin(7/2*d*x + 7/2*c) - 21*a*sin(5/2*d*x + 5/2*c) + 85*a*sin(3/2*d*x + 3/2*c))*cos(6*d*x + 6*c) + 6240*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) + 6000*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) + 24*(280*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 254*a*sin(7/2*d*x + 7/2*c) - 21*a*sin(5/2*d*x + 5/2*c) + 85*a*sin(3/2*d*x + 3/2*c))*cos(4*d*x + 4*c) - 75*(sqrt(2)*a*cos(8*d*x + 8*c)^2 + 16*sqrt(2)*a*cos(6*d*x + 6*c)^2 + 36*sqrt(2)*a*cos(4*d*x + 4*c)^2 + 16*sqrt(2)*a*cos(2*d*x + 2*c)^2 + sqrt(2)*a*sin(8*d*x + 8*c)^2 + 16*sqrt(2)*a*sin(6*d*x + 6*c)^2 + 36*sqrt(2)*a*sin(4*d*x + 4*c)^2 + 48*sqrt(2)*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 8*sqrt(2)*a*cos(2*d*x + 2*c) + 2*(4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(8*d*x + 8*c) + 8*(6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(6*d*x + 6*c) + 12*(4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(4*d*x + 4*c) + 4*(2*sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sqrt(2)*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) + 75*(sqrt(2)*a*cos(8*d*x + 8*c)^2 + 16*sqrt(2)*a*cos(6*d*x + 6*c)^2 + 36*sqrt(2)*a*cos(4*d*x + 4*c)^2 + 16*sqrt(2)*a*cos(2*d*x + 2*c)^2 + sqrt(2)*a*sin(8*d*x + 8*c)^2 + 16*sqrt(2)*a*sin(6*d*x + 6*c)^2 + 36*sqrt(2)*a*sin(4*d*x + 4*c)^2 + 48*sqrt(2)*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 8*sqrt(2)*a*cos(2*d*x + 2*c) + 2*(4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(8*d*x + 8*c) + 8*(6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(6*d*x + 6*c) + 12*(4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(4*d*x + 4*c) + 4*(2*sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sqrt(2)*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) - 75*(sqrt(2)*a*cos(8*d*x + 8*c)^2 + 16*sqrt(2)*a*cos(6*d*x + 6*c)^2 + 36*sqrt(2)*a*cos(4*d*x + 4*c)^2 + 16*sqrt(2)*a*cos(2*d*x + 2*c)^2 + sqrt(2)*a*sin(8*d*x + 8*c)^2 + 16*sqrt(2)*a*sin(6*d*x + 6*c)^2 + 36*sqrt(2)*a*sin(4*d*x + 4*c)^2 + 48*sqrt(2)*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 8*sqrt(2)*a*cos(2*d*x + 2*c) + 2*(4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(8*d*x + 8*c) + 8*(6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(6*d*x + 6*c) + 12*(4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(4*d*x + 4*c) + 4*(2*sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sqrt(2)*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) + 75*(sqrt(2)*a*cos(8*d*x + 8*c)^2 + 16*sqrt(2)*a*cos(6*d*x + 6*c)^2 + 36*sqrt(2)*a*cos(4*d*x + 4*c)^2 + 16*sqrt(2)*a*cos(2*d*x + 2*c)^2 + sqrt(2)*a*sin(8*d*x + 8*c)^2 + 16*sqrt(2)*a*sin(6*d*x + 6*c)^2 + 36*sqrt(2)*a*sin(4*d*x + 4*c)^2 + 48*sqrt(2)*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sqrt(2)*a*sin(2*d*x + 2*c)^2 + 8*sqrt(2)*a*cos(2*d*x + 2*c) + 2*(4*sqrt(2)*a*cos(6*d*x + 6*c) + 6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(8*d*x + 8*c) + 8*(6*sqrt(2)*a*cos(4*d*x + 4*c) + 4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(6*d*x + 6*c) + 12*(4*sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*cos(4*d*x + 4*c) + 4*(2*sqrt(2)*a*sin(6*d*x + 6*c) + 3*sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*sqrt(2)*a*sin(4*d*x + 4*c) + 2*sqrt(2)*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sqrt(2)*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) + 36*(a*cos(8*d*x + 8*c) + 4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(21/2*d*x + 21/2*c) - 140*(a*cos(8*d*x + 8*c) + 4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(19/2*d*x + 19/2*c) - 456*(a*cos(8*d*x + 8*c) + 4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(17/2*d*x + 17/2*c) + 4*(280*a*sin(6*d*x + 6*c)*sin(3/2*d*x + 3/2*c) + 420*a*sin(4*d*x + 4*c)*sin(3/2*d*x + 3/2*c) + 280*a*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 290*a*cos(15/2*d*x + 15/2*c) + 596*a*cos(13/2*d*x + 13/2*c) + 780*a*cos(11/2*d*x + 11/2*c) + 750*a*cos(9/2*d*x + 9/2*c) + 254*a*cos(7/2*d*x + 7/2*c) + 21*a*cos(5/2*d*x + 5/2*c) - 15*a*cos(3/2*d*x + 3/2*c))*sin(8*d*x + 8*c) - 1160*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(15/2*d*x + 15/2*c) - 2384*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(13/2*d*x + 13/2*c) + 16*(420*a*sin(4*d*x + 4*c)*sin(3/2*d*x + 3/2*c) + 280*a*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 780*a*cos(11/2*d*x + 11/2*c) + 750*a*cos(9/2*d*x + 9/2*c) + 254*a*cos(7/2*d*x + 7/2*c) + 21*a*cos(5/2*d*x + 5/2*c) - 15*a*cos(3/2*d*x + 3/2*c))*sin(6*d*x + 6*c) - 3120*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(11/2*d*x + 11/2*c) - 3000*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(9/2*d*x + 9/2*c) + 24*(280*a*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 254*a*cos(7/2*d*x + 7/2*c) + 21*a*cos(5/2*d*x + 5/2*c) - 15*a*cos(3/2*d*x + 3/2*c))*sin(4*d*x + 4*c) - 1016*(4*a*cos(2*d*x + 2*c) + a)*sin(7/2*d*x + 7/2*c) - 84*(4*a*cos(2*d*x + 2*c) + a)*sin(5/2*d*x + 5/2*c) + 200*a*sin(3/2*d*x + 3/2*c) - 36*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 600*(a*cos(8*d*x + 8*c)^2 + 16*a*cos(6*d*x + 6*c)^2 + 36*a*cos(4*d*x + 4*c)^2 + 16*a*cos(2*d*x + 2*c)^2 + a*sin(8*d*x + 8*c)^2 + 16*a*sin(6*d*x + 6*c)^2 + 36*a*sin(4*d*x + 4*c)^2 + 48*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*a*sin(2*d*x + 2*c)^2 + 2*(4*a*cos(6*d*x + 6*c) + 6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(8*d*x + 8*c) + 8*(6*a*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*cos(6*d*x + 6*c) + 12*(4*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 8*a*cos(2*d*x + 2*c) + 4*(2*a*sin(6*d*x + 6*c) + 3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + a)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/(sqrt(2)*cos(8*d*x + 8*c)^2 + 16*sqrt(2)*cos(6*d*x + 6*c)^2 + 36*sqrt(2)*cos(4*d*x + 4*c)^2 + 16*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(8*d*x + 8*c)^2 + 16*sqrt(2)*sin(6*d*x + 6*c)^2 + 36*sqrt(2)*sin(4*d*x + 4*c)^2 + 48*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 16*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(4*sqrt(2)*cos(6*d*x + 6*c) + 6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(8*d*x + 8*c) + 8*(6*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 12*(4*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 4*(2*sqrt(2)*sin(6*d*x + 6*c) + 3*sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*sin(8*d*x + 8*c) + 16*(3*sqrt(2)*sin(4*d*x + 4*c) + 2*sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 8*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)) + 16*(12*a*cos(4*d*x + 4*c)^2*sin(3/2*d*x + 3/2*c) + 48*a*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 12*a*sin(4*d*x + 4*c)^2*sin(3/2*d*x + 3/2*c) + 48*a*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 160*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 168*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 72*a*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 24*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 4*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) + 12*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) + 48*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) + 4*(12*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 20*a*sin(7/2*d*x + 7/2*c) - 21*a*sin(5/2*d*x + 5/2*c) - 3*a*sin(3/2*d*x + 3/2*c))*cos(4*d*x + 4*c) - 7*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(13/2*d*x + 13/2*c) - 12*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(11/2*d*x + 11/2*c) - 48*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(9/2*d*x + 9/2*c) + 4*(12*a*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 20*a*cos(7/2*d*x + 7/2*c) + 21*a*cos(5/2*d*x + 5/2*c) + 9*a*cos(3/2*d*x + 3/2*c))*sin(4*d*x + 4*c) - 80*(2*a*cos(2*d*x + 2*c) + a)*sin(7/2*d*x + 7/2*c) - 84*(2*a*cos(2*d*x + 2*c) + a)*sin(5/2*d*x + 5/2*c) - 24*a*sin(3/2*d*x + 3/2*c) - 4*(a*cos(4*d*x + 4*c)^2 + 4*a*cos(2*d*x + 2*c)^2 + a*sin(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*sin(2*d*x + 2*c)^2 + 2*(2*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 56*(a*cos(4*d*x + 4*c)^2 + 4*a*cos(2*d*x + 2*c)^2 + a*sin(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*sin(2*d*x + 2*c)^2 + 2*(2*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*C*sqrt(a)/(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)))/d","B",0
91,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,1,223,0,0.608894," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{572 \, {\left(35 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 756 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2100 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8190 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + {\left(3465 \, \sqrt{2} a^{2} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, \sqrt{2} a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 70070 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 193050 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 459459 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 1066065 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3783780 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{1441440 \, d}"," ",0,"1/1441440*(572*(35*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 225*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 756*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 2100*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 8190*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + (3465*sqrt(2)*a^2*sin(13/2*d*x + 13/2*c) + 20475*sqrt(2)*a^2*sin(11/2*d*x + 11/2*c) + 70070*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 193050*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 459459*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 1066065*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 3783780*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
93,1,189,0,0.594935," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{132 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 77 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 315 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + {\left(63 \, \sqrt{2} a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1287 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3465 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8778 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 31878 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{11088 \, d}"," ",0,"1/11088*(132*(3*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 21*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 77*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 315*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + (63*sqrt(2)*a^2*sin(11/2*d*x + 11/2*c) + 385*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 1287*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 3465*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 8778*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 31878*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
94,1,155,0,0.556056," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{84 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + {\left(35 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 756 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2100 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8190 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(84*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + (35*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 225*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 756*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 2100*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 8190*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
95,1,78,0,0.504315," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{{\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 77 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 315 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{84 \, d}"," ",0,"1/84*(3*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 21*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 77*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 315*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a)/d","A",0
96,1,8175,0,1.047690," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{42 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a} - \frac{5 \, {\left(1449 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{3} \sin\left(2 \, d x + 2 \, c\right) - 1260 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1449 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{3} + 21 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, {\left(5 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(25 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 198 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 21 \, {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 21 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 69 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 198 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 198 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 5 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 21 \, {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 35 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 98 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 390 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, {\left(50 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 50 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(50 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 189 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 69 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 21 \, {\left(60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 35 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 7 \, {\left(9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 9 \, \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 9 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 390 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, {\left(69 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 189 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 69 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 2 \, {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, \sqrt{2} a^{2} + 138 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(69 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 50 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 189 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 10 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 105 \, {\left(12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 252 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 63 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1260 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{1260 \, d}"," ",0,"1/1260*(42*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a) - 5*(1449*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^3*sin(2*d*x + 2*c) - 1260*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 - 1449*(sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^3 + 21*(25*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 25*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 60*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 5*(5*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + (25*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 198*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*cos(5/2*d*x + 5/2*c)^2 - 21*(12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*cos(2*d*x + 2*c)^2 + 21*(25*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 25*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 69*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 198*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + (25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 198*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 5*(5*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(5/2*d*x + 5/2*c)^2 - 21*(12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c)^2 - 35*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) - 135*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) - 98*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) + 390*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(7/2*d*x + 7/2*c) + 21*(50*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c)*sin(3/2*d*x + 3/2*c) + 50*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 120*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 10*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + (50*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 189*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 69*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(5/2*d*x + 5/2*c) - 21*(60*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c) + 12*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*a^2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) - 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 35*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(13/2*d*x + 13/2*c) + 135*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(11/2*d*x + 11/2*c) + 7*(9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 9*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 - (5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c) - 9*sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 - 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 - (5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c) - 9*sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 - 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 - 2*(5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) - 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 4*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) - 2*(5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) - 4*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) - 9*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(9/2*d*x + 9/2*c) - 390*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(7/2*d*x + 7/2*c) - 21*(69*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 189*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + 69*(sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 - 2*(25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) - 6*sqrt(2)*a^2)*cos(2*d*x + 2*c)^2 - 2*(25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) - 6*sqrt(2)*a^2)*sin(2*d*x + 2*c)^2 + 12*sqrt(2)*a^2 + 138*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) - sqrt(2)*a^2*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (69*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 - 50*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + 189*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + 24*sqrt(2)*a^2)*cos(2*d*x + 2*c) - 10*(5*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(5/2*d*x + 5/2*c) + 105*(12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c) - 252*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2)*sin(1/2*d*x + 1/2*c) - 135*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 63*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1260*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(5/2*d*x + 5/2*c)^2 + (cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(5/2*d*x + 5/2*c)^2 + (cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + cos(1/2*d*x + 1/2*c)^2 + 2*(cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c) + sin(1/2*d*x + 1/2*c)^2))/d","B",0
97,1,3668,0,4.192529," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","-\frac{{\left(150 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 154 \, \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) - {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 17 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 55 \, \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(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(17 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 55 \, \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)^{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) - {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 17 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 55 \, \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)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(17 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 55 \, \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)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 3 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{2} \, d x + \frac{15}{2} \, c\right) - 5 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 11 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 45 \, {\left(\sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - {\left(11 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 99 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 38 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(17 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 55 \, \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) + 3 \, {\left(4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 27 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + {\left(20 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 87 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 2 \, {\left(11 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 99 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 38 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{15}{2} \, d x + \frac{15}{2} \, c\right) + 5 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 11 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 45 \, {\left(\sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 20 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 75 \, \sqrt{2} a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 77 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 45 \, \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) - 4 \, {\left(17 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 55 \, \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)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 6 \, {\left(2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 27 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 13 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 2 \, {\left(10 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 10 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 87 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 41 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(45 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 11 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{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*(150*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 154*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) - (3*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 5*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) - 17*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 55*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(4*d*x + 4*c)^2 + 4*(17*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 55*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)^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) - (3*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 5*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) - 17*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 55*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))*sin(4*d*x + 4*c)^2 + 4*(17*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 55*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))*sin(2*d*x + 2*c)^2 - 3*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 2*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(15/2*d*x + 15/2*c) - 5*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 2*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) + 11*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 2*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) + 45*(sqrt(2)*a^2*sin(4*d*x + 4*c) + 2*sqrt(2)*a^2*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) - (11*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 99*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 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) - 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) + 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) - 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) - 4*(17*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 55*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) + 3*(4*sqrt(2)*a^2*cos(2*d*x + 2*c) + 27*sqrt(2)*a^2)*sin(7/2*d*x + 7/2*c) + (20*sqrt(2)*a^2*cos(2*d*x + 2*c) + 87*sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c))*cos(4*d*x + 4*c) - 2*(11*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 99*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 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) - 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) + 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) - 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))*cos(2*d*x + 2*c) + 3*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(15/2*d*x + 15/2*c) + 5*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(13/2*d*x + 13/2*c) - 11*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(11/2*d*x + 11/2*c) - 45*(sqrt(2)*a^2*cos(4*d*x + 4*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(9/2*d*x + 9/2*c) - (12*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 20*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 75*sqrt(2)*a^2*cos(7/2*d*x + 7/2*c) - 77*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c) - 45*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) - 4*(17*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 55*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))*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) - 6*(2*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 27*sqrt(2)*a^2*cos(2*d*x + 2*c) + 13*sqrt(2)*a^2)*sin(7/2*d*x + 7/2*c) - 2*(10*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 10*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 87*sqrt(2)*a^2*cos(2*d*x + 2*c) + 41*sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c) + 2*(45*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 11*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*d)","B",0
98,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(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
119,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
125,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
127,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
128,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
129,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
130,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
131,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
132,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
133,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
134,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
135,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
136,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
137,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
138,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
139,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
140,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
141,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(11/2), x)","F",0
142,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
143,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
145,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
146,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
147,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
148,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
149,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
150,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(13/2), x)","F",0
151,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
152,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
153,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
154,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
155,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
156,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
157,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
158,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
159,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
160,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
161,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
162,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^3, x)","F",0
165,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^3, x)","F",0
166,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
167,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
168,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(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
170,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,1,7358,0,2.698926," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{48 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A + \frac{{\left(2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(156 \, {\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} + 39 \, \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 39 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 156 \, {\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} + 39 \, {\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) + 156 \, {\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} - 55 \, \cos\left(4 \, d x + 4 \, c\right) + 39\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) + 55 \, \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) - 39 \, \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) - 156 \, {\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(39 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 4 \, {\left(39 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(39 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 86 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 55 \, \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(39 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(39 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(39 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 70 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 23 \, \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} - 55 \, \cos\left(4 \, d x + 4 \, c\right) + 39\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) + 55 \, \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) - 39 \, \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(39 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(39 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 47 \, \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) - 39 \, {\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(39 \, \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(39 \, \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(4 \, {\left(11 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 11 \, {\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) - 24 \, {\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} + 11 \, \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 11 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 4 \, {\left(11 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 11 \, {\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) - 24 \, {\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} + 2 \, {\left(22 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 22 \, {\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) + 11 \, \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(48 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 37 \, \cos\left(4 \, d x + 4 \, c\right) - 11\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) + 11 \, \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(8 \, {\left(11 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 24 \, \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)} \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) + 11 \, {\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) + 22 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 37 \, \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) - {\left(24 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 24 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 11 \, \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(11 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 4 \, {\left(11 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(11 \, \cos\left(4 \, d x + 4 \, c\right) + 24\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right)^{2} - 24 \, {\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(11 \, \cos\left(4 \, d x + 4 \, c\right) + 24\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(11 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(11 \, \cos\left(4 \, d x + 4 \, c\right) + 24\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 46 \, \cos\left(4 \, d x + 4 \, c\right)^{2} - 24 \, {\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) + 59 \, \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(22 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 2 \, {\left(11 \, \cos\left(4 \, d x + 4 \, c\right) + 24\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 26 \, \cos\left(4 \, d x + 4 \, c\right)^{2} - {\left(48 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 48 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 37 \, \cos\left(4 \, d x + 4 \, c\right) - 11\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) - 11 \, \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(24 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 24 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 11 \, \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(8 \, {\left({\left(11 \, \cos\left(4 \, d x + 4 \, c\right) + 24\right)} \sin\left(4 \, d x + 4 \, c\right) - 24 \, \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(11 \, \cos\left(4 \, d x + 4 \, c\right) + 24\right)} \sin\left(4 \, d x + 4 \, c\right) - 37 \, \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) - 11 \, {\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) - 11 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 105 \, {\left({\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left(-{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left(-{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + 1\right) + {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)}}{768 \, d}"," ",0,"1/768*(48*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A + (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)*((156*(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 + 39*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 39*sin(4*d*x + 4*c)^3 + 156*(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 + 39*(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))) + 156*(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 - 55*cos(4*d*x + 4*c) + 39)*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) + 55*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 39*cos(4*d*x + 4*c))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 156*(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)) - (39*cos(4*d*x + 4*c)^3 + 4*(39*cos(4*d*x + 4*c)^3 + (39*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 - 86*cos(4*d*x + 4*c)^2 + 55*cos(4*d*x + 4*c) - 8)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (39*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 + 4*(39*cos(4*d*x + 4*c)^3 + (39*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 + 70*cos(4*d*x + 4*c)^2 + 23*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 - 55*cos(4*d*x + 4*c) + 39)*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) + 55*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 39*cos(4*d*x + 4*c))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(39*cos(4*d*x + 4*c)^3 + (39*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 - 47*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))) - 39*(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*(39*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) + (39*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)*((4*(11*sin(4*d*x + 4*c)^3 + 11*(cos(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*sin(4*d*x + 4*c) - 24*(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 + 11*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 11*sin(4*d*x + 4*c)^3 + 4*(11*sin(4*d*x + 4*c)^3 + 11*(cos(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*sin(4*d*x + 4*c) - 24*(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 + 2*(22*sin(4*d*x + 4*c)^3 + 22*(cos(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*sin(4*d*x + 4*c) + 11*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - (48*cos(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)^2 - 37*cos(4*d*x + 4*c) - 11)*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))) + 11*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - 2*(8*(11*sin(4*d*x + 4*c)^2 - 24*sin(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(4*d*x + 4*c), cos(4*d*x + 4*c))) + 11*(cos(4*d*x + 4*c) + 1)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 22*sin(4*d*x + 4*c)^2 - 37*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))) - (24*cos(4*d*x + 4*c)^2 + 24*sin(4*d*x + 4*c)^2 + 11*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)) - (11*cos(4*d*x + 4*c)^3 + 4*(11*cos(4*d*x + 4*c)^3 + (11*cos(4*d*x + 4*c) + 24)*sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c)^2 - 24*(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 + (11*cos(4*d*x + 4*c) + 24)*sin(4*d*x + 4*c)^2 + 4*(11*cos(4*d*x + 4*c)^3 + (11*cos(4*d*x + 4*c) + 24)*sin(4*d*x + 4*c)^2 + 46*cos(4*d*x + 4*c)^2 - 24*(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))) + 59*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*(22*cos(4*d*x + 4*c)^3 + 2*(11*cos(4*d*x + 4*c) + 24)*sin(4*d*x + 4*c)^2 + 26*cos(4*d*x + 4*c)^2 - (48*cos(4*d*x + 4*c)^2 + 48*sin(4*d*x + 4*c)^2 - 37*cos(4*d*x + 4*c) - 11)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 11*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))) - (24*cos(4*d*x + 4*c)^2 + 24*sin(4*d*x + 4*c)^2 + 11*cos(4*d*x + 4*c))*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(8*((11*cos(4*d*x + 4*c) + 24)*sin(4*d*x + 4*c) - 24*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*(11*cos(4*d*x + 4*c) + 24)*sin(4*d*x + 4*c) - 37*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - 11*(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))) - 11*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))*C/(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
172,1,2713,0,2.077246," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A + {\left(4 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(\cos\left(3 \, d x + 3 \, c\right) - 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 15 \, \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)}\right)} C}{96 \, d}"," ",0,"1/96*(24*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A + (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)))*C)/d","B",0
173,1,1207,0,1.102122," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{16 \, A \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C}{16 \, d}"," ",0,"1/16*(16*A*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C)/d","B",0
174,1,890,0,2.036552," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C + \frac{8 \, A {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}}}{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)))*C + 8*A*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)))/d","B",0
175,1,339,0,2.166639," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, C \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + \frac{2 \, A {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{3 \, d}"," ",0,"1/3*(3*C*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + 2*A*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
176,1,336,0,0.887303," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{15 \, C {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}} + \frac{A {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{15 \, d}"," ",0,"2/15*(15*C*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)) + A*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 17*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
177,1,475,0,0.914960," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{35 \, C {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{3 \, A {\left(\frac{35 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{70 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{84 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{58 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{105 \, d}"," ",0,"2/105*(35*C*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + 3*A*(35*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 70*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 84*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 58*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
178,1,567,0,0.535699," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{21 \, C {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{A {\left(\frac{315 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{735 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1302 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1206 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{431 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{107 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{315 \, d}"," ",0,"2/315*(21*C*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 17*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + A*(315*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 735*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1302*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1206*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 431*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 107*sqrt(2)*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
179,1,4470,0,2.488036," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{80 \, {\left(4 \, {\left(a \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(a \cos\left(3 \, d x + 3 \, c\right) - a\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)} {\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}} \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(3 \, a \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) + 11 \, a \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(3 \, a \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) + 5 \, a \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) - 8 \, a\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} + 33 \, {\left(a \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) - a \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) - a \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) + a \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)} \sqrt{a}\right)} A + {\left(10 \, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(117 \, a \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 40 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 117 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - {\left(117 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 40 \, a \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 117 \, a \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 40 \, a\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(8 \, {\left(a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} \sin\left(5 \, d x + 5 \, c\right) + a \sin\left(5 \, d x + 5 \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(5 \, d x + 5 \, c\right) + a \sin\left(5 \, d x + 5 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 5 \, {\left(33 \, a \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 33 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 4 \, a \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 100 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 8 \, {\left({\left(a \cos\left(5 \, d x + 5 \, c\right) - a\right)} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + {\left(a \cos\left(5 \, d x + 5 \, c\right) - a\right)} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + a \cos\left(5 \, d x + 5 \, c\right) + 2 \, {\left(a \cos\left(5 \, d x + 5 \, c\right) - a\right)} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - a\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + 5 \, {\left(33 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 33 \, a \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 4 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 92 \, a \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 96 \, a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 1995 \, {\left(a \arctan\left(-{\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{7680 \, d}"," ",0,"1/7680*(80*(4*(a*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) - (a*cos(3*d*x + 3*c) - a)*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)))*(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)*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)*((3*a*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 11*a*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)) - (3*a*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 8*a)*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) + 33*(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) - 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) - 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)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a*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))*sqrt(a))*A + (10*(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(3/4)*((117*a*sin(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 40*a*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 117*a*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*cos(3/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - (117*a*cos(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 40*a*cos(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 117*a*cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 40*a)*sin(3/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)))*sqrt(a) + 6*(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(8*(a*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2*sin(5*d*x + 5*c) + a*sin(5*d*x + 5*c)*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*a*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(5*d*x + 5*c) + a*sin(5*d*x + 5*c))*cos(5/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 5*(33*a*sin(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 33*a*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 4*a*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 100*a*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 8*((a*cos(5*d*x + 5*c) - a)*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + (a*cos(5*d*x + 5*c) - a)*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + a*cos(5*d*x + 5*c) + 2*(a*cos(5*d*x + 5*c) - a)*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - a)*sin(5/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + 5*(33*a*cos(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 33*a*cos(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 4*a*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 92*a*cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 96*a)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)))*sqrt(a) + 1995*(a*arctan2(-(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))) + 1) - a*arctan2(-(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))) - 1) - a*arctan2((cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + 1) + a*arctan2((cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 1))*sqrt(a))*C)/d","B",0
180,1,8041,0,1.763458," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{16 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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) \sin\left(2 \, d x + 2 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right) - {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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)\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(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) - a \cos\left(2 \, d x + 2 \, c\right) + {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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) + 6 \, 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} + 7 \, {\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)} \sqrt{a}\right)} A + \frac{{\left(2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 9 \, a \sin\left(4 \, d x + 4 \, c\right)^{3} + 36 \, {\left(a \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 36 \, {\left(a \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, a \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) + a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + a\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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 36 \, {\left(a \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} - a \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(8 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 32 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 32 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, a \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 25 \, a \cos\left(4 \, d x + 4 \, c\right) + 9 \, a\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(64 \, a \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) + 25 \, a \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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 36 \, {\left(4 \, a \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} + a \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 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} - 8 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(9 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} - 26 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(9 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 25 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\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 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(9 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} + 10 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(9 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 7 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\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} + {\left(8 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 32 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 32 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, a \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 25 \, a \cos\left(4 \, d x + 4 \, c\right) + 9 \, a\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(64 \, a \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) + 25 \, a \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)} \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 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} - 17 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(9 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 8 \, a \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 \, a \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) + a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + a\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}{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 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\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 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\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} - 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{1}{4}} {\left({\left(7 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, a \sin\left(4 \, d x + 4 \, c\right)^{3} - 48 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(7 \, a \sin\left(4 \, d x + 4 \, c\right)^{3} + 7 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\right)} \sin\left(4 \, d x + 4 \, c\right) - 68 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 7 \, a \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) + 4 \, {\left(7 \, a \sin\left(4 \, d x + 4 \, c\right)^{3} + 48 \, a \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(7 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 14 \, a \cos\left(4 \, d x + 4 \, c\right) + 19 \, a\right)} \sin\left(4 \, d x + 4 \, c\right) - 68 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 2 \, {\left(14 \, a \sin\left(4 \, d x + 4 \, c\right)^{3} + 7 \, a \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) + 14 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} - a \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(136 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 136 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 129 \, a \cos\left(4 \, d x + 4 \, c\right) - 7 \, a\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 \, {\left(6 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 24 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 20 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 129 \, a \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) + 8 \, {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 10 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 68 \, a \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) - 3 \, a \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) + 7 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + a\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)\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) - {\left(68 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 68 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 7 \, a \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(7 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} - 48 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 56 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(7 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} + 30 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(7 \, a \cos\left(4 \, d x + 4 \, c\right) + 44 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 93 \, a \cos\left(4 \, d x + 4 \, c\right) - 44 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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) + 56 \, a\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} + 7 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(7 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} + 70 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 7 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 119 \, a \cos\left(4 \, d x + 4 \, c\right) - 12 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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) - 44 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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) + 56 \, a\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} - 7 \, a \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) + 2 \, {\left(14 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} + 92 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(7 \, a \cos\left(4 \, d x + 4 \, c\right) + 53 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 7 \, a \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) - 112 \, a \cos\left(4 \, d x + 4 \, c\right) - {\left(88 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 88 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 81 \, a \cos\left(4 \, d x + 4 \, c\right) - 7 \, a\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)\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(44 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 44 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 7 \, a \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(96 \, a \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) + 81 \, a \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) + 8 \, {\left(44 \, a \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(7 \, a \cos\left(4 \, d x + 4 \, c\right) + 53 \, a\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) - 14 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right) + 7 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + a\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)\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} + 75 \, {\left({\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) - 4 \, {\left(4 \, a \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) + a \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(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) - 4 \, {\left(4 \, a \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) + a \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(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) - 4 \, {\left(4 \, a \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) + a \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(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) - 4 \, {\left(4 \, a \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) + a \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{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)}}{256 \, d}"," ",0,"1/256*(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)*((a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a*sin(2*d*x + 2*c) - (a*cos(2*d*x + 2*c) - 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a*cos(2*d*x + 2*c) + (a*cos(2*d*x + 2*c) - 6*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 7*(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))*sqrt(a))*A + (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)*((9*a*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 9*a*sin(4*d*x + 4*c)^3 + 36*(a*sin(4*d*x + 4*c)^3 + (a*cos(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 36*(a*sin(4*d*x + 4*c)^3 + (a*cos(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*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*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*sin(4*d*x + 4*c) - 2*(a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 36*(a*sin(4*d*x + 4*c)^3 + (a*cos(4*d*x + 4*c)^2 - a*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))) + (8*a*cos(4*d*x + 4*c)^2 + 32*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*a*sin(4*d*x + 4*c)^2 + 32*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 - 9*a*cos(4*d*x + 4*c) + 2*(16*a*cos(4*d*x + 4*c)^2 + 16*a*sin(4*d*x + 4*c)^2 - 25*a*cos(4*d*x + 4*c) + 9*a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 25*a*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 36*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c)^2 + a*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*a*cos(4*d*x + 4*c)^3 - 8*a*cos(4*d*x + 4*c)^2 + 4*(9*a*cos(4*d*x + 4*c)^3 - 26*a*cos(4*d*x + 4*c)^2 + (9*a*cos(4*d*x + 4*c) - 8*a)*sin(4*d*x + 4*c)^2 + 25*a*cos(4*d*x + 4*c) - 8*a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (9*a*cos(4*d*x + 4*c) - 8*a)*sin(4*d*x + 4*c)^2 + 4*(9*a*cos(4*d*x + 4*c)^3 + 10*a*cos(4*d*x + 4*c)^2 + (9*a*cos(4*d*x + 4*c) - 8*a)*sin(4*d*x + 4*c)^2 - 7*a*cos(4*d*x + 4*c) - 8*a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (8*a*cos(4*d*x + 4*c)^2 + 32*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*a*sin(4*d*x + 4*c)^2 + 32*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 - 9*a*cos(4*d*x + 4*c) + 2*(16*a*cos(4*d*x + 4*c)^2 + 16*a*sin(4*d*x + 4*c)^2 - 25*a*cos(4*d*x + 4*c) + 9*a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 25*a*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(9*a*cos(4*d*x + 4*c)^3 - 17*a*cos(4*d*x + 4*c)^2 + (9*a*cos(4*d*x + 4*c) - 8*a)*sin(4*d*x + 4*c)^2 + 8*a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 9*(2*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*sin(4*d*x + 4*c) - 2*(a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*(9*a*cos(4*d*x + 4*c) - 8*a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (9*a*cos(4*d*x + 4*c) - 8*a)*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) - 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)^(1/4)*((7*a*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 7*a*sin(4*d*x + 4*c)^3 - 48*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 + 4*(7*a*sin(4*d*x + 4*c)^3 + 7*(a*cos(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*sin(4*d*x + 4*c) - 68*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*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 + 7*a*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 4*(7*a*sin(4*d*x + 4*c)^3 + 48*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (7*a*cos(4*d*x + 4*c)^2 + 14*a*cos(4*d*x + 4*c) + 19*a)*sin(4*d*x + 4*c) - 68*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*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 + 2*(14*a*sin(4*d*x + 4*c)^3 + 7*a*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 14*(a*cos(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*sin(4*d*x + 4*c) - (136*a*cos(4*d*x + 4*c)^2 + 136*a*sin(4*d*x + 4*c)^2 - 129*a*cos(4*d*x + 4*c) - 7*a)*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*(6*a*cos(4*d*x + 4*c)^2 + 24*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 20*a*sin(4*d*x + 4*c)^2 - 129*a*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 8*(3*a*cos(4*d*x + 4*c)^2 + 10*a*sin(4*d*x + 4*c)^2 - 68*a*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 3*a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 7*(a*cos(4*d*x + 4*c) + a)*cos(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))) - (68*a*cos(4*d*x + 4*c)^2 + 68*a*sin(4*d*x + 4*c)^2 + 7*a*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)) - (7*a*cos(4*d*x + 4*c)^3 - 48*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 + 56*a*cos(4*d*x + 4*c)^2 + 4*(7*a*cos(4*d*x + 4*c)^3 + 30*a*cos(4*d*x + 4*c)^2 + (7*a*cos(4*d*x + 4*c) + 44*a)*sin(4*d*x + 4*c)^2 - 93*a*cos(4*d*x + 4*c) - 44*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 56*a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 7*(a*cos(4*d*x + 4*c) + 8*a)*sin(4*d*x + 4*c)^2 + 4*(7*a*cos(4*d*x + 4*c)^3 + 70*a*cos(4*d*x + 4*c)^2 + 7*(a*cos(4*d*x + 4*c) + 8*a)*sin(4*d*x + 4*c)^2 + 119*a*cos(4*d*x + 4*c) - 12*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 44*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 56*a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 - 7*a*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 2*(14*a*cos(4*d*x + 4*c)^3 + 92*a*cos(4*d*x + 4*c)^2 + 2*(7*a*cos(4*d*x + 4*c) + 53*a)*sin(4*d*x + 4*c)^2 - 7*a*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 112*a*cos(4*d*x + 4*c) - (88*a*cos(4*d*x + 4*c)^2 + 88*a*sin(4*d*x + 4*c)^2 - 81*a*cos(4*d*x + 4*c) - 7*a)*cos(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))) - (44*a*cos(4*d*x + 4*c)^2 + 44*a*sin(4*d*x + 4*c)^2 + 7*a*cos(4*d*x + 4*c))*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 2*(96*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2*sin(4*d*x + 4*c) + 81*a*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 8*(44*a*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - (7*a*cos(4*d*x + 4*c) + 53*a)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 14*(a*cos(4*d*x + 4*c) + 8*a)*sin(4*d*x + 4*c) + 7*(a*cos(4*d*x + 4*c) + a)*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))))*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) + 75*((a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + a*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*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) - (a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + a*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*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) - (a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + a*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*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) + (a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + a*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*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))*C/(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
181,1,2746,0,1.497746," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A + {\left(4 \, {\left(a \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(a \cos\left(3 \, d x + 3 \, c\right) - a\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)} {\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}} \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(3 \, a \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) + 11 \, a \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(3 \, a \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) + 5 \, a \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) - 8 \, a\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} + 33 \, {\left(a \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) - a \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) - a \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) + a \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)} \sqrt{a}\right)} C}{96 \, d}"," ",0,"1/96*(24*(2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A + (4*(a*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) - (a*cos(3*d*x + 3*c) - a)*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)))*(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)*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)*((3*a*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 11*a*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)) - (3*a*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 8*a)*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) + 33*(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) - 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) - 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)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a*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))*sqrt(a))*C)/d","B",0
182,1,2078,0,1.486932," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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) \sin\left(2 \, d x + 2 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right) - {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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)\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(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) - a \cos\left(2 \, d x + 2 \, c\right) + {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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) + 6 \, 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} + 7 \, {\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)} \sqrt{a}\right)} C + \frac{8 \, {\left({\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} A}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}}{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)*((a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a*sin(2*d*x + 2*c) - (a*cos(2*d*x + 2*c) - 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a*cos(2*d*x + 2*c) + (a*cos(2*d*x + 2*c) - 6*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 7*(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))*sqrt(a))*C + 8*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*A/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4))/d","B",0
183,1,930,0,1.330103," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C + \frac{16 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} A}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}}{12 \, d}"," ",0,"1/12*(3*(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))*C + 16*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*A/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)))/d","B",0
184,1,1216,0,1.644066," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{5 \, {\left({\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}} + \frac{8 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{10 \, d}"," ",0,"1/10*(5*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 8*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
185,1,389,0,1.508278," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{35 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} C}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}} + \frac{{\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{245 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{273 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{171 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{105 \, d}"," ",0,"4/105*(35*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*C/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)) + (105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 245*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 273*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 171*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
186,1,527,0,1.015259," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{63 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{{\left(\frac{315 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{840 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1344 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1242 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{517 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{94 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{315 \, d}"," ",0,"4/315*(63*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + (315*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 840*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1344*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1242*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 517*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 94*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
187,1,620,0,0.738270," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{11 \, {\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{245 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{273 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{171 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{7 \, {\left(\frac{165 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{495 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1056 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1254 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{781 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{299 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{46 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{1155 \, d}"," ",0,"4/1155*(11*(105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 245*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 273*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 171*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 7*(165*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 495*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1056*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1254*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 781*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 299*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 46*sqrt(2)*a^(3/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
188,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,1,4556,0,3.293003," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{80 \, {\left(4 \, {\left(a^{2} \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(a^{2} \cos\left(3 \, d x + 3 \, c\right) - a^{2}\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)} {\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}} \sqrt{a} + 30 \, {\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(a^{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) + 5 \, a^{2} \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(a^{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) + 3 \, a^{2} \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 \, a^{2}\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} + 75 \, {\left(a^{2} \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) - a^{2} \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) - a^{2} \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) + a^{2} \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)} \sqrt{a}\right)} A + {\left(10 \, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(135 \, a^{2} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 88 \, a^{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 135 \, a^{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - {\left(135 \, a^{2} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 88 \, a^{2} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 135 \, a^{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 88 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(8 \, {\left(a^{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} \sin\left(5 \, d x + 5 \, c\right) + a^{2} \sin\left(5 \, d x + 5 \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(5 \, d x + 5 \, c\right) + a^{2} \sin\left(5 \, d x + 5 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 5 \, {\left(35 \, a^{2} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 35 \, a^{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 40 \, a^{2} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 248 \, a^{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 8 \, {\left(a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(a^{2} \cos\left(5 \, d x + 5 \, c\right) - a^{2}\right)} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + {\left(a^{2} \cos\left(5 \, d x + 5 \, c\right) - a^{2}\right)} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} - a^{2} + 2 \, {\left(a^{2} \cos\left(5 \, d x + 5 \, c\right) - a^{2}\right)} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + 5 \, {\left(35 \, a^{2} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 35 \, a^{2} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 40 \, a^{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 168 \, a^{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 208 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 4245 \, {\left(a^{2} \arctan\left(-{\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - a^{2} \arctan\left(-{\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - a^{2} \arctan\left({\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + 1\right) + a^{2} \arctan\left({\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{7680 \, d}"," ",0,"1/7680*(80*(4*(a^2*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) - (a^2*cos(3*d*x + 3*c) - a^2)*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)))*(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)*sqrt(a) + 30*(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)*((a^2*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a^2*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)) - (a^2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 3*a^2*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 4*a^2)*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) + 75*(a^2*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) - a^2*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) - a^2*arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a^2*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))*sqrt(a))*A + (10*(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(3/4)*((135*a^2*sin(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 88*a^2*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 135*a^2*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*cos(3/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - (135*a^2*cos(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 88*a^2*cos(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 135*a^2*cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 88*a^2)*sin(3/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)))*sqrt(a) + 6*(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(8*(a^2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2*sin(5*d*x + 5*c) + a^2*sin(5*d*x + 5*c)*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*a^2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(5*d*x + 5*c) + a^2*sin(5*d*x + 5*c))*cos(5/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 5*(35*a^2*sin(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 35*a^2*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 40*a^2*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 248*a^2*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 8*(a^2*cos(5*d*x + 5*c) + (a^2*cos(5*d*x + 5*c) - a^2)*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + (a^2*cos(5*d*x + 5*c) - a^2)*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 - a^2 + 2*(a^2*cos(5*d*x + 5*c) - a^2)*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*sin(5/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + 5*(35*a^2*cos(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 35*a^2*cos(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 40*a^2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 168*a^2*cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 208*a^2)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)))*sqrt(a) + 4245*(a^2*arctan2(-(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))) + 1) - a^2*arctan2(-(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))) - 1) - a^2*arctan2((cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + 1) + a^2*arctan2((cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 1))*sqrt(a))*C)/d","B",0
190,1,8557,0,1.863611," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{48 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\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(a^{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) - a^{2} \cos\left(2 \, d x + 2 \, c\right) + 10 \, a^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, 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)\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} + 19 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A + \frac{{\left(10 \, {\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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 12 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 12 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 3 \, {\left(2 \, a^{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) + a^{2} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 12 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - a^{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(8 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 8 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 32 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 2 \, {\left(16 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 19 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, a^{2}\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(64 \, a^{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) + 19 \, a^{2} \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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 12 \, {\left(4 \, a^{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} + a^{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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} - 8 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} - 14 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 19 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 8 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 8 \, a^{2}\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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 8 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 13 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 8 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 8 \, a^{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)^{2} + {\left(8 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 8 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 32 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 2 \, {\left(16 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 19 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, a^{2}\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(64 \, a^{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) + 19 \, a^{2} \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)} \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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} - 11 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 8 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 8 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2}\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 \, {\left(2 \, a^{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) + a^{2} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)} \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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 8 \, a^{2}\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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 8 \, a^{2}\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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 3 \, a^{2} \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) - 160 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{3} + 4 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 3 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) - 160 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 4 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 160 \, a^{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) + {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 43 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) - 160 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 2 \, {\left(6 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 3 \, a^{2} \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) + 6 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - a^{2} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(320 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 320 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 317 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 3 \, a^{2}\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 \, {\left(20 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 26 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 317 \, a^{2} \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) + 80 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 13 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 160 \, a^{2} \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) - 10 \, a^{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) + 3 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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)\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) - {\left(160 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 160 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 3 \, a^{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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} + 120 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 160 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} - 3 \, a^{2} \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 \, {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} + 74 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 197 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 80 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 120 \, a^{2} - 80 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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)\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} + 3 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} + 126 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 243 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 120 \, a^{2} - 40 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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) - 80 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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)\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} + 2 \, {\left(6 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} + 214 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 3 \, a^{2} \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) - 240 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 110 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - {\left(160 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 160 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 157 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 3 \, a^{2}\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)\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(80 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 80 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 3 \, a^{2} \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(320 \, a^{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)^{2} \sin\left(4 \, d x + 4 \, c\right) + 157 \, a^{2} \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) + 8 \, {\left(80 \, a^{2} \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(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 110 \, a^{2}\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) - 6 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 3 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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)\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} + 489 \, {\left({\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - a^{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) - 4 \, {\left(4 \, a^{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) + a^{2} \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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - a^{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) - 4 \, {\left(4 \, a^{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) + a^{2} \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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - a^{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) - 4 \, {\left(4 \, a^{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) + a^{2} \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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - a^{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) - 4 \, {\left(4 \, a^{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) + a^{2} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)}}{768 \, d}"," ",0,"1/768*(48*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a^2*sin(2*d*x + 2*c) - (a^2*cos(2*d*x + 2*c) - 10*a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a^2*cos(2*d*x + 2*c) + 10*a^2 + (a^2*cos(2*d*x + 2*c) - 10*a^2)*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)))*sqrt(a) + 19*(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*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*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*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A + (10*(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)*((3*a^2*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 3*a^2*sin(4*d*x + 4*c)^3 + 12*(a^2*sin(4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 12*(a^2*sin(4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 3*(2*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d*x + 4*c) - 2*(a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 12*(a^2*sin(4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*c)^2 - a^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))) + (8*a^2*cos(4*d*x + 4*c)^2 + 8*a^2*sin(4*d*x + 4*c)^2 - 3*a^2*cos(4*d*x + 4*c) + 32*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 32*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*(16*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*sin(4*d*x + 4*c)^2 - 19*a^2*cos(4*d*x + 4*c) + 3*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 19*a^2*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 12*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c)^2 + a^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)) - (3*a^2*cos(4*d*x + 4*c)^3 - 8*a^2*cos(4*d*x + 4*c)^2 + 4*(3*a^2*cos(4*d*x + 4*c)^3 - 14*a^2*cos(4*d*x + 4*c)^2 + 19*a^2*cos(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*sin(4*d*x + 4*c)^2 - 8*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*sin(4*d*x + 4*c)^2 + 4*(3*a^2*cos(4*d*x + 4*c)^3 - 2*a^2*cos(4*d*x + 4*c)^2 - 13*a^2*cos(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*sin(4*d*x + 4*c)^2 - 8*a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (8*a^2*cos(4*d*x + 4*c)^2 + 8*a^2*sin(4*d*x + 4*c)^2 - 3*a^2*cos(4*d*x + 4*c) + 32*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 32*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*(16*a^2*cos(4*d*x + 4*c)^2 + 16*a^2*sin(4*d*x + 4*c)^2 - 19*a^2*cos(4*d*x + 4*c) + 3*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 19*a^2*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(3*a^2*cos(4*d*x + 4*c)^3 - 11*a^2*cos(4*d*x + 4*c)^2 + 8*a^2*cos(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*sin(4*d*x + 4*c)^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 3*(2*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d*x + 4*c) - 2*(a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*(3*a^2*cos(4*d*x + 4*c) - 8*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) - 8*a^2)*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)*((3*a^2*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 3*a^2*sin(4*d*x + 4*c)^3 + 3*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 + 4*(3*a^2*sin(4*d*x + 4*c)^3 + 3*(a^2*cos(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(4*d*x + 4*c) - 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*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 + 4*(3*a^2*sin(4*d*x + 4*c)^3 + 160*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c)^2 + 6*a^2*cos(4*d*x + 4*c) + 43*a^2)*sin(4*d*x + 4*c) - 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*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 + 2*(6*a^2*sin(4*d*x + 4*c)^3 + 3*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 6*(a^2*cos(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*sin(4*d*x + 4*c) - (320*a^2*cos(4*d*x + 4*c)^2 + 320*a^2*sin(4*d*x + 4*c)^2 - 317*a^2*cos(4*d*x + 4*c) - 3*a^2)*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*(20*a^2*cos(4*d*x + 4*c)^2 + 26*a^2*sin(4*d*x + 4*c)^2 - 317*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 80*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*(10*a^2*cos(4*d*x + 4*c)^2 + 13*a^2*sin(4*d*x + 4*c)^2 - 160*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 10*a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 3*(a^2*cos(4*d*x + 4*c) + a^2)*cos(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))) - (160*a^2*cos(4*d*x + 4*c)^2 + 160*a^2*sin(4*d*x + 4*c)^2 + 3*a^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)) - (3*a^2*cos(4*d*x + 4*c)^3 + 120*a^2*cos(4*d*x + 4*c)^2 - 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 - 3*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(3*a^2*cos(4*d*x + 4*c)^3 + 74*a^2*cos(4*d*x + 4*c)^2 - 197*a^2*cos(4*d*x + 4*c) + (3*a^2*cos(4*d*x + 4*c) + 80*a^2)*sin(4*d*x + 4*c)^2 + 120*a^2 - 80*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(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 + 3*(a^2*cos(4*d*x + 4*c) + 40*a^2)*sin(4*d*x + 4*c)^2 + 4*(3*a^2*cos(4*d*x + 4*c)^3 + 126*a^2*cos(4*d*x + 4*c)^2 + 243*a^2*cos(4*d*x + 4*c) + 3*(a^2*cos(4*d*x + 4*c) + 40*a^2)*sin(4*d*x + 4*c)^2 + 120*a^2 - 40*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 80*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(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 + 2*(6*a^2*cos(4*d*x + 4*c)^3 + 214*a^2*cos(4*d*x + 4*c)^2 - 3*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 240*a^2*cos(4*d*x + 4*c) + 2*(3*a^2*cos(4*d*x + 4*c) + 110*a^2)*sin(4*d*x + 4*c)^2 - (160*a^2*cos(4*d*x + 4*c)^2 + 160*a^2*sin(4*d*x + 4*c)^2 - 157*a^2*cos(4*d*x + 4*c) - 3*a^2)*cos(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))) - (80*a^2*cos(4*d*x + 4*c)^2 + 80*a^2*sin(4*d*x + 4*c)^2 + 3*a^2*cos(4*d*x + 4*c))*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 2*(320*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2*sin(4*d*x + 4*c) + 157*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 8*(80*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - (3*a^2*cos(4*d*x + 4*c) + 110*a^2)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 6*(a^2*cos(4*d*x + 4*c) + 40*a^2)*sin(4*d*x + 4*c) + 3*(a^2*cos(4*d*x + 4*c) + a^2)*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))))*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) + 489*((a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*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) - (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*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) - (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*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) + (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*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))*C/(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
191,1,2938,0,1.383760," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(4 \, {\left(a^{2} \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(a^{2} \cos\left(3 \, d x + 3 \, c\right) - a^{2}\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)} {\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}} \sqrt{a} + 30 \, {\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(a^{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) + 5 \, a^{2} \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(a^{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) + 3 \, a^{2} \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 \, a^{2}\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} + 75 \, {\left(a^{2} \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) - a^{2} \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) - a^{2} \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) + a^{2} \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)} \sqrt{a}\right)} C + \frac{24 \, {\left(2 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} \sqrt{a} + 5 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \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} + 8 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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}\right)} A}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}}{96 \, d}"," ",0,"1/96*((4*(a^2*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) - (a^2*cos(3*d*x + 3*c) - a^2)*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)))*(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)*sqrt(a) + 30*(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)*((a^2*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a^2*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)) - (a^2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 3*a^2*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 4*a^2)*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) + 75*(a^2*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) - a^2*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) - a^2*arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a^2*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))*sqrt(a))*C + 24*(2*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a) + 5*(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*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*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*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) + 8*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*A/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4))/d","B",0
192,1,2503,0,1.233726," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\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(a^{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) - a^{2} \cos\left(2 \, d x + 2 \, c\right) + 10 \, a^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, 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)\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} + 19 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C + \frac{8 \, {\left(30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{48 \, d}"," ",0,"1/48*(3*(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)*((a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a^2*sin(2*d*x + 2*c) - (a^2*cos(2*d*x + 2*c) - 10*a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a^2*cos(2*d*x + 2*c) + 10*a^2 + (a^2*cos(2*d*x + 2*c) - 10*a^2)*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)))*sqrt(a) + 19*(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*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*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*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*C + 8*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
193,1,1126,0,1.007090," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(2 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} \sqrt{a} + 5 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \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} + 8 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}} + \frac{32 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{28 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} A}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}}{60 \, d}"," ",0,"1/60*(15*(2*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a) + 5*(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*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*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*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) + 8*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 32*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 28*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*A/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)))/d","B",0
194,1,1640,0,1.010202," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\frac{7 \, {\left(30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{16 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{56 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{42 \, d}"," ",0,"1/42*(7*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 16*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 56*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
195,1,441,0,0.961306," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{21 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{28 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} C}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}} + \frac{{\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{945 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1449 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1287 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{572 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{315 \, d}"," ",0,"8/315*(21*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 28*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*C/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)) + (315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 945*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1449*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1287*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 572*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
196,1,579,0,1.006701," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{33 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{56 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{{\left(\frac{693 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2310 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4620 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5478 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3575 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{1300 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{200 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{693 \, d}"," ",0,"8/693*(33*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 56*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + (693*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 2310*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4620*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5478*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3575*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 1300*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 200*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
197,1,671,0,0.774932," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{143 \, {\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{945 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1449 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1287 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{572 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{{\left(\frac{45045 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{165165 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{414414 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{604890 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{522665 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{289185 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{88980 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{11864 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{45045 \, d}"," ",0,"8/45045*(143*(315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 945*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1449*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1287*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 572*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + (45045*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 165165*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 414414*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 604890*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 522665*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 289185*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 88980*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 11864*sqrt(2)*a^(5/2)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
198,-2,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(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
199,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(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
200,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(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
201,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(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
202,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(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
203,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(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
204,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+a*cos(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
205,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
206,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
207,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
208,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
209,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
212,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
213,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
214,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,1,69,0,0.444723," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{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 + 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)} C}{480 \, d}"," ",0,"1/480*(15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C)/d","A",0
217,1,57,0,0.488848," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B - 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)} C}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C)/d","A",0
218,1,46,0,0.406796," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C)/d","A",0
219,1,35,0,0.422176," ","integrate(B*cos(d*x+c)+C*cos(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C}{4 \, d} + \frac{B \sin\left(d x + c\right)}{d}"," ",0,"1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*C/d + B*sin(d*x + c)/d","A",0
220,1,20,0,0.322714," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} B + C \sin\left(d x + c\right)}{d}"," ",0,"((d*x + c)*B + C*sin(d*x + c))/d","A",0
221,1,37,0,0.563814," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C + B {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C + B*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)))/d","B",0
222,1,38,0,0.324007," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{C {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(C*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*tan(d*x + c))/d","A",0
223,1,58,0,0.544029," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,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 \, C \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*C*tan(d*x + c))/d","A",0
224,1,70,0,0.398123," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B - 3 \, C {\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*C*(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
225,1,95,0,0.482949," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C - 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))*C - 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
226,1,124,0,0.623848," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 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)} C a - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a}{480 \, d}"," ",0,"-1/480*(160*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a)/d","A",0
227,1,101,0,0.654100," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a - 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)} C a}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a)/d","A",0
228,1,79,0,0.451137," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 12 \, B a \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a + 12*B*a*sin(d*x + c))/d","A",0
229,1,55,0,0.471201," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 4 \, B a \sin\left(d x + c\right) + 4 \, C a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a + 4*B*a*sin(d*x + c) + 4*C*a*sin(d*x + c))/d","A",0
230,1,58,0,0.737977," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a + 2 \, {\left(d x + c\right)} C a + B a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a + 2*(d*x + c)*C*a + B*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a*sin(d*x + c))/d","A",0
231,1,73,0,0.449753," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C a + B a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a + B*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a*tan(d*x + c))/d","B",0
232,1,95,0,0.520056," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","-\frac{B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 2 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, B a \tan\left(d x + c\right) - 4 \, C a \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 2*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 4*B*a*tan(d*x + c) - 4*C*a*tan(d*x + c))/d","A",0
233,1,127,0,0.501204," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a - 3 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a - 3*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*C*a*tan(d*x + c))/d","A",0
234,1,163,0,0.964941," ","integrate((a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 3 \, B a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 3*B*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
235,1,178,0,0.450928," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 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)} C a^{2} + 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2}}{480 \, d}"," ",0,"-1/480*(320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^2 + 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2)/d","A",0
236,1,144,0,0.566470," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} - 48 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} + 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 96 \, B a^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 - 48*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 + 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 96*B*a^2*sin(d*x + c))/d","A",0
237,1,110,0,0.512193," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} + 12 \, {\left(d x + c\right)} B a^{2} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 24 \, B a^{2} \sin\left(d x + c\right) + 12 \, C a^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 + 12*(d*x + c)*B*a^2 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 24*B*a^2*sin(d*x + c) + 12*C*a^2*sin(d*x + c))/d","A",0
238,1,101,0,0.534123," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{8 \, {\left(d x + c\right)} B a^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 4 \, {\left(d x + c\right)} C a^{2} + 2 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{2} \sin\left(d x + c\right) + 8 \, C a^{2} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(8*(d*x + c)*B*a^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 4*(d*x + c)*C*a^2 + 2*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^2*sin(d*x + c) + 8*C*a^2*sin(d*x + c))/d","A",0
239,1,105,0,0.517135," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a^{2} + 4 \, {\left(d x + c\right)} C a^{2} + 2 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} \sin\left(d x + c\right) + 2 \, B a^{2} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a^2 + 4*(d*x + c)*C*a^2 + 2*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^2*sin(d*x + c) + 2*B*a^2*tan(d*x + c))/d","A",0
240,1,142,0,1.040288," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C a^{2} - B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, B a^{2} \tan\left(d x + c\right) + 4 \, C a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*a^2 - B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*B*a^2*tan(d*x + c) + 4*C*a^2*tan(d*x + c))/d","A",0
241,1,174,0,0.484143," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} - 6 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a^{2} \tan\left(d x + c\right) + 24 \, C a^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 - 6*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*B*a^2*tan(d*x + c) + 24*C*a^2*tan(d*x + c))/d","A",0
242,1,230,0,0.518109," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 3 \, B a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 3*B*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 24*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*C*a^2*tan(d*x + c))/d","A",0
243,1,278,0,0.461738," ","integrate((a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,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)} B a^{2} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 30 \, B a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, C a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^2 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 30*B*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*C*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
244,1,262,0,0.761979," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 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)} C 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)} C a^{3} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3}}{960 \, d}"," ",0,"1/960*(64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 + 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*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))*C*a^3 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3)/d","A",0
245,1,213,0,0.480083," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 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)} C a^{3} + 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 480 \, B a^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"-1/480*(480*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 - 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^3 + 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 480*B*a^3*sin(d*x + c))/d","A",0
246,1,167,0,0.578530," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*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)} B a^{3} - 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 96 \, {\left(d x + c\right)} B a^{3} + 96 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 288 \, B a^{3} \sin\left(d x + c\right) - 96 \, C a^{3} \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 96*(d*x + c)*B*a^3 + 96*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 288*B*a^3*sin(d*x + c) - 96*C*a^3*sin(d*x + c))/d","A",0
247,1,148,0,0.472387," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 36 \, {\left(d x + c\right)} B a^{3} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 12 \, {\left(d x + c\right)} C a^{3} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, B a^{3} \sin\left(d x + c\right) + 36 \, C a^{3} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 + 36*(d*x + c)*B*a^3 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 12*(d*x + c)*C*a^3 + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*B*a^3*sin(d*x + c) + 36*C*a^3*sin(d*x + c))/d","A",0
248,1,140,0,0.563569," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} B a^{3} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 12 \, {\left(d x + c\right)} C a^{3} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{3} \sin\left(d x + c\right) + 12 \, C a^{3} \sin\left(d x + c\right) + 4 \, B a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(12*(d*x + c)*B*a^3 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 12*(d*x + c)*C*a^3 + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^3*sin(d*x + c) + 12*C*a^3*sin(d*x + c) + 4*B*a^3*tan(d*x + c))/d","A",0
249,1,165,0,1.843739," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a^{3} + 12 \, {\left(d x + c\right)} C a^{3} - B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{3} \sin\left(d x + c\right) + 12 \, B a^{3} \tan\left(d x + c\right) + 4 \, C a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a^3 + 12*(d*x + c)*C*a^3 - B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*a^3*sin(d*x + c) + 12*B*a^3*tan(d*x + c) + 4*C*a^3*tan(d*x + c))/d","A",0
250,1,212,0,0.326352," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 12 \, {\left(d x + c\right)} C a^{3} - 9 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, B a^{3} \tan\left(d x + c\right) + 36 \, C a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 12*(d*x + c)*C*a^3 - 9*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*B*a^3*tan(d*x + c) + 36*C*a^3*tan(d*x + c))/d","A",0
251,1,269,0,0.698756," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\frac{48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 3 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a^{3} \tan\left(d x + c\right) + 144 \, C a^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(48*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 3*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 36*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*B*a^3*tan(d*x + c) + 144*C*a^3*tan(d*x + c))/d","A",0
252,1,337,0,0.800866," ","integrate((a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,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)} B a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 45 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, C a^{3} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 45*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*C*a^3*tan(d*x + c))/d","A",0
253,1,310,0,1.084099," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, B {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{3 \, d}"," ",0,"1/3*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*B*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
254,1,225,0,0.933137," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + B {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(C*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))) + B*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
255,1,143,0,0.798649," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - B*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
256,1,73,0,0.957402," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{B \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + B*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
257,1,99,0,0.774345," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{B {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{C \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(B*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + C*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
258,1,196,0,0.684839," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{B {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(B*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
259,1,282,0,0.720008," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{B {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 2 \, C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{2 \, d}"," ",0,"-1/2*(B*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 2*C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
260,1,368,0,0.776604," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{B {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, C {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(B*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a - 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 6*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*C*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
261,1,372,0,1.036486," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{60 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - B {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"1/6*(C*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 60*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - B*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","B",0
262,1,283,0,0.956273," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - B {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"-1/6*(C*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - B*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
263,1,191,0,1.020276," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"1/6*(C*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) - B*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","B",0
264,1,120,0,0.943122," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - \frac{B {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - B*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
265,1,93,0,0.674179," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{B {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}} + \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(B*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 + C*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
266,1,145,0,0.709542," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(B*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 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) - C*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","A",0
267,1,244,0,0.840209," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{B {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"1/6*(B*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) - C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2))/d","B",0
268,1,336,0,0.422977," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{B {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"-1/6*(B*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 21*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 21*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - C*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
269,1,322,0,1.148184," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - 3 \, B {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(C*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - 3*B*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","A",0
270,1,231,0,1.158590," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - B {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(3*C*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - B*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","A",0
271,1,160,0,1.046266," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - \frac{B {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(C*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - B*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
272,1,115,0,0.521741," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{3 \, B {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(C*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + 3*B*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
273,1,115,0,0.713308," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{B {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{3 \, C {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(B*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + 3*C*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
274,1,187,0,0.697035," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{B {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - \frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(B*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 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) - C*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
275,1,286,0,0.580056," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, B {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(3*B*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - C*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","B",0
276,1,377,0,0.358091," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{B {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - 3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(B*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 - 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 390*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 390*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - 3*C*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","B",0
277,1,88,0,0.550706," ","integrate((a+a*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{10 \, {\left(\sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(3 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{30 \, d}"," ",0,"1/30*(10*(sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (3*sqrt(2)*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*sin(3/2*d*x + 3/2*c) + 30*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
278,1,123,0,0.567426," ","integrate((a+a*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{42 \, {\left(\sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(15 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 175 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 735 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{420 \, d}"," ",0,"1/420*(42*(sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 20*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (15*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 63*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 175*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 735*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
279,1,172,0,0.577315," ","integrate((a+a*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{30 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 77 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 315 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(35 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 756 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2100 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8190 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(30*(3*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 21*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 77*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 315*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (35*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 225*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 756*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 2100*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 8190*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
280,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2), x)","F",0
284,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
285,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/sqrt(cos(d*x + c)), x)","F",0
286,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/cos(d*x + c)^(3/2), x)","F",0
287,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/cos(d*x + c)^(5/2), x)","F",0
288,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/cos(d*x + c)^(7/2), x)","F",0
289,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/cos(d*x + c)^(9/2), x)","F",0
290,1,115,0,0.329327," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A + 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B - 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)} C}{960 \, d}"," ",0,"1/960*(30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A + 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B - 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))*C)/d","A",0
291,1,89,0,0.404319," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \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 - 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)} C}{480 \, d}"," ",0,"-1/480*(160*(sin(d*x + c)^3 - 3*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 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C)/d","A",0
292,1,77,0,0.352106," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \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 + 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)} C}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C)/d","A",0
293,1,55,0,0.357920," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C + 12 \, A \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C + 12*A*sin(d*x + c))/d","A",0
294,1,38,0,0.382222," ","integrate(A+B*cos(d*x+c)+C*cos(d*x+c)^2,x, algorithm=""maxima"")","A x + \frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C}{4 \, d} + \frac{B \sin\left(d x + c\right)}{d}"," ",0,"A*x + 1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*C/d + B*sin(d*x + c)/d","A",0
295,1,36,0,0.358059," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} B + A \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + C \sin\left(d x + c\right)}{d}"," ",0,"((d*x + c)*B + A*log(sec(d*x + c) + tan(d*x + c)) + C*sin(d*x + c))/d","A",0
296,1,46,0,0.345868," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C + B {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C + B*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*tan(d*x + c))/d","A",0
297,1,82,0,0.353416," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,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)} - 2 \, C {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, B \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)) - 2*C*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 4*B*tan(d*x + c))/d","A",0
298,1,79,0,0.519696," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} 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)} + 12 \, C \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A - 3*B*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*C*tan(d*x + c))/d","A",0
299,1,139,0,0.337203," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B - 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)} - 12 \, C {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B - 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)) - 12*C*(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
300,1,127,0,0.348800," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C - 15 \, B {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C - 15*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
301,1,166,0,0.361099," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a + 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 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)} C a - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a}{480 \, d}"," ",0,"-1/480*(160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a + 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a)/d","A",0
302,1,132,0,0.357498," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a + 96 \, A a \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a + 96*A*a*sin(d*x + c))/d","A",0
303,1,98,0,0.322171," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 12 \, A a \sin\left(d x + c\right) + 12 \, B a \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a + 12*A*a*sin(d*x + c) + 12*B*a*sin(d*x + c))/d","A",0
304,1,82,0,0.335542," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a + 4 \, {\left(d x + c\right)} B a + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 4 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, B a \sin\left(d x + c\right) + 4 \, C a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a + 4*(d*x + c)*B*a + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a + 4*A*a*log(sec(d*x + c) + tan(d*x + c)) + 4*B*a*sin(d*x + c) + 4*C*a*sin(d*x + c))/d","A",0
305,1,92,0,0.338753," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} B a + 2 \, {\left(d x + c\right)} C a + A a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + B a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a \sin\left(d x + c\right) + 2 \, A a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*B*a + 2*(d*x + c)*C*a + A*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + B*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a*sin(d*x + c) + 2*A*a*tan(d*x + c))/d","A",0
306,1,130,0,0.344378," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C a - A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a \tan\left(d x + c\right) + 4 \, B a \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*a - A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*B*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a*tan(d*x + c) + 4*B*a*tan(d*x + c))/d","B",0
307,1,162,0,0.410343," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a - 3 \, A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a \tan\left(d x + c\right) + 12 \, C a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a - 3*A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*B*a*tan(d*x + c) + 12*C*a*tan(d*x + c))/d","A",0
308,1,218,0,0.588267," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a - 3 \, A a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a - 3*A*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*C*a*tan(d*x + c))/d","A",0
309,1,296,0,0.467652," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{2} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} - 60 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 128 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{2} + 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2}}{960 \, d}"," ",0,"-1/960*(640*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 - 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^2 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 - 60*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 - 128*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^2 + 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^2 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2)/d","A",0
310,1,236,0,0.569032," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 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)} C a^{2} + 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 480 \, A a^{2} \sin\left(d x + c\right)}{480 \, d}"," ",0,"-1/480*(160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^2 + 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 - 480*A*a^2*sin(d*x + c))/d","A",0
311,1,190,0,0.611007," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 96 \, {\left(d x + c\right)} A a^{2} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} + 48 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a^{2} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 192 \, A a^{2} \sin\left(d x + c\right) + 96 \, B a^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 96*(d*x + c)*A*a^2 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2 + 48*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 192*A*a^2*sin(d*x + c) + 96*B*a^2*sin(d*x + c))/d","A",0
312,1,153,0,0.345570," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{24 \, {\left(d x + c\right)} A a^{2} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} + 12 \, {\left(d x + c\right)} B a^{2} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 12 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, A a^{2} \sin\left(d x + c\right) + 24 \, B a^{2} \sin\left(d x + c\right) + 12 \, C a^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(24*(d*x + c)*A*a^2 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 + 12*(d*x + c)*B*a^2 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 12*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 12*A*a^2*sin(d*x + c) + 24*B*a^2*sin(d*x + c) + 12*C*a^2*sin(d*x + c))/d","A",0
313,1,151,0,0.426701," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a^{2} + 8 \, {\left(d x + c\right)} B a^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 4 \, {\left(d x + c\right)} C a^{2} + 4 \, A a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{2} \sin\left(d x + c\right) + 8 \, C a^{2} \sin\left(d x + c\right) + 4 \, A a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a^2 + 8*(d*x + c)*B*a^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 4*(d*x + c)*C*a^2 + 4*A*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^2*sin(d*x + c) + 8*C*a^2*sin(d*x + c) + 4*A*a^2*tan(d*x + c))/d","A",0
314,1,192,0,0.642350," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a^{2} + 8 \, {\left(d x + c\right)} C a^{2} - A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{2} \sin\left(d x + c\right) + 8 \, A a^{2} \tan\left(d x + c\right) + 4 \, B a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a^2 + 8*(d*x + c)*C*a^2 - A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*A*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*a^2*sin(d*x + c) + 8*A*a^2*tan(d*x + c) + 4*B*a^2*tan(d*x + c))/d","A",0
315,1,224,0,0.391043," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 12 \, {\left(d x + c\right)} C a^{2} - 6 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{2} \tan\left(d x + c\right) + 24 \, B a^{2} \tan\left(d x + c\right) + 12 \, C a^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 12*(d*x + c)*C*a^2 - 6*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^2*tan(d*x + c) + 24*B*a^2*tan(d*x + c) + 12*C*a^2*tan(d*x + c))/d","A",0
316,1,316,0,0.420577," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} - 3 \, A a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a^{2} \tan\left(d x + c\right) + 96 \, C a^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 - 3*A*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 24*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*B*a^2*tan(d*x + c) + 96*C*a^2*tan(d*x + c))/d","B",0
317,1,360,0,0.769526," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{2} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} - 30 \, A a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, C a^{2} \tan\left(d x + c\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*a^2 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 - 30*A*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 120*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*C*a^2*tan(d*x + c))/d","A",0
318,1,425,0,0.387248," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{448 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{3} - 6720 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} + 630 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 1344 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 2240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} + 630 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 192 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} C a^{3} + 1344 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{3} - 105 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3}}{6720 \, d}"," ",0,"1/6720*(448*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^3 - 6720*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 + 630*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 + 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 + 1344*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 - 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*a^3 - 2240*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 + 630*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 - 192*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*C*a^3 + 1344*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^3 - 105*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^3 + 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3)/d","A",0
319,1,354,0,0.430502," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{3} + 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 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)} C 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)} C a^{3} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 960 \, A a^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(960*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 - 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^3 + 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*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))*C*a^3 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 960*A*a^3*sin(d*x + c))/d","A",0
320,1,282,0,0.560535," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{3} - 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 480 \, {\left(d x + c\right)} A a^{3} + 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 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)} C a^{3} + 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 1440 \, A a^{3} \sin\left(d x + c\right) - 480 \, B a^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"-1/480*(160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^3 - 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 480*(d*x + c)*A*a^3 + 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^3 - 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^3 + 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 1440*A*a^3*sin(d*x + c) - 480*B*a^3*sin(d*x + c))/d","A",0
321,1,233,0,0.488885," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 288 \, {\left(d x + c\right)} A a^{3} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 96 \, {\left(d x + c\right)} B a^{3} - 96 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 96 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 288 \, A a^{3} \sin\left(d x + c\right) + 288 \, B a^{3} \sin\left(d x + c\right) + 96 \, C a^{3} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 + 288*(d*x + c)*A*a^3 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3 + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 + 96*(d*x + c)*B*a^3 - 96*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3 + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 96*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 288*A*a^3*sin(d*x + c) + 288*B*a^3*sin(d*x + c) + 96*C*a^3*sin(d*x + c))/d","A",0
322,1,210,0,0.340656," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{36 \, {\left(d x + c\right)} A a^{3} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} + 36 \, {\left(d x + c\right)} B a^{3} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 12 \, {\left(d x + c\right)} C a^{3} + 18 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{3} \sin\left(d x + c\right) + 36 \, B a^{3} \sin\left(d x + c\right) + 36 \, C a^{3} \sin\left(d x + c\right) + 12 \, A a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(36*(d*x + c)*A*a^3 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 + 36*(d*x + c)*B*a^3 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 12*(d*x + c)*C*a^3 + 18*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^3*sin(d*x + c) + 36*B*a^3*sin(d*x + c) + 36*C*a^3*sin(d*x + c) + 12*A*a^3*tan(d*x + c))/d","A",0
323,1,237,0,0.344250," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A a^{3} + 12 \, {\left(d x + c\right)} B a^{3} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 12 \, {\left(d x + c\right)} C a^{3} - A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a^{3} \sin\left(d x + c\right) + 12 \, C a^{3} \sin\left(d x + c\right) + 12 \, A a^{3} \tan\left(d x + c\right) + 4 \, B a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*a^3 + 12*(d*x + c)*B*a^3 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 12*(d*x + c)*C*a^3 - A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a^3*sin(d*x + c) + 12*C*a^3*sin(d*x + c) + 12*A*a^3*tan(d*x + c) + 4*B*a^3*tan(d*x + c))/d","A",0
324,1,274,0,0.361234," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 12 \, {\left(d x + c\right)} B a^{3} + 36 \, {\left(d x + c\right)} C a^{3} - 9 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a^{3} \sin\left(d x + c\right) + 36 \, A a^{3} \tan\left(d x + c\right) + 36 \, B a^{3} \tan\left(d x + c\right) + 12 \, C 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*a^3 + 12*(d*x + c)*B*a^3 + 36*(d*x + c)*C*a^3 - 9*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*A*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a^3*sin(d*x + c) + 36*A*a^3*tan(d*x + c) + 36*B*a^3*tan(d*x + c) + 12*C*a^3*tan(d*x + c))/d","A",0
325,1,366,0,0.367831," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 48 \, {\left(d x + c\right)} C a^{3} - 3 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 72 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, A a^{3} \tan\left(d x + c\right) + 144 \, B a^{3} \tan\left(d x + c\right) + 144 \, C a^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(48*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 48*(d*x + c)*C*a^3 - 3*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 36*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 72*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*A*a^3*tan(d*x + c) + 144*B*a^3*tan(d*x + c) + 144*C*a^3*tan(d*x + c))/d","B",0
326,1,446,0,0.367157," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 45 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, B a^{3} \tan\left(d x + c\right) + 720 \, C a^{3} \tan\left(d x + c\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*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 45*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 240*B*a^3*tan(d*x + c) + 720*C*a^3*tan(d*x + c))/d","B",0
327,1,559,0,0.373128," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\frac{96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{3} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{3} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} - 5 \, A a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, C a^{3} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^3 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^3 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 - 5*A*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 90*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 360*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*C*a^3*tan(d*x + c))/d","B",0
328,1,579,0,0.355028," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{28672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 143360 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} + 20160 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 26880 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 3072 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} B a^{4} + 43008 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{4} - 2240 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 35840 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} + 13440 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 12288 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} C a^{4} + 28672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{4} - 35 \, {\left(128 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 840 \, d x - 840 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 168 \, \sin\left(4 \, d x + 4 \, c\right) - 768 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 3360 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 3360 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4}}{107520 \, d}"," ",0,"1/107520*(28672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 560*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^4 - 143360*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 + 20160*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 26880*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 3072*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*B*a^4 + 43008*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^4 - 2240*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*a^4 - 35840*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 + 13440*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 - 12288*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*C*a^4 + 28672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 - 35*(128*sin(2*d*x + 2*c)^3 - 840*d*x - 840*c - 3*sin(8*d*x + 8*c) - 168*sin(4*d*x + 4*c) - 768*sin(2*d*x + 2*c))*C*a^4 - 3360*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^4 + 3360*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4)/d","B",0
329,1,483,0,0.349661," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{448 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A a^{4} - 13440 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} + 840 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 6720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 1792 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{4} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 8960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} + 1260 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} + 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 192 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} C a^{4} + 2688 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{4} - 140 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 2240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 840 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 6720 \, A a^{4} \sin\left(d x + c\right)}{6720 \, d}"," ",0,"1/6720*(448*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*a^4 - 13440*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 + 840*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 + 6720*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 1792*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^4 - 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*a^4 - 8960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 + 1260*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 + 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 192*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*C*a^4 + 2688*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 - 140*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a^4 - 2240*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 840*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 + 6720*A*a^4*sin(d*x + c))/d","B",0
330,1,400,0,0.344150," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 1440 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 960 \, {\left(d x + c\right)} A a^{4} - 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a^{4} + 1920 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} - 120 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 960 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 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)} C 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)} C a^{4} + 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a^{4} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 3840 \, A a^{4} \sin\left(d x + c\right) - 960 \, B a^{4} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^4 - 1440*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 960*(d*x + c)*A*a^4 - 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^4 + 1920*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 - 120*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 - 960*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*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))*C*a^4 + 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 - 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 3840*A*a^4*sin(d*x + c) - 960*B*a^4*sin(d*x + c))/d","B",0
331,1,325,0,0.397271," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","-\frac{160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{4} - 480 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} - 1920 \, {\left(d x + c\right)} A a^{4} + 640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 480 \, {\left(d x + c\right)} B a^{4} - 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)} C a^{4} + 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} - 60 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 480 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 480 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 2880 \, A a^{4} \sin\left(d x + c\right) - 1920 \, B a^{4} \sin\left(d x + c\right) - 480 \, C a^{4} \sin\left(d x + c\right)}{480 \, d}"," ",0,"-1/480*(160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^4 - 480*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 - 1920*(d*x + c)*A*a^4 + 640*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 - 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 480*(d*x + c)*B*a^4 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^4 + 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 - 60*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 - 480*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 480*A*a^4*log(sec(d*x + c) + tan(d*x + c)) - 2880*A*a^4*sin(d*x + c) - 1920*B*a^4*sin(d*x + c) - 480*C*a^4*sin(d*x + c))/d","A",0
332,1,290,0,0.351333," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{4} + 576 \, {\left(d x + c\right)} A a^{4} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{4} + 96 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} + 384 \, {\left(d x + c\right)} B a^{4} - 128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C 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)} C a^{4} + 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 96 \, {\left(d x + c\right)} C a^{4} + 192 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 384 \, A a^{4} \sin\left(d x + c\right) + 576 \, B a^{4} \sin\left(d x + c\right) + 384 \, C a^{4} \sin\left(d x + c\right) + 96 \, A a^{4} \tan\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^4 + 576*(d*x + c)*A*a^4 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 + 96*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 + 384*(d*x + c)*B*a^4 - 128*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^4 + 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 96*(d*x + c)*C*a^4 + 192*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 384*A*a^4*sin(d*x + c) + 576*B*a^4*sin(d*x + c) + 384*C*a^4*sin(d*x + c) + 96*A*a^4*tan(d*x + c))/d","A",0
333,1,296,0,0.349904," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{48 \, {\left(d x + c\right)} A a^{4} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} + 72 \, {\left(d x + c\right)} B a^{4} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 12 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 48 \, {\left(d x + c\right)} C a^{4} - 3 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, A a^{4} \sin\left(d x + c\right) + 48 \, B a^{4} \sin\left(d x + c\right) + 72 \, C a^{4} \sin\left(d x + c\right) + 48 \, A a^{4} \tan\left(d x + c\right) + 12 \, B a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(48*(d*x + c)*A*a^4 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 + 72*(d*x + c)*B*a^4 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 12*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 48*(d*x + c)*C*a^4 - 3*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 36*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*A*a^4*sin(d*x + c) + 48*B*a^4*sin(d*x + c) + 72*C*a^4*sin(d*x + c) + 48*A*a^4*tan(d*x + c) + 12*B*a^4*tan(d*x + c))/d","A",0
334,1,320,0,0.359975," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 12 \, {\left(d x + c\right)} A a^{4} + 48 \, {\left(d x + c\right)} B a^{4} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 72 \, {\left(d x + c\right)} C a^{4} - 12 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, B a^{4} \sin\left(d x + c\right) + 48 \, C a^{4} \sin\left(d x + c\right) + 72 \, A a^{4} \tan\left(d x + c\right) + 48 \, B a^{4} \tan\left(d x + c\right) + 12 \, C a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 12*(d*x + c)*A*a^4 + 48*(d*x + c)*B*a^4 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 72*(d*x + c)*C*a^4 - 12*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*B*a^4*sin(d*x + c) + 48*C*a^4*sin(d*x + c) + 72*A*a^4*tan(d*x + c) + 48*B*a^4*tan(d*x + c) + 12*C*a^4*tan(d*x + c))/d","A",0
335,1,416,0,0.379939," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 48 \, {\left(d x + c\right)} B a^{4} + 192 \, {\left(d x + c\right)} C a^{4} - 3 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 48 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 96 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a^{4} \sin\left(d x + c\right) + 192 \, A a^{4} \tan\left(d x + c\right) + 288 \, B a^{4} \tan\left(d x + c\right) + 192 \, C a^{4} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(64*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 48*(d*x + c)*B*a^4 + 192*(d*x + c)*C*a^4 - 3*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 72*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 48*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*A*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 96*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 144*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*C*a^4*sin(d*x + c) + 192*A*a^4*tan(d*x + c) + 288*B*a^4*tan(d*x + c) + 192*C*a^4*tan(d*x + c))/d","B",0
336,1,496,0,0.386828," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{4} + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 320 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} + 240 \, {\left(d x + c\right)} C a^{4} - 60 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, B a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 240 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 240 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, A a^{4} \tan\left(d x + c\right) + 960 \, B a^{4} \tan\left(d x + c\right) + 1440 \, C a^{4} \tan\left(d x + c\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*a^4 + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 320*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 + 240*(d*x + c)*C*a^4 - 60*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*B*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 240*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 360*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 240*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 480*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 240*A*a^4*tan(d*x + c) + 960*B*a^4*tan(d*x + c) + 1440*C*a^4*tan(d*x + c))/d","B",0
337,1,645,0,0.362574," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,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 a^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{4} + 960 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 5 \, A 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 a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 480 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 720 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, B a^{4} \tan\left(d x + c\right) + 1920 \, C a^{4} \tan\left(d x + c\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*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^4 + 960*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 5*A*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*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*B*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 480*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 720*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 480*B*a^4*tan(d*x + c) + 1920*C*a^4*tan(d*x + c))/d","B",0
338,1,731,0,0.385245," ","integrate((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^8,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 a^{4} + 1344 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{4} + 1120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 896 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{4} + 4480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 224 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 6720 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} - 140 \, A 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)} - 35 \, B a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 1260 \, B a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3360 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 3360 \, C a^{4} \tan\left(d x + c\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*a^4 + 1344*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^4 + 1120*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 896*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^4 + 4480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 224*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 6720*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 - 140*A*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)) - 35*B*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 840*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 1260*B*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3360*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 3360*C*a^4*tan(d*x + c))/d","B",0
339,1,525,0,0.450335," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{109 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{115 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{12 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 4 \, B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 12 \, A {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{12 \, d}"," ",0,"-1/12*(C*((21*sin(d*x + c)/(cos(d*x + c) + 1) + 109*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 115*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 12*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 4*B*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 12*A*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
340,1,400,0,0.456217," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, B {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, A {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{3 \, d}"," ",0,"1/3*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*B*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*A*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
341,1,273,0,0.442083," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + B {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - A {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{d}"," ",0,"-(C*((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1))) + B*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - A*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
342,1,165,0,0.446231," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - \frac{A \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - B*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - A*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
343,1,146,0,0.445797," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{C {\left(\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + A {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{B \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(C*(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + A*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + B*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
344,1,218,0,0.362291," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - \frac{C \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(A*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - B*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - C*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
345,1,356,0,0.353150," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{A {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 2 \, B {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 2 \, C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{2 \, d}"," ",0,"-1/2*(A*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 2*B*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 2*C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
346,1,485,0,0.387785," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{A {\left(\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 3 \, B {\left(\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - 6 \, C {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(A*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a - 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 6*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 3*B*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1))) - 6*C*(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1))))/d","B",0
347,1,487,0,0.450755," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{60 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - B {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + A {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(C*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 60*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - B*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + A*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
348,1,352,0,0.510072," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - B {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"-1/6*(C*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - B*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) + A*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2))/d","B",0
349,1,235,0,0.447990," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} + \frac{A {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(C*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) - B*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) + A*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
350,1,164,0,0.440097," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)} - \frac{A {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{B {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(C*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2) - A*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - B*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
351,1,190,0,0.358953," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - \frac{B {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}} - \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"-1/6*(A*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - B*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - C*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
352,1,287,0,0.349655," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{A {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - B {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{C {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2}}}{6 \, d}"," ",0,"1/6*(A*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) - B*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) + C*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2)/d","B",0
353,1,431,0,0.364962," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{A {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - B {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + C {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)}}{6 \, d}"," ",0,"-1/6*(A*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 21*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 21*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - B*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))) + C*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2))/d","B",0
354,1,567,0,0.361371," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{A {\left(\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} - B {\left(\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}\right)} + C {\left(\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}\right)}}{6 \, d}"," ",0,"1/6*(A*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 - 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 30*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 30*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) - B*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 21*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 21*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2) + C*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1))))/d","B",0
355,1,547,0,0.455304," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{C {\left(\frac{20 \, {\left(\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{76 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{51 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{735 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{50 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{1380 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - B {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + 3 \, A {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(C*(20*(33*sin(d*x + c)/(cos(d*x + c) + 1) + 76*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 51*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3 + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (735*sin(d*x + c)/(cos(d*x + c) + 1) - 50*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 1380*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - B*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + 3*A*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
356,1,411,0,0.445392," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - 3 \, B {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(C*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - 3*B*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + A*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
357,1,295,0,0.453252," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - B {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + \frac{A {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(3*C*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - B*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + A*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","B",0
358,1,205,0,0.441407," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - \frac{B {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{3 \, A {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(C*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - B*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 3*A*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
359,1,179,0,0.351554," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{A {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} + \frac{3 \, B {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(A*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + C*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 + 3*B*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
360,1,232,0,0.356395," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - \frac{B {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}} - \frac{3 \, C {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"-1/60*(A*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - B*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 3*C*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","A",0
361,1,350,0,0.366561," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, A {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - B {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{C {\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3}}}{60 \, d}"," ",0,"1/60*(3*A*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - B*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) + C*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3)/d","B",0
362,1,493,0,0.363717," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - 3 \, B {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + C {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"-1/60*(A*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 - 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 390*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 390*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - 3*B*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) + C*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","B",0
363,1,630,0,0.363796," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{A {\left(\frac{20 \, {\left(\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{76 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{51 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{3} - \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{735 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{50 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{690 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{690 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} - B {\left(\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)} + 3 \, C {\left(\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}\right)}}{60 \, d}"," ",0,"1/60*(A*(20*(33*sin(d*x + c)/(cos(d*x + c) + 1) - 76*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 51*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3 - 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (735*sin(d*x + c)/(cos(d*x + c) + 1) + 50*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 690*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 690*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) - B*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 - 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 390*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 390*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3) + 3*C*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3))/d","B",0
364,1,474,0,0.487623," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, C {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} + \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{5880 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} - B {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} + \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + 5 \, A {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"-1/840*(3*C*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) + 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 + 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) - 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 5880*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) - B*(1680*sin(d*x + c)/((a^4 + a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) - 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + 5*A*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4))/d","B",0
365,1,356,0,0.447314," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{C {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} + \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} - 5 \, B {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} + \frac{3 \, A {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(C*(1680*sin(d*x + c)/((a^4 + a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) - 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) - 5*B*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) + 3*A*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
366,1,286,0,0.452967," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, C {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}\right)} - \frac{A {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} - \frac{3 \, B {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"-1/840*(5*C*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4) - A*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3*B*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
367,1,259,0,0.359869," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{A {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{B {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{3 \, C {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(A*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + B*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + 3*C*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
368,1,259,0,0.349178," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{B {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{C {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} + \frac{3 \, A {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(B*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + C*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 + 3*A*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","A",0
369,1,313,0,0.373844," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, A {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - \frac{C {\left(\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}} - \frac{3 \, B {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"-1/840*(5*A*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 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) - C*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3*B*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","B",0
370,1,411,0,0.355243," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{A {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - 5 \, B {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + \frac{3 \, C {\left(\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{4}}}{840 \, d}"," ",0,"1/840*(A*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) - 5*B*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + 3*C*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4)/d","B",0
371,1,556,0,0.367170," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, A {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} - \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - B {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + 5 \, C {\left(\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"-1/840*(3*A*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 - 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) + 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) - B*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) + 5*C*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4))/d","B",0
372,1,690,0,0.374990," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{A {\left(\frac{560 \, {\left(\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{62 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{39 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{4} - \frac{3 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{21945 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2065 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{231 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{18480 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{18480 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} - 3 \, B {\left(\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} - \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)} + C {\left(\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}\right)}}{840 \, d}"," ",0,"1/840*(A*(560*(27*sin(d*x + c)/(cos(d*x + c) + 1) - 62*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 39*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^4 - 3*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (21945*sin(d*x + c)/(cos(d*x + c) + 1) + 2065*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 231*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 18480*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 18480*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4) - 3*B*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 - 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) + 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 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) + C*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4))/d","B",0
373,1,237,0,0.663038," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{396 \, {\left(5 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 35 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 105 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 22 \, {\left(35 \, \sqrt{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 252 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 420 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 1890 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + 5 \, {\left(63 \, \sqrt{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 77 \, \sqrt{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 495 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 693 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2310 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6930 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{55440 \, d}"," ",0,"1/55440*(396*(5*sqrt(2)*sin(7/2*d*x + 7/2*c) + 7*sqrt(2)*sin(5/2*d*x + 5/2*c) + 35*sqrt(2)*sin(3/2*d*x + 3/2*c) + 105*sqrt(2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 22*(35*sqrt(2)*sin(9/2*d*x + 9/2*c) + 45*sqrt(2)*sin(7/2*d*x + 7/2*c) + 252*sqrt(2)*sin(5/2*d*x + 5/2*c) + 420*sqrt(2)*sin(3/2*d*x + 3/2*c) + 1890*sqrt(2)*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + 5*(63*sqrt(2)*sin(11/2*d*x + 11/2*c) + 77*sqrt(2)*sin(9/2*d*x + 9/2*c) + 495*sqrt(2)*sin(7/2*d*x + 7/2*c) + 693*sqrt(2)*sin(5/2*d*x + 5/2*c) + 2310*sqrt(2)*sin(3/2*d*x + 3/2*c) + 6930*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
374,1,194,0,0.660082," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{84 \, {\left(3 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 18 \, {\left(5 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 35 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 105 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(35 \, \sqrt{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 252 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 420 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 1890 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(84*(3*sqrt(2)*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*sin(3/2*d*x + 3/2*c) + 30*sqrt(2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 18*(5*sqrt(2)*sin(7/2*d*x + 7/2*c) + 7*sqrt(2)*sin(5/2*d*x + 5/2*c) + 35*sqrt(2)*sin(3/2*d*x + 3/2*c) + 105*sqrt(2)*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (35*sqrt(2)*sin(9/2*d*x + 9/2*c) + 45*sqrt(2)*sin(7/2*d*x + 7/2*c) + 252*sqrt(2)*sin(5/2*d*x + 5/2*c) + 420*sqrt(2)*sin(3/2*d*x + 3/2*c) + 1890*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
375,1,152,0,0.615992," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{140 \, {\left(\sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 14 \, {\left(3 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + 3 \, {\left(5 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 35 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 105 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{420 \, d}"," ",0,"1/420*(140*(sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 14*(3*sqrt(2)*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*sin(3/2*d*x + 3/2*c) + 30*sqrt(2)*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + 3*(5*sqrt(2)*sin(7/2*d*x + 7/2*c) + 7*sqrt(2)*sin(5/2*d*x + 5/2*c) + 35*sqrt(2)*sin(3/2*d*x + 3/2*c) + 105*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
376,1,106,0,0.588440," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{60 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, {\left(\sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(3 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 30 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{30 \, d}"," ",0,"1/30*(60*sqrt(2)*A*sqrt(a)*sin(1/2*d*x + 1/2*c) + 10*(sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (3*sqrt(2)*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*sin(3/2*d*x + 3/2*c) + 30*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
377,1,57,0,0.540463," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{6 \, \sqrt{2} B \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{3 \, d}"," ",0,"1/3*(6*sqrt(2)*B*sqrt(a)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*sin(3/2*d*x + 3/2*c) + 3*sqrt(2)*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
378,1,731,0,0.604893," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{8 \, \sqrt{2} C \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{{\left(4 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{4 \, d}"," ",0,"1/4*(8*sqrt(2)*C*sqrt(a)*sin(1/2*d*x + 1/2*c) - (4*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 4*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
379,1,3352,0,4.198269," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, {\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)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 12 \, {\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)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\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)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, {\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)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 24 \, \sqrt{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 8 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(6 \, {\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)} \cos\left(2 \, d x + 2 \, c\right) + 6 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 6 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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) - 4 \, {\left(2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(3 \, {\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)} \sin\left(2 \, d x + 2 \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 12 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 4 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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)} A \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{4 \, {\left(4 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} B \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{16 \, d}"," ",0,"1/16*((3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(4*d*x + 4*c)^2 + 12*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(2*d*x + 2*c)^2 + 3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(4*d*x + 4*c)^2 + 12*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(2*d*x + 2*c)^2 - 24*sqrt(2)*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) - 8*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 2*(6*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(2*d*x + 2*c) + 6*sqrt(2)*sin(7/2*d*x + 7/2*c) + 2*sqrt(2)*sin(5/2*d*x + 5/2*c) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) - 6*sqrt(2)*sin(1/2*d*x + 1/2*c) + 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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) - 4*(2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*sin(1/2*d*x + 1/2*c) - 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*(3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(2*d*x + 2*c) - 3*sqrt(2)*cos(7/2*d*x + 7/2*c) - sqrt(2)*cos(5/2*d*x + 5/2*c) + sqrt(2)*cos(3/2*d*x + 3/2*c) + 3*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c) + 12*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*d*x + 7/2*c) + 4*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 8*(sqrt(2)*cos(3/2*d*x + 3/2*c) + 3*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*sin(1/2*d*x + 1/2*c) + 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*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) - 4*(4*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 4*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c))*B*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
380,1,5728,0,4.566413," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","-\frac{\frac{{\left(120 \, {\left(\sin\left(6 \, d x + 6 \, c\right) + 3 \, \sin\left(4 \, d x + 4 \, c\right) + 3 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 8 \, {\left(15 \, \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 50 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 42 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 360 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 1200 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 24 \, {\left(42 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 15 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 15 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + 15 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 120 \, {\left(\cos\left(6 \, d x + 6 \, c\right) + 3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 8 \, {\left(15 \, \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 50 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 42 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3 \, \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)\right)} \sin\left(6 \, d x + 6 \, c\right) - 120 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 400 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 24 \, {\left(42 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3 \, \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)\right)} \sin\left(4 \, d x + 4 \, c\right) - 336 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 24 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 1008 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 72 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 120 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 120 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 120 \, {\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)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 40 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} A \sqrt{a}}{\sqrt{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(\sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + 6 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}} - \frac{6 \, {\left(3 \, {\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)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 12 \, {\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)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 \, {\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)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 12 \, {\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)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 24 \, \sqrt{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 8 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(6 \, {\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)} \cos\left(2 \, d x + 2 \, c\right) + 6 \, \sqrt{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 6 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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) - 4 \, {\left(2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(3 \, {\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)} \sin\left(2 \, d x + 2 \, c\right) - 3 \, \sqrt{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 12 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 4 \, {\left(2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8 \, {\left(\sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} B \sqrt{a}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{24 \, {\left(4 \, \sqrt{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) + 2\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right)\right)\right) - 4 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} C \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{96 \, d}"," ",0,"-1/96*((120*(sin(6*d*x + 6*c) + 3*sin(4*d*x + 4*c) + 3*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) - 8*(15*sin(11/2*d*x + 11/2*c) + 50*sin(9/2*d*x + 9/2*c) + 42*sin(7/2*d*x + 7/2*c) + 3*sin(5/2*d*x + 5/2*c) - 5*sin(3/2*d*x + 3/2*c))*cos(6*d*x + 6*c) + 360*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) + 1200*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) - 24*(42*sin(7/2*d*x + 7/2*c) + 3*sin(5/2*d*x + 5/2*c) - 5*sin(3/2*d*x + 3/2*c))*cos(4*d*x + 4*c) - 15*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 15*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + 15*(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 120*(cos(6*d*x + 6*c) + 3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*sin(13/2*d*x + 13/2*c) + 8*(15*cos(11/2*d*x + 11/2*c) + 50*cos(9/2*d*x + 9/2*c) + 42*cos(7/2*d*x + 7/2*c) + 3*cos(5/2*d*x + 5/2*c) - 5*cos(3/2*d*x + 3/2*c))*sin(6*d*x + 6*c) - 120*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*sin(11/2*d*x + 11/2*c) - 400*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*sin(9/2*d*x + 9/2*c) + 24*(42*cos(7/2*d*x + 7/2*c) + 3*cos(5/2*d*x + 5/2*c) - 5*cos(3/2*d*x + 3/2*c))*sin(4*d*x + 4*c) - 336*(3*cos(2*d*x + 2*c) + 1)*sin(7/2*d*x + 7/2*c) - 24*(3*cos(2*d*x + 2*c) + 1)*sin(5/2*d*x + 5/2*c) + 1008*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 72*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 120*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) + 120*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 120*(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)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 40*sin(3/2*d*x + 3/2*c))*A*sqrt(a)/(sqrt(2)*cos(6*d*x + 6*c)^2 + 9*sqrt(2)*cos(4*d*x + 4*c)^2 + 9*sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(6*d*x + 6*c)^2 + 9*sqrt(2)*sin(4*d*x + 4*c)^2 + 18*sqrt(2)*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sqrt(2)*sin(2*d*x + 2*c)^2 + 2*(3*sqrt(2)*cos(4*d*x + 4*c) + 3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(6*d*x + 6*c) + 6*(3*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*cos(4*d*x + 4*c) + 6*(sqrt(2)*sin(4*d*x + 4*c) + sqrt(2)*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + 6*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2)) - 6*(3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(4*d*x + 4*c)^2 + 12*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(2*d*x + 2*c)^2 + 3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(4*d*x + 4*c)^2 + 12*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(2*d*x + 2*c)^2 - 24*sqrt(2)*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) - 8*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 2*(6*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*cos(2*d*x + 2*c) + 6*sqrt(2)*sin(7/2*d*x + 7/2*c) + 2*sqrt(2)*sin(5/2*d*x + 5/2*c) - 2*sqrt(2)*sin(3/2*d*x + 3/2*c) - 6*sqrt(2)*sin(1/2*d*x + 1/2*c) + 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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) - 4*(2*sqrt(2)*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*sin(1/2*d*x + 1/2*c) - 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*(3*(log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*sin(2*d*x + 2*c) - 3*sqrt(2)*cos(7/2*d*x + 7/2*c) - sqrt(2)*cos(5/2*d*x + 5/2*c) + sqrt(2)*cos(3/2*d*x + 3/2*c) + 3*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c) + 12*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(7/2*d*x + 7/2*c) + 4*(2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 8*(sqrt(2)*cos(3/2*d*x + 3/2*c) + 3*sqrt(2)*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*sin(1/2*d*x + 1/2*c) + 3*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*B*sqrt(a)/(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) + 24*(4*sqrt(2)*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 4*sqrt(2)*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 4*sqrt(2)*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(2*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 + 2*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c)))^2 - 2*sqrt(2)*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 2*sqrt(2)*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) + 2) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) + 4*(sqrt(2)*cos(2*d*x + 2*c)^2 + sqrt(2)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c))) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c))*C*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
381,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,1,252,0,1.439148," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{132 \, {\left(15 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 175 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 735 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 22 \, {\left(35 \, \sqrt{2} a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 378 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 1050 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3780 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + 21 \, {\left(15 \, \sqrt{2} a \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 55 \, \sqrt{2} a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 165 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 429 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 990 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3630 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{55440 \, d}"," ",0,"1/55440*(132*(15*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 63*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 175*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 735*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 22*(35*sqrt(2)*a*sin(9/2*d*x + 9/2*c) + 135*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 378*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 1050*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 3780*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + 21*(15*sqrt(2)*a*sin(11/2*d*x + 11/2*c) + 55*sqrt(2)*a*sin(9/2*d*x + 9/2*c) + 165*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 429*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 990*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 3630*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
383,1,205,0,1.619854," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{252 \, {\left(\sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 6 \, {\left(15 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 175 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 735 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(35 \, \sqrt{2} a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 135 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 378 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 1050 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3780 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(252*(sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 20*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 6*(15*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 63*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 175*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 735*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (35*sqrt(2)*a*sin(9/2*d*x + 9/2*c) + 135*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 378*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 1050*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 3780*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
384,1,159,0,1.043225," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{140 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 42 \, {\left(\sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(15 \, \sqrt{2} a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 63 \, \sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 175 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 735 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{420 \, d}"," ",0,"1/420*(140*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 42*(sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 20*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (15*sqrt(2)*a*sin(7/2*d*x + 7/2*c) + 63*sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 175*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 735*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
385,1,93,0,1.148915," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{10 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + 3 \, {\left(\sqrt{2} a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{30 \, d}"," ",0,"1/30*(10*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + 3*(sqrt(2)*a*sin(5/2*d*x + 5/2*c) + 5*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 20*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
386,1,1354,0,1.643947," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a} - \frac{3 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 6 \, \sqrt{2} a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 2 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 6 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{12 \, d}"," ",0,"1/12*(4*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*C*sqrt(a) - 3*(2*sqrt(2)*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 6*sqrt(2)*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 5*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 2*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/2*d*x + 7/2*c) - 6*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/2*d*x + 5/2*c) + 2*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*A*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
387,1,3339,0,1.614171," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(12 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 48 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 48 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 160 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 168 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 72 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 24 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 12 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 48 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 4 \, {\left(12 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 20 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 3 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 7 \, {\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(\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} + \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 \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) + \sqrt{2} 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(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 12 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 48 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 4 \, {\left(12 \, a \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 20 \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 9 \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 80 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 84 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 24 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + 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) + 56 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{\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}} + \frac{4 \, {\left(2 \, \sqrt{2} a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 6 \, \sqrt{2} a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 6 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 4 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 5 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 3 \, a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 2 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 6 \, {\left(\sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(3 \, \sqrt{2} a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + \sqrt{2} a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} B \sqrt{a}}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{16 \, d}"," ",0,"-1/16*((12*a*cos(4*d*x + 4*c)^2*sin(3/2*d*x + 3/2*c) + 48*a*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 12*a*sin(4*d*x + 4*c)^2*sin(3/2*d*x + 3/2*c) + 48*a*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 160*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 168*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 72*a*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 24*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 4*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) + 12*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) + 48*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) + 4*(12*a*cos(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) - 20*a*sin(7/2*d*x + 7/2*c) - 21*a*sin(5/2*d*x + 5/2*c) - 3*a*sin(3/2*d*x + 3/2*c))*cos(4*d*x + 4*c) - 7*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(sqrt(2)*a*cos(4*d*x + 4*c)^2 + 4*sqrt(2)*a*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*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) + sqrt(2)*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*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(13/2*d*x + 13/2*c) - 12*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(11/2*d*x + 11/2*c) - 48*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(9/2*d*x + 9/2*c) + 4*(12*a*sin(2*d*x + 2*c)*sin(3/2*d*x + 3/2*c) + 20*a*cos(7/2*d*x + 7/2*c) + 21*a*cos(5/2*d*x + 5/2*c) + 9*a*cos(3/2*d*x + 3/2*c))*sin(4*d*x + 4*c) - 80*(2*a*cos(2*d*x + 2*c) + a)*sin(7/2*d*x + 7/2*c) - 84*(2*a*cos(2*d*x + 2*c) + a)*sin(5/2*d*x + 5/2*c) - 24*a*sin(3/2*d*x + 3/2*c) - 4*(a*cos(4*d*x + 4*c)^2 + 4*a*cos(2*d*x + 2*c)^2 + a*sin(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*sin(2*d*x + 2*c)^2 + 2*(2*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 56*(a*cos(4*d*x + 4*c)^2 + 4*a*cos(2*d*x + 2*c)^2 + a*sin(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*a*sin(2*d*x + 2*c)^2 + 2*(2*a*cos(2*d*x + 2*c) + a)*cos(4*d*x + 4*c) + 4*a*cos(2*d*x + 2*c) + a)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/(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)) + 4*(2*sqrt(2)*a*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 6*sqrt(2)*a*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c)^2 + (2*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 6*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 4*sqrt(2)*a*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) - 5*sqrt(2)*a*sin(1/2*d*x + 1/2*c) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2))*cos(2*d*x + 2*c) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 3*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 2*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(7/2*d*x + 7/2*c) - 6*(sqrt(2)*a*cos(2*d*x + 2*c) + sqrt(2)*a)*sin(5/2*d*x + 5/2*c) + 2*(3*sqrt(2)*a*cos(3/2*d*x + 3/2*c) + sqrt(2)*a*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*B*sqrt(a)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
388,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,1,332,0,0.729342," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{572 \, {\left(35 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 756 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2100 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8190 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 130 \, {\left(63 \, \sqrt{2} a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1287 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3465 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8778 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 31878 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(3465 \, \sqrt{2} a^{2} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 20475 \, \sqrt{2} a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 70070 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 193050 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 459459 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 1066065 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3783780 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{1441440 \, d}"," ",0,"1/1441440*(572*(35*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 225*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 756*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 2100*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 8190*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 130*(63*sqrt(2)*a^2*sin(11/2*d*x + 11/2*c) + 385*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 1287*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 3465*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 8778*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 31878*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (3465*sqrt(2)*a^2*sin(13/2*d*x + 13/2*c) + 20475*sqrt(2)*a^2*sin(11/2*d*x + 11/2*c) + 70070*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 193050*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 459459*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 1066065*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 3783780*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
392,1,282,0,0.679662," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{660 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 77 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 315 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 22 \, {\left(35 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 756 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2100 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8190 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + 5 \, {\left(63 \, \sqrt{2} a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 385 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 1287 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 3465 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 8778 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 31878 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{55440 \, d}"," ",0,"1/55440*(660*(3*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 21*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 77*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 315*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 22*(35*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 225*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 756*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 2100*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 8190*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + 5*(63*sqrt(2)*a^2*sin(11/2*d*x + 11/2*c) + 385*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 1287*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 3465*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 8778*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 31878*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
393,1,230,0,0.648074," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{84 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} A \sqrt{a} + 30 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 77 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 315 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + {\left(35 \, \sqrt{2} a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 225 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 756 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2100 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8190 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(84*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*A*sqrt(a) + 30*(3*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 21*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 77*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 315*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + (35*sqrt(2)*a^2*sin(9/2*d*x + 9/2*c) + 225*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 756*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 2100*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 8190*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
394,1,139,0,0.575935," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{14 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} B \sqrt{a} + 5 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 77 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 315 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a}}{420 \, d}"," ",0,"1/420*(14*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*B*sqrt(a) + 5*(3*sqrt(2)*a^2*sin(7/2*d*x + 7/2*c) + 21*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 77*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 315*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a))/d","A",0
395,1,8175,0,1.030960," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{42 \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} C \sqrt{a} - \frac{5 \, {\left(1449 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{3} \sin\left(2 \, d x + 2 \, c\right) - 1260 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1449 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{3} + 21 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, {\left(5 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(25 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 198 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 21 \, {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 21 \, {\left(25 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 69 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 198 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 198 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 5 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 21 \, {\left(12 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 35 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 98 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 390 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 21 \, {\left(50 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 50 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(50 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 189 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 69 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 21 \, {\left(60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 12 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 315 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 35 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 7 \, {\left(9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 9 \, \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 9 \, \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 4 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 9 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 390 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 21 \, {\left(69 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 189 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 69 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} - 2 \, {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, {\left(25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, \sqrt{2} a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 12 \, \sqrt{2} a^{2} + 138 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + {\left(69 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 50 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 189 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, \sqrt{2} a^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 10 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 105 \, {\left(12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 252 \, {\left(5 \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2}\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 135 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 63 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1260 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} A \sqrt{a}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)^{2} + {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 2 \, {\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{1260 \, d}"," ",0,"1/1260*(42*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*C*sqrt(a) - 5*(1449*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^3*sin(2*d*x + 2*c) - 1260*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 - 1449*(sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^3 + 21*(25*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 25*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 60*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + 5*(5*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + (25*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 198*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*cos(5/2*d*x + 5/2*c)^2 - 21*(12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*cos(2*d*x + 2*c)^2 + 21*(25*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 25*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) + 69*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 198*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) + (25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) - 198*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 5*(5*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c) + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(5/2*d*x + 5/2*c)^2 - 21*(12*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c) - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c)^2 - 35*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) - 135*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) - 98*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) + 390*(sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*cos(5/2*d*x + 5/2*c)*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c) + sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)^2*sin(2*d*x + 2*c) + 2*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(7/2*d*x + 7/2*c) + 21*(50*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c)*sin(3/2*d*x + 3/2*c) + 50*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2*sin(3/2*d*x + 3/2*c) - 120*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c) + 10*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(3/2*d*x + 3/2*c) - 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + (50*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*cos(1/2*d*x + 1/2*c) + 189*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 69*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c))*cos(5/2*d*x + 5/2*c) - 21*(60*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^3 - 25*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(3/2*d*x + 3/2*c) + 12*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*a^2)*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) - 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 315*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*cos(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(5/2*d*x + 5/2*c)^2 + (a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(a^2*cos(1/2*d*x + 1/2*c)^2 + a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 35*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(13/2*d*x + 13/2*c) + 135*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(11/2*d*x + 11/2*c) + 7*(9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 9*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 - (5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c) - 9*sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 - 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 - (5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c) - 9*sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 - 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 - 2*(5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 - 4*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) - 9*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 4*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) - 2*(5*sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 5*sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) - 4*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) - 9*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(9/2*d*x + 9/2*c) - 390*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(7/2*d*x + 7/2*c) - 21*(69*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + 189*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + 69*(sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 - 2*(25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) - 6*sqrt(2)*a^2)*cos(2*d*x + 2*c)^2 - 2*(25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) - 6*sqrt(2)*a^2)*sin(2*d*x + 2*c)^2 + 12*sqrt(2)*a^2 + 138*(sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) - sqrt(2)*a^2*sin(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + (69*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 - 50*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + 189*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + 24*sqrt(2)*a^2)*cos(2*d*x + 2*c) - 10*(5*sqrt(2)*a^2*cos(3/2*d*x + 3/2*c)*sin(1/2*d*x + 1/2*c) + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(5/2*d*x + 5/2*c) + 105*(12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^3 + 12*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(1/2*d*x + 1/2*c)^2 + 5*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(3/2*d*x + 3/2*c))*sin(2*d*x + 2*c) - 252*(5*sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2)*sin(1/2*d*x + 1/2*c) - 135*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 63*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1260*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*cos(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*d*x + 5/2*c)^2 + (sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + sqrt(2)*a^2*cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(sqrt(2)*a^2*cos(1/2*d*x + 1/2*c)^2 + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + 2*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*a^2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*A*sqrt(a)/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(5/2*d*x + 5/2*c)^2 + (cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c)^2 + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(5/2*d*x + 5/2*c)^2 + (cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*sin(2*d*x + 2*c)^2 + 2*(cos(2*d*x + 2*c)^2*cos(1/2*d*x + 1/2*c) + cos(1/2*d*x + 1/2*c)*sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c)*cos(1/2*d*x + 1/2*c) + cos(1/2*d*x + 1/2*c))*cos(5/2*d*x + 5/2*c) + 2*(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2)*cos(2*d*x + 2*c) + cos(1/2*d*x + 1/2*c)^2 + 2*(cos(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + sin(2*d*x + 2*c)^2*sin(1/2*d*x + 1/2*c) + 2*cos(2*d*x + 2*c)*sin(1/2*d*x + 1/2*c) + sin(1/2*d*x + 1/2*c))*sin(5/2*d*x + 5/2*c) + sin(1/2*d*x + 1/2*c)^2))/d","B",0
396,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(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
418,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
424,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2), x)","F",0
426,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c)), x)","F",0
427,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(cos(d*x + c)), x)","F",0
428,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(3/2), x)","F",0
429,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(5/2), x)","F",0
430,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/cos(d*x + c)^(7/2), x)","F",0
431,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
432,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
433,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
434,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
435,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
436,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
437,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
438,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
439,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
440,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
441,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
442,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
443,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
444,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
445,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
446,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/cos(d*x + c)^(11/2), x)","F",0
447,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
448,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
449,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
450,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
451,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
452,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
453,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
454,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
455,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/cos(d*x + c)^(13/2), x)","F",0
456,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
457,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
458,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
459,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
460,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
461,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
462,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
464,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
465,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
466,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
472,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
473,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(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
475,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,1,3770,0,3.579729," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A + 6 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} B + {\left(4 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(\cos\left(3 \, d x + 3 \, c\right) - 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 15 \, \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)}\right)} C}{96 \, d}"," ",0,"1/96*(24*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A + 6*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*B + (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)))*C)/d","B",0
478,1,1996,0,1.523253," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{16 \, A \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + 4 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} B + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C}{16 \, d}"," ",0,"1/16*(16*A*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + 4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*B + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C)/d","B",0
479,1,1035,0,3.220083," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{4 \, B \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C + \frac{8 \, A {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}}}{4 \, d}"," ",0,"1/4*(4*B*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C + 8*A*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)))/d","B",0
480,1,435,0,3.246555," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, C \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + \frac{6 \, B {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}} + \frac{2 \, A {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{3 \, d}"," ",0,"1/3*(3*C*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + 6*B*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)) + 2*A*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
481,1,524,0,0.858897," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{15 \, C {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}} + \frac{5 \, B {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{A {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{15 \, d}"," ",0,"2/15*(15*C*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)) + 5*B*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + A*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 17*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
482,1,710,0,1.146907," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{35 \, C {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{7 \, B {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{3 \, A {\left(\frac{35 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{70 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{84 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{58 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{105 \, d}"," ",0,"2/105*(35*C*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + 7*B*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 17*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 3*A*(35*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 70*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 84*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 58*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
483,1,848,0,0.890456," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{21 \, C {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{9 \, B {\left(\frac{35 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{70 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{84 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{58 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{A {\left(\frac{315 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{735 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1302 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1206 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{431 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{107 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{315 \, d}"," ",0,"2/315*(21*C*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 17*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 9*B*(35*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 70*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 84*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 58*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + A*(315*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 735*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1302*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1206*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 431*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 107*sqrt(2)*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
484,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,1,3824,0,3.231463," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A + 6 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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) \sin\left(2 \, d x + 2 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right) - {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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)\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(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) - a \cos\left(2 \, d x + 2 \, c\right) + {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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) + 6 \, 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} + 7 \, {\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)} \sqrt{a}\right)} B + {\left(4 \, {\left(a \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(a \cos\left(3 \, d x + 3 \, c\right) - a\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)} {\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}} \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(3 \, a \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) + 11 \, a \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(3 \, a \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) + 5 \, a \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) - 8 \, a\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} + 33 \, {\left(a \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) - a \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) - a \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) + a \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)} \sqrt{a}\right)} C}{96 \, d}"," ",0,"1/96*(24*(2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A + 6*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a*sin(2*d*x + 2*c) - (a*cos(2*d*x + 2*c) - 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a*cos(2*d*x + 2*c) + (a*cos(2*d*x + 2*c) - 6*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 7*(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))*sqrt(a))*B + (4*(a*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) - (a*cos(3*d*x + 3*c) - a)*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)))*(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)*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)*((3*a*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 11*a*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)) - (3*a*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 8*a)*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) + 33*(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) - 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) - 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)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a*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))*sqrt(a))*C)/d","B",0
487,1,2879,0,2.191668," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} B + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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) \sin\left(2 \, d x + 2 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right) - {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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)\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(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) - a \cos\left(2 \, d x + 2 \, c\right) + {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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) + 6 \, 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} + 7 \, {\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)} \sqrt{a}\right)} C + \frac{8 \, {\left({\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} A}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}}{16 \, d}"," ",0,"1/16*(4*(2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*B + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a*sin(2*d*x + 2*c) - (a*cos(2*d*x + 2*c) - 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a*cos(2*d*x + 2*c) + (a*cos(2*d*x + 2*c) - 6*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 7*(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))*sqrt(a))*C + 8*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*A/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4))/d","B",0
488,1,1925,0,1.703044," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C + \frac{6 \, {\left({\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} B}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}} + \frac{16 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} A}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}}{12 \, d}"," ",0,"1/12*(3*(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))*C + 6*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*B/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 16*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*A/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)))/d","B",0
489,1,1339,0,1.441356," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{15 \, {\left({\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}} + \frac{40 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} B}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}} + \frac{24 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{30 \, d}"," ",0,"1/30*(15*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 40*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*B/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)) + 24*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
490,1,604,0,1.422033," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{35 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} C}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}} + \frac{21 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{{\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{245 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{273 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{171 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{105 \, d}"," ",0,"4/105*(35*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*C/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)) + 21*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + (105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 245*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 273*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 171*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
491,1,788,0,0.911342," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{63 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{3 \, {\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{245 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{273 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{171 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{{\left(\frac{315 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{840 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1344 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1242 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{517 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{94 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{315 \, d}"," ",0,"4/315*(63*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + 3*(105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 245*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 273*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 171*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + (315*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 840*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1344*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1242*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 517*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 94*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
492,1,927,0,1.791303," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{33 \, {\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{245 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{273 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{171 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{11 \, {\left(\frac{315 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{840 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1344 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1242 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{517 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{94 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{21 \, {\left(\frac{165 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{495 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1056 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1254 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{781 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{299 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{46 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{3465 \, d}"," ",0,"4/3465*(33*(105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 245*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 273*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 171*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 11*(315*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 840*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1344*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1242*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 517*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 94*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 21*(165*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 495*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1056*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1254*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 781*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 299*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 46*sqrt(2)*a^(3/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
493,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,1,4042,0,5.446083," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{6 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\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(a^{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) - a^{2} \cos\left(2 \, d x + 2 \, c\right) + 10 \, a^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, 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)\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} + 19 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} B + {\left(4 \, {\left(a^{2} \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(a^{2} \cos\left(3 \, d x + 3 \, c\right) - a^{2}\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)} {\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}} \sqrt{a} + 30 \, {\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(a^{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) + 5 \, a^{2} \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(a^{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) + 3 \, a^{2} \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 \, a^{2}\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} + 75 \, {\left(a^{2} \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) - a^{2} \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) - a^{2} \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) + a^{2} \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)} \sqrt{a}\right)} C + \frac{24 \, {\left(2 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} \sqrt{a} + 5 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \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} + 8 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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}\right)} A}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}}}{96 \, d}"," ",0,"1/96*(6*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a^2*sin(2*d*x + 2*c) - (a^2*cos(2*d*x + 2*c) - 10*a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a^2*cos(2*d*x + 2*c) + 10*a^2 + (a^2*cos(2*d*x + 2*c) - 10*a^2)*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)))*sqrt(a) + 19*(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*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*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*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*B + (4*(a^2*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) - (a^2*cos(3*d*x + 3*c) - a^2)*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)))*(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)*sqrt(a) + 30*(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)*((a^2*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a^2*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)) - (a^2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 3*a^2*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 4*a^2)*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) + 75*(a^2*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) - a^2*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) - a^2*arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a^2*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))*sqrt(a))*C + 24*(2*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a) + 5*(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*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*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*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) + 8*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*A/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4))/d","B",0
497,1,3474,0,3.610594," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\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(a^{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) - a^{2} \cos\left(2 \, d x + 2 \, c\right) + 10 \, a^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, 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)\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} + 19 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C + \frac{12 \, {\left(2 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} \sqrt{a} + 5 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \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} + 8 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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}\right)} B}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}} + \frac{8 \, {\left(30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{48 \, d}"," ",0,"1/48*(3*(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)*((a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a^2*sin(2*d*x + 2*c) - (a^2*cos(2*d*x + 2*c) - 10*a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a^2*cos(2*d*x + 2*c) + 10*a^2 + (a^2*cos(2*d*x + 2*c) - 10*a^2)*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)))*sqrt(a) + 19*(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*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*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*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*C + 12*(2*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a) + 5*(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*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*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*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) + 8*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*B/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 8*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
498,1,2519,0,2.171456," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(2 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} \sqrt{a} + 5 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \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} + 8 \, {\left(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) + 1\right)\right) \sin\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right) - a^{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}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}}} + \frac{10 \, {\left(30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} B}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{32 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{28 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} A}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}}{60 \, d}"," ",0,"1/60*(15*(2*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a) + 5*(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*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*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*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) + 8*(a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a^2*cos(d*x + c) - a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 10*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*B/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 32*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 28*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*A/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)))/d","B",0
499,1,1789,0,2.512988," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\frac{35 \, {\left(30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{112 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{28 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} B}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}} + \frac{80 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{56 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{210 \, d}"," ",0,"1/210*(35*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 112*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 28*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*B/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)) + 80*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 56*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
500,1,682,0,1.190183," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{21 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{28 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} C}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}} + \frac{15 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{56 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{{\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{945 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1449 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1287 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{572 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{315 \, d}"," ",0,"8/315*(21*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 28*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*C/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)) + 15*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 56*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + (315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 945*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1449*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1287*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 572*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
501,1,867,0,1.198157," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{165 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{56 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{11 \, {\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{945 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1449 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1287 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{572 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{5 \, {\left(\frac{693 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2310 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4620 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5478 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3575 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{1300 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{200 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{3465 \, d}"," ",0,"8/3465*(165*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 56*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + 11*(315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 945*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1449*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1287*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 572*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 5*(693*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 2310*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4620*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5478*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3575*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 1300*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 200*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
502,1,1004,0,1.222477," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{143 \, {\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{945 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1449 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1287 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{572 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{65 \, {\left(\frac{693 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2310 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4620 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5478 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3575 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{1300 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{200 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{{\left(\frac{45045 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{165165 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{414414 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{604890 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{522665 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{289185 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{88980 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{11864 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{45045 \, d}"," ",0,"8/45045*(143*(315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 945*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1449*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1287*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 572*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 65*(693*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 2310*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4620*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5478*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3575*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 1300*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 200*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + (45045*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 165165*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 414414*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 604890*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 522665*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 289185*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 88980*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 11864*sqrt(2)*a^(5/2)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
503,-2,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(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
504,-2,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(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
505,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(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
506,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(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
507,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(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
508,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(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
509,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+a*cos(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
510,-2,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+a*cos(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
511,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
512,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
513,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
514,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
518,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
519,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
520,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,1,113,0,0.587201," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b + 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)} C b}{480 \, d}"," ",0,"1/480*(120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b)/d","A",0
523,1,90,0,0.410493," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b - 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)} C b - 96 \, A a \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b - 96*A*a*sin(d*x + c))/d","A",0
524,1,67,0,0.342735," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b + 12 \, A b \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b + 12*A*b*sin(d*x + c))/d","A",0
525,1,63,0,0.338653," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} A b + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b + 4 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, C a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*A*b + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b + 4*A*a*log(sec(d*x + c) + tan(d*x + c)) + 4*C*a*sin(d*x + c))/d","A",0
526,1,59,0,0.433629," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C a + A b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C b \sin\left(d x + c\right) + 2 \, A a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a + A*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*b*sin(d*x + c) + 2*A*a*tan(d*x + c))/d","A",0
527,1,95,0,0.696006," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C b - A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*b - A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*b*tan(d*x + c))/d","A",0
528,1,107,0,0.666266," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a - 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 \, C b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a - 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*C*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a*tan(d*x + c))/d","A",0
529,1,152,0,0.677553," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b - 3 \, A a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C b \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b - 3*A*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*C*b*tan(d*x + c))/d","A",0
530,1,175,0,0.770931," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a - 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)} - 60 \, C b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a - 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)) - 60*C*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
531,1,202,0,0.572598," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b + 128 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a b + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{2} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{2}}{960 \, d}"," ",0,"1/960*(240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2 - 640*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b + 128*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a*b + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*b^2 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*b^2)/d","A",0
532,1,154,0,0.794199," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a b + 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{2} - 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)} C b^{2} - 240 \, A a^{2} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(80*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b + 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^2 - 16*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^2 - 240*A*a^2*sin(d*x + c))/d","A",0
533,1,130,0,0.445661," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{96 \, {\left(d x + c\right)} A a^{2} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{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)} C b^{2} + 192 \, A a b \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(96*(d*x + c)*A*a^2 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^2 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^2 + 192*A*a*b*sin(d*x + c))/d","A",0
534,1,105,0,0.378865," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a b + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b - 2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{2} + 6 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 6 \, C a^{2} \sin\left(d x + c\right) + 6 \, A b^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(12*(d*x + c)*A*a*b + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b - 2*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^2 + 6*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 6*C*a^2*sin(d*x + c) + 6*A*b^2*sin(d*x + c))/d","A",0
535,1,99,0,0.394289," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C a^{2} + 4 \, {\left(d x + c\right)} A b^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{2} + 4 \, A a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, C a b \sin\left(d x + c\right) + 4 \, A a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*a^2 + 4*(d*x + c)*A*b^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^2 + 4*A*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*C*a*b*sin(d*x + c) + 4*A*a^2*tan(d*x + c))/d","A",0
536,1,140,0,0.390682," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{8 \, {\left(d x + c\right)} C a b - A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C b^{2} \sin\left(d x + c\right) + 8 \, A a b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(8*(d*x + c)*C*a*b - A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*b^2*sin(d*x + c) + 8*A*a*b*tan(d*x + c))/d","A",0
537,1,136,0,0.430986," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 6 \, {\left(d x + c\right)} C b^{2} - 3 \, A a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{2} \tan\left(d x + c\right) + 6 \, A b^{2} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 6*(d*x + c)*C*b^2 - 3*A*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*C*a^2*tan(d*x + c) + 6*A*b^2*tan(d*x + c))/d","A",0
538,1,232,0,0.360408," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b - 3 \, A a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 96 \, C a b \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b - 3*A*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 96*C*a*b*tan(d*x + c))/d","A",0
539,1,216,0,0.727090," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{2} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{2} - 15 \, A a b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, C b^{2} \tan\left(d x + c\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*a^2 + 40*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 + 40*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^2 - 15*A*a*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*C*b^2*tan(d*x + c))/d","A",0
540,1,243,0,0.575298," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} - 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b + 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b^{2} - 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)} C a b^{2} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{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)} C b^{3} - 960 \, A a^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"-1/960*(320*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 - 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2*b - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2*b + 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b^2 - 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a*b^2 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*b^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))*C*b^3 - 960*A*a^3*sin(d*x + c))/d","A",0
541,1,194,0,0.400577," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{480 \, {\left(d x + c\right)} A a^{3} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{2} + 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)} C a b^{2} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{3} + 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)} C b^{3} + 1440 \, A a^{2} b \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(480*(d*x + c)*A*a^3 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b^2 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b^2 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^3 + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^3 + 1440*A*a^2*b*sin(d*x + c))/d","A",0
542,1,167,0,0.703763," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{96 \, {\left(d x + c\right)} A a^{2} b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b^{2} + 8 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{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)} C b^{3} + 32 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 32 \, C a^{3} \sin\left(d x + c\right) + 96 \, A a b^{2} \sin\left(d x + c\right)}{32 \, d}"," ",0,"1/32*(96*(d*x + c)*A*a^2*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b^2 + 8*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^3 + (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^3 + 32*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 32*C*a^3*sin(d*x + c) + 96*A*a*b^2*sin(d*x + c))/d","A",0
543,1,141,0,0.403145," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} C a^{3} + 36 \, {\left(d x + c\right)} A a b^{2} + 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{2} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{3} + 18 \, A a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, C a^{2} b \sin\left(d x + c\right) + 12 \, A b^{3} \sin\left(d x + c\right) + 12 \, A a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*C*a^3 + 36*(d*x + c)*A*a*b^2 + 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^2 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^3 + 18*A*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*C*a^2*b*sin(d*x + c) + 12*A*b^3*sin(d*x + c) + 12*A*a^3*tan(d*x + c))/d","A",0
544,1,179,0,0.382106," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} C a^{2} b + 4 \, {\left(d x + c\right)} A b^{3} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{3} - A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a b^{2} \sin\left(d x + c\right) + 12 \, A a^{2} b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(12*(d*x + c)*C*a^2*b + 4*(d*x + c)*A*b^3 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^3 - A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*A*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a*b^2*sin(d*x + c) + 12*A*a^2*b*tan(d*x + c))/d","A",0
545,1,181,0,0.408649," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 36 \, {\left(d x + c\right)} C a b^{2} - 9 \, A a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, C a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C b^{3} \sin\left(d x + c\right) + 12 \, C a^{3} \tan\left(d x + c\right) + 36 \, A a b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 36*(d*x + c)*C*a*b^2 - 9*A*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 18*C*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*A*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*b^3*sin(d*x + c) + 12*C*a^3*tan(d*x + c) + 36*A*a*b^2*tan(d*x + c))/d","A",0
546,1,261,0,0.531975," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} b + 16 \, {\left(d x + c\right)} C b^{3} - A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a^{2} b \tan\left(d x + c\right) + 16 \, A b^{3} \tan\left(d x + c\right)}{16 \, d}"," ",0,"1/16*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2*b + 16*(d*x + c)*C*b^3 - A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 4*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*C*a^2*b*tan(d*x + c) + 16*A*b^3*tan(d*x + c))/d","A",0
547,1,296,0,0.623405," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{3} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b^{2} - 45 \, A a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, 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)} + 120 \, C b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 720 \, C a b^{2} \tan\left(d x + c\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*a^3 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^2 - 45*A*a^2*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*C*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*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)) + 120*C*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 720*C*a*b^2*tan(d*x + c))/d","A",0
548,1,386,0,0.642821," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\frac{96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{2} b + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{3} - 5 \, A a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, A 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)} - 360 \, C a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, C b^{3} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^2*b + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^3 - 5*A*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*A*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)) - 360*C*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*C*b^3*tan(d*x + c))/d","A",0
549,1,329,0,0.594507," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{560 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} - 1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} b - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b + 3360 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} b^{2} - 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)} C a^{2} b^{2} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{3} + 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)} C a b^{3} - 112 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A b^{4} + 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)} C b^{4} - 1680 \, A a^{4} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"-1/1680*(560*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 - 1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3*b - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3*b + 3360*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2*b^2 - 672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^2*b^2 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a*b^3 + 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))*C*a*b^3 - 112*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*b^4 + 48*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*C*b^4 - 1680*A*a^4*sin(d*x + c))/d","A",0
550,1,283,0,0.396507," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{960 \, {\left(d x + c\right)} A a^{4} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} b + 1440 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b^{2} + 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)} C a^{2} b^{2} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b^{3} + 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)} C a b^{3} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{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)} C b^{4} + 3840 \, A a^{3} b \sin\left(d x + c\right)}{960 \, d}"," ",0,"1/960*(960*(d*x + c)*A*a^4 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3*b + 1440*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2*b^2 + 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2*b^2 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b^3 + 256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a*b^3 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*b^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))*C*b^4 + 3840*A*a^3*b*sin(d*x + c))/d","A",0
551,1,232,0,0.675089," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{480 \, {\left(d x + c\right)} A a^{3} b + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b - 240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b^{2} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{3} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{3} - 40 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{4} + 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)} C b^{4} + 120 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 120 \, C a^{4} \sin\left(d x + c\right) + 720 \, A a^{2} b^{2} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(480*(d*x + c)*A*a^3*b + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3*b - 240*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b^2 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b^3 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b^3 - 40*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^4 + 8*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^4 + 120*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 120*C*a^4*sin(d*x + c) + 720*A*a^2*b^2*sin(d*x + c))/d","A",0
552,1,204,0,0.349131," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{96 \, {\left(d x + c\right)} C a^{4} + 576 \, {\left(d x + c\right)} A a^{2} b^{2} + 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b^{2} - 128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b^{3} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{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)} C b^{4} + 192 \, A a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 384 \, C a^{3} b \sin\left(d x + c\right) + 384 \, A a b^{3} \sin\left(d x + c\right) + 96 \, A a^{4} \tan\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(96*(d*x + c)*C*a^4 + 576*(d*x + c)*A*a^2*b^2 + 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b^2 - 128*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b^3 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^4 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^4 + 192*A*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 384*C*a^3*b*sin(d*x + c) + 384*A*a*b^3*sin(d*x + c) + 96*A*a^4*tan(d*x + c))/d","A",0
553,1,221,0,0.503149," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{48 \, {\left(d x + c\right)} C a^{3} b + 48 \, {\left(d x + c\right)} A a b^{3} + 12 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{3} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{4} - 3 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, A a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 72 \, C a^{2} b^{2} \sin\left(d x + c\right) + 12 \, A b^{4} \sin\left(d x + c\right) + 48 \, A a^{3} b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(48*(d*x + c)*C*a^3*b + 48*(d*x + c)*A*a*b^3 + 12*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^3 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^4 - 3*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*A*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 72*C*a^2*b^2*sin(d*x + c) + 12*A*b^4*sin(d*x + c) + 48*A*a^3*b*tan(d*x + c))/d","A",0
554,1,221,0,0.782378," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 72 \, {\left(d x + c\right)} C a^{2} b^{2} + 12 \, {\left(d x + c\right)} A b^{4} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{4} - 12 \, A a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a b^{3} \sin\left(d x + c\right) + 12 \, C a^{4} \tan\left(d x + c\right) + 72 \, A a^{2} b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 72*(d*x + c)*C*a^2*b^2 + 12*(d*x + c)*A*b^4 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^4 - 12*A*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*A*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*C*a*b^3*sin(d*x + c) + 12*C*a^4*tan(d*x + c) + 72*A*a^2*b^2*tan(d*x + c))/d","A",0
555,1,306,0,0.397089," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} b + 192 \, {\left(d x + c\right)} C a b^{3} - 3 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, A a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, C a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C b^{4} \sin\left(d x + c\right) + 192 \, C a^{3} b \tan\left(d x + c\right) + 192 \, A a b^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(64*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3*b + 192*(d*x + c)*C*a*b^3 - 3*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 72*A*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 144*C*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*A*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*C*b^4*sin(d*x + c) + 192*C*a^3*b*tan(d*x + c) + 192*A*a*b^3*tan(d*x + c))/d","A",0
556,1,325,0,0.352508," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{4} + 20 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} + 120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} b^{2} + 60 \, {\left(d x + c\right)} C b^{4} - 15 \, A 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)} - 60 \, C a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, C a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 360 \, C a^{2} b^{2} \tan\left(d x + c\right) + 60 \, A b^{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*a^4 + 20*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 + 120*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2*b^2 + 60*(d*x + c)*C*b^4 - 15*A*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)) - 60*C*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*A*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 120*C*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 360*C*a^2*b^2*tan(d*x + c) + 60*A*b^4*tan(d*x + c))/d","A",0
557,1,466,0,0.353354," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,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 a^{3} b + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} b + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b^{3} - 5 \, A a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, A 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)} - 720 \, C a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, A b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, C b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 1920 \, C a b^{3} \tan\left(d x + c\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*a^3*b + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3*b + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^3 - 5*A*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*A*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)) - 720*C*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 120*A*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*C*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 1920*C*a*b^3*tan(d*x + c))/d","A",0
558,1,472,0,0.376099," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^8,x, algorithm=""maxima"")","\frac{24 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} A a^{4} + 56 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 336 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{2} b^{2} + 1680 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b^{2} + 280 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{4} - 35 \, A a^{3} b {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, C a^{3} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 210 \, A a b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, C a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 840 \, C b^{4} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(24*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*A*a^4 + 56*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 336*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^2*b^2 + 1680*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b^2 + 280*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^4 - 35*A*a^3*b*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 210*C*a^3*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 210*A*a*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*C*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 840*C*b^4*tan(d*x + c))/d","A",0
559,1,146,0,0.356881," ","integrate((a+b*cos(d*x+c))^3*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{480 \, {\left(d x + c\right)} a^{5} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} b^{2} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} b^{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 b^{4} - 32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} b^{5} + 1440 \, a^{4} b \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(480*(d*x + c)*a^5 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3*b^2 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2*b^3 - 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a*b^4 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*b^5 + 1440*a^4*b*sin(d*x + c))/d","A",0
560,1,84,0,0.331154," ","integrate((a+b*cos(d*x+c))^2*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{96 \, {\left(d x + c\right)} a^{4} + 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a b^{3} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b^{4} + 192 \, a^{3} b \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(96*(d*x + c)*a^4 + 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*a*b^3 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b^4 + 192*a^3*b*sin(d*x + c))/d","A",0
561,1,73,0,0.326860," ","integrate((a+b*cos(d*x+c))*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} a^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{2} + 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} b^{3} + 12 \, a^{2} b \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*a^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b^2 + 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*b^3 + 12*a^2*b*sin(d*x + c))/d","A",0
562,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
563,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
564,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
565,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
566,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
567,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
568,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
569,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
570,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
571,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
572,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
573,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
574,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
575,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
576,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
577,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
578,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
579,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
580,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
581,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
582,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
583,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
584,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
585,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
586,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
587,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
588,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
589,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
590,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
591,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
592,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
593,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
594,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
595,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
596,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
597,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
598,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
599,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
600,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
601,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
602,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
603,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
604,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
605,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
606,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
607,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
608,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
609,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
610,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
611,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
612,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
613,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
614,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
615,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
616,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
617,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
618,-2,0,0,0.000000," ","integrate((1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
619,-2,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
620,-2,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
621,-2,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
622,-2,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
623,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
624,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c), x)","F",0
625,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a), x)","F",0
626,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
627,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
628,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
629,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
630,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
631,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
632,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2), x)","F",0
633,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
634,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
635,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
637,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^5, x)","F",0
638,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
639,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
640,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2), x)","F",0
641,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
642,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
643,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
644,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
645,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^5, x)","F",0
646,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(a^2-b^2*cos(d*x+c)^2),x, algorithm=""maxima"")","-\int {\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"-integrate((b^2*cos(d*x + c)^2 - a^2)*(b*cos(d*x + c) + a)^(3/2), x)","F",0
647,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\int {\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"-integrate((b^2*cos(d*x + c)^2 - a^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
648,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
649,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
650,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
651,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/sqrt(b*cos(d*x + c) + a), x)","F",0
652,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
653,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
654,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
655,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{4}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^4/sqrt(b*cos(d*x + c) + a), x)","F",0
656,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
657,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
658,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
659,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
660,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
661,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
662,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
663,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
664,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
665,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
666,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
667,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
668,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
669,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(b*cos(d*x + c) + a)^(7/2), x)","F",0
670,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\int \frac{b^{2} \cos\left(d x + c\right)^{2} - a^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"-integrate((b^2*cos(d*x + c)^2 - a^2)/sqrt(b*cos(d*x + c) + a), x)","F",0
671,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","-\int \frac{b^{2} \cos\left(d x + c\right)^{2} - a^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((b^2*cos(d*x + c)^2 - a^2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
672,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","-\int \frac{b^{2} \cos\left(d x + c\right)^{2} - a^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"-integrate((b^2*cos(d*x + c)^2 - a^2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
673,0,0,0,0.000000," ","integrate((a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","-\int \frac{b^{2} \cos\left(d x + c\right)^{2} - a^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"-integrate((b^2*cos(d*x + c)^2 - a^2)/(b*cos(d*x + c) + a)^(7/2), x)","F",0
674,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
675,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
676,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
677,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
678,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
679,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
680,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
681,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
682,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
683,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
684,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
685,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
686,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
687,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
688,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
689,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
690,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
691,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
692,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
693,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
694,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
695,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
696,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sqrt(cos(d*x + c)), x)","F",0
697,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/sqrt(cos(d*x + c)), x)","F",0
698,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(3/2), x)","F",0
699,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(5/2), x)","F",0
700,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(7/2), x)","F",0
701,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(9/2), x)","F",0
702,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(11/2), x)","F",0
703,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(13/2), x)","F",0
704,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(7/2)/(b*cos(d*x + c) + a), x)","F",0
705,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
706,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
707,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
708,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
709,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
710,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
711,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
712,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
713,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(11/2)), x)","F",0
714,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
715,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
716,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
717,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
718,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
721,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
723,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
724,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(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
726,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
728,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
729,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
730,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
731,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
732,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
733,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
734,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
735,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
736,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
737,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(7/2), x)","F",0
738,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(9/2), x)","F",0
739,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(11/2), x)","F",0
740,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
741,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
742,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
743,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
744,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(7/2), x)","F",0
745,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(9/2), x)","F",0
746,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(11/2), x)","F",0
747,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(13/2), x)","F",0
748,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
749,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
750,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
751,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
752,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
753,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
754,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
755,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
756,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
757,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
758,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
759,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
760,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
761,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
762,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
763,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
764,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
765,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
766,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^m, x)","F",0
767,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^m, x)","F",0
768,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a), x)","F",0
769,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \cos\left(d x + c\right)^{m}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a)^2, x)","F",0
770,1,101,0,0.332522," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b + 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)} C b}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b)/d","A",0
771,1,79,0,0.311087," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b + 12 \, B a \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b + 12*B*a*sin(d*x + c))/d","A",0
772,1,55,0,0.307626," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b + 4 \, C a \sin\left(d x + c\right) + 4 \, B b \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b + 4*C*a*sin(d*x + c) + 4*B*b*sin(d*x + c))/d","A",0
773,1,58,0,0.317862," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C a + 2 \, {\left(d x + c\right)} B b + B a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C b \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a + 2*(d*x + c)*B*b + B*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*b*sin(d*x + c))/d","A",0
774,1,73,0,0.322658," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C b + C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + B b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*b + C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + B*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a*tan(d*x + c))/d","B",0
775,1,95,0,0.335626," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","-\frac{B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 2 \, C b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, C a \tan\left(d x + c\right) - 4 \, B b \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 2*C*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 4*C*a*tan(d*x + c) - 4*B*b*tan(d*x + c))/d","A",0
776,1,127,0,0.334927," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a - 3 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, B b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a - 3*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*B*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*C*b*tan(d*x + c))/d","A",0
777,1,163,0,0.324162," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b - 3 \, B a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b - 3*B*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
778,1,176,0,0.325648," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a b + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{2} + 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)} C b^{2}}{480 \, d}"," ",0,"1/480*(120*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*b^2 + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^2)/d","A",0
779,1,142,0,0.329125," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 48 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b^{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)} C b^{2} + 96 \, B a^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 48*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b^2 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^2 + 96*B*a^2*sin(d*x + c))/d","A",0
780,1,108,0,0.324273," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} B a^{2} + 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{2} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{2} + 12 \, C a^{2} \sin\left(d x + c\right) + 24 \, B a b \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*B*a^2 + 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^2 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^2 + 12*C*a^2*sin(d*x + c) + 24*B*a*b*sin(d*x + c))/d","A",0
781,1,99,0,0.327045," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C a^{2} + 8 \, {\left(d x + c\right)} B a b + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{2} + 2 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, C a b \sin\left(d x + c\right) + 4 \, B b^{2} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*a^2 + 8*(d*x + c)*B*a*b + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^2 + 2*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*C*a*b*sin(d*x + c) + 4*B*b^2*sin(d*x + c))/d","A",0
782,1,103,0,0.336378," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C a b + 2 \, {\left(d x + c\right)} B b^{2} + C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C b^{2} \sin\left(d x + c\right) + 2 \, B a^{2} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*C*a*b + 2*(d*x + c)*B*b^2 + C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*b^2*sin(d*x + c) + 2*B*a^2*tan(d*x + c))/d","A",0
783,1,140,0,0.327946," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C b^{2} - B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C a^{2} \tan\left(d x + c\right) + 8 \, B a b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*b^2 - B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 4*C*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*a^2*tan(d*x + c) + 8*B*a*b*tan(d*x + c))/d","A",0
784,1,172,0,0.335529," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} - 3 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, B a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a b \tan\left(d x + c\right) + 12 \, B b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 - 3*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 6*B*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*C*a*b*tan(d*x + c) + 12*B*b^2*tan(d*x + c))/d","A",0
785,1,228,0,0.326219," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} + 32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b - 3 \, B a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, C a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, B b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C b^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 + 32*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b - 3*B*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 24*C*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*B*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*C*b^2*tan(d*x + c))/d","A",0
786,1,217,0,0.336086," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b^{2} + 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)} C a b^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{3} + 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)} C b^{3} + 480 \, B a^{3} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2*b - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b^2 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*b^3 + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^3 + 480*B*a^3*sin(d*x + c))/d","A",0
787,1,171,0,0.333198," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{96 \, {\left(d x + c\right)} B a^{3} + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{2} - 96 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b^{2} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b^{3} + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{3} + 96 \, C a^{3} \sin\left(d x + c\right) + 288 \, B a^{2} b \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(96*(d*x + c)*B*a^3 + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b^2 - 96*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b^2 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b^3 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^3 + 96*C*a^3*sin(d*x + c) + 288*B*a^2*b*sin(d*x + c))/d","A",0
788,1,152,0,0.327712," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} C a^{3} + 36 \, {\left(d x + c\right)} B a^{2} b + 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{2} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{3} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{3} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, C a^{2} b \sin\left(d x + c\right) + 36 \, B a b^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*C*a^3 + 36*(d*x + c)*B*a^2*b + 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^2 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^3 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^3 + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*C*a^2*b*sin(d*x + c) + 36*B*a*b^2*sin(d*x + c))/d","A",0
789,1,144,0,0.335495," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} C a^{2} b + 12 \, {\left(d x + c\right)} B a b^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{3} + 2 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a b^{2} \sin\left(d x + c\right) + 4 \, B b^{3} \sin\left(d x + c\right) + 4 \, B a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(12*(d*x + c)*C*a^2*b + 12*(d*x + c)*B*a*b^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^3 + 2*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a*b^2*sin(d*x + c) + 4*B*b^3*sin(d*x + c) + 4*B*a^3*tan(d*x + c))/d","A",0
790,1,169,0,0.333552," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} C a b^{2} + 4 \, {\left(d x + c\right)} B b^{3} - B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C b^{3} \sin\left(d x + c\right) + 4 \, C a^{3} \tan\left(d x + c\right) + 12 \, B a^{2} b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(12*(d*x + c)*C*a*b^2 + 4*(d*x + c)*B*b^3 - B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*b^3*sin(d*x + c) + 4*C*a^3*tan(d*x + c) + 12*B*a^2*b*tan(d*x + c))/d","A",0
791,1,216,0,0.332222," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 12 \, {\left(d x + c\right)} C b^{3} - 3 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 9 \, B a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, C a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, C a^{2} b \tan\left(d x + c\right) + 36 \, B a b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 12*(d*x + c)*C*b^3 - 3*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 9*B*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 18*C*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*C*a^2*b*tan(d*x + c) + 36*B*a*b^2*tan(d*x + c))/d","A",0
792,1,273,0,0.341564," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} + 48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} b - 3 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, C a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, C a b^{2} \tan\left(d x + c\right) + 48 \, B b^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 + 48*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2*b - 3*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 36*C*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*B*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 144*C*a*b^2*tan(d*x + c) + 48*B*b^3*tan(d*x + c))/d","A",0
793,1,341,0,0.340818," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,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)} B a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b^{2} - 15 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 45 \, B a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, C b^{3} \tan\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b^2 - 15*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 45*B*a^2*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*C*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*B*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*C*b^3*tan(d*x + c))/d","A",0
794,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
795,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
796,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
797,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
798,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
799,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
800,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
801,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
802,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
803,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
804,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
805,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
806,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
807,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
808,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
809,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
810,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
811,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
812,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
813,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
814,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*cos(d*x + c), x)","F",0
815,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
816,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
817,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
818,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
819,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
820,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
821,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2), x)","F",0
822,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
823,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
824,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
825,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
826,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^5, x)","F",0
827,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
828,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2), x)","F",0
829,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
830,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
831,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
832,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
833,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^5, x)","F",0
834,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^6, x)","F",0
835,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
836,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
837,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
838,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
839,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
840,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{4}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^4/sqrt(b*cos(d*x + c) + a), x)","F",0
841,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
842,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
843,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
844,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
845,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
846,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
848,0,0,0,0.000000," ","integrate(cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
849,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
850,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
851,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
852,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
854,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
855,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
856,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
857,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
858,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
859,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
860,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
861,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
862,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
863,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
864,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
865,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
866,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
867,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(11/2), x)","F",0
868,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
869,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
870,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
871,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
872,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
873,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
874,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
875,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(13/2), x)","F",0
876,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
877,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
878,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
879,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
880,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
881,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
882,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
886,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
887,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
890,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
891,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
892,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
893,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,-2,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(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
896,-1,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
898,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
899,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
900,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
901,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
902,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
903,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(11/2), x)","F",0
904,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
905,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
906,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
907,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
908,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(7/2), x)","F",0
909,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(9/2), x)","F",0
910,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(11/2), x)","F",0
911,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
912,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
913,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
914,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
915,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(7/2), x)","F",0
916,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(9/2), x)","F",0
917,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(11/2), x)","F",0
918,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(13/2), x)","F",0
919,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(15/2), x)","F",0
920,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
921,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
922,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
923,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
924,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
925,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
926,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
927,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
928,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
929,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
930,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
931,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
932,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
933,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
934,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
935,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
936,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
937,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
938,1,166,0,0.328825," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b + 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)} C b}{480 \, d}"," ",0,"1/480*(120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*b + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b)/d","A",0
939,1,132,0,0.337132," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b + 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)} C b + 96 \, A a \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b + 96*A*a*sin(d*x + c))/d","A",0
940,1,98,0,0.314859," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b + 12 \, B a \sin\left(d x + c\right) + 12 \, A b \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b + 12*B*a*sin(d*x + c) + 12*A*b*sin(d*x + c))/d","A",0
941,1,82,0,0.330420," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} B a + 4 \, {\left(d x + c\right)} A b + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b + 4 \, A a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 4 \, C a \sin\left(d x + c\right) + 4 \, B b \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*B*a + 4*(d*x + c)*A*b + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b + 4*A*a*log(sec(d*x + c) + tan(d*x + c)) + 4*C*a*sin(d*x + c) + 4*B*b*sin(d*x + c))/d","A",0
942,1,92,0,0.332487," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} C a + 2 \, {\left(d x + c\right)} B b + B a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + A b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C b \sin\left(d x + c\right) + 2 \, A a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*C*a + 2*(d*x + c)*B*b + B*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + A*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*C*b*sin(d*x + c) + 2*A*a*tan(d*x + c))/d","A",0
943,1,130,0,0.335088," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C b - A a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, B b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a \tan\left(d x + c\right) + 4 \, A b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*b - A*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*B*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a*tan(d*x + c) + 4*A*b*tan(d*x + c))/d","A",0
944,1,162,0,0.367518," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a - 3 \, B a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3 \, 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 \, C b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a \tan\left(d x + c\right) + 12 \, B b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a - 3*B*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 3*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*C*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a*tan(d*x + c) + 12*B*b*tan(d*x + c))/d","A",0
945,1,218,0,0.366555," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a + 16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b - 3 \, A a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, B b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C b \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a + 16*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b - 3*A*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*B*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 48*C*b*tan(d*x + c))/d","A",0
946,1,266,0,0.340209," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B b - 15 \, B a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 15 \, A b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, C b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*b - 15*B*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 15*A*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*C*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
947,1,233,0,0.336300," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a b - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{2} + 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)} C b^{2} + 480 \, A a^{2} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(120*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*b^2 + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^2 + 480*A*a^2*sin(d*x + c))/d","A",0
948,1,187,0,0.330987," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{96 \, {\left(d x + c\right)} A a^{2} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} + 48 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{2} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b^{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)} C b^{2} + 96 \, B a^{2} \sin\left(d x + c\right) + 192 \, A a b \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(96*(d*x + c)*A*a^2 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2 + 48*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^2 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b^2 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^2 + 96*B*a^2*sin(d*x + c) + 192*A*a*b*sin(d*x + c))/d","A",0
949,1,150,0,0.332270," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} B a^{2} + 24 \, {\left(d x + c\right)} A a b + 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{2} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{2} + 12 \, A a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, C a^{2} \sin\left(d x + c\right) + 24 \, B a b \sin\left(d x + c\right) + 12 \, A b^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*B*a^2 + 24*(d*x + c)*A*a*b + 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^2 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^2 + 12*A*a^2*log(sec(d*x + c) + tan(d*x + c)) + 12*C*a^2*sin(d*x + c) + 24*B*a*b*sin(d*x + c) + 12*A*b^2*sin(d*x + c))/d","A",0
950,1,148,0,0.334121," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} C a^{2} + 8 \, {\left(d x + c\right)} B a b + 4 \, {\left(d x + c\right)} A b^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{2} + 2 \, B a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, A a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 8 \, C a b \sin\left(d x + c\right) + 4 \, B b^{2} \sin\left(d x + c\right) + 4 \, A a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*C*a^2 + 8*(d*x + c)*B*a*b + 4*(d*x + c)*A*b^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^2 + 2*B*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*A*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 8*C*a*b*sin(d*x + c) + 4*B*b^2*sin(d*x + c) + 4*A*a^2*tan(d*x + c))/d","A",0
951,1,189,0,0.339154," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{8 \, {\left(d x + c\right)} C a b + 4 \, {\left(d x + c\right)} B b^{2} - A a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, B a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, A b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, C b^{2} \sin\left(d x + c\right) + 4 \, B a^{2} \tan\left(d x + c\right) + 8 \, A a b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(8*(d*x + c)*C*a*b + 4*(d*x + c)*B*b^2 - A*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*B*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*A*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*C*b^2*sin(d*x + c) + 4*B*a^2*tan(d*x + c) + 8*A*a*b*tan(d*x + c))/d","A",0
952,1,221,0,0.333063," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} + 12 \, {\left(d x + c\right)} C b^{2} - 3 \, B a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 6 \, A a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, 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)} + 12 \, C a^{2} \tan\left(d x + c\right) + 24 \, B a b \tan\left(d x + c\right) + 12 \, A b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 + 12*(d*x + c)*C*b^2 - 3*B*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 6*A*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*C*a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a^2*tan(d*x + c) + 24*B*a*b*tan(d*x + c) + 12*A*b^2*tan(d*x + c))/d","A",0
953,1,313,0,0.362136," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} + 32 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b - 3 \, A a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 24 \, B a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 96 \, C a b \tan\left(d x + c\right) + 48 \, B b^{2} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2 + 32*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b - 3*A*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 24*B*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 96*C*a*b*tan(d*x + c) + 48*B*b^2*tan(d*x + c))/d","A",0
954,1,357,0,0.343644," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{2} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{2} - 15 \, B a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, A 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 \, C a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, B b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, C b^{2} \tan\left(d x + c\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*a^2 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^2 - 15*B*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*A*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)) - 120*C*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*B*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*C*b^2*tan(d*x + c))/d","A",0
955,1,360,0,0.339983," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} + 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B 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)} C a^{2} b - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b^{2} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{2} + 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)} C a b^{2} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{3} + 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B b^{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)} C b^{3} + 960 \, A a^{3} \sin\left(d x + c\right)}{960 \, d}"," ",0,"1/960*(240*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3 + 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2*b - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2*b + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2*b - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b^2 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a*b^2 + 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a*b^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*b^3 + 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*b^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))*C*b^3 + 960*A*a^3*sin(d*x + c))/d","A",0
956,1,288,0,0.334402," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{480 \, {\left(d x + c\right)} A a^{3} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b + 360 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{2} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b^{2} + 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)} C a b^{2} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{3} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{3} + 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)} C b^{3} + 480 \, B a^{3} \sin\left(d x + c\right) + 1440 \, A a^{2} b \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(480*(d*x + c)*A*a^3 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3 + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2*b - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b + 360*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b^2 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b^2 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b^2 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^3 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*b^3 + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^3 + 480*B*a^3*sin(d*x + c) + 1440*A*a^2*b*sin(d*x + c))/d","A",0
957,1,239,0,0.336113," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{96 \, {\left(d x + c\right)} B a^{3} + 288 \, {\left(d x + c\right)} A a^{2} b + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b + 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{2} - 96 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b^{2} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{3} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b^{3} + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{3} + 96 \, A a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 96 \, C a^{3} \sin\left(d x + c\right) + 288 \, B a^{2} b \sin\left(d x + c\right) + 288 \, A a b^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(96*(d*x + c)*B*a^3 + 288*(d*x + c)*A*a^2*b + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b + 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b^2 - 96*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b^2 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^3 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b^3 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^3 + 96*A*a^3*log(sec(d*x + c) + tan(d*x + c)) + 96*C*a^3*sin(d*x + c) + 288*B*a^2*b*sin(d*x + c) + 288*A*a*b^2*sin(d*x + c))/d","A",0
958,1,216,0,0.362688," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} C a^{3} + 36 \, {\left(d x + c\right)} B a^{2} b + 36 \, {\left(d x + c\right)} A a b^{2} + 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{2} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{3} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{3} + 6 \, B a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, A a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, C a^{2} b \sin\left(d x + c\right) + 36 \, B a b^{2} \sin\left(d x + c\right) + 12 \, A b^{3} \sin\left(d x + c\right) + 12 \, A a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*C*a^3 + 36*(d*x + c)*B*a^2*b + 36*(d*x + c)*A*a*b^2 + 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^2 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^3 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^3 + 6*B*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*A*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*C*a^2*b*sin(d*x + c) + 36*B*a*b^2*sin(d*x + c) + 12*A*b^3*sin(d*x + c) + 12*A*a^3*tan(d*x + c))/d","A",0
959,1,243,0,0.368647," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} C a^{2} b + 12 \, {\left(d x + c\right)} B a b^{2} + 4 \, {\left(d x + c\right)} A b^{3} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{3} - A a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, C a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, B a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C a b^{2} \sin\left(d x + c\right) + 4 \, B b^{3} \sin\left(d x + c\right) + 4 \, B a^{3} \tan\left(d x + c\right) + 12 \, A a^{2} b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(12*(d*x + c)*C*a^2*b + 12*(d*x + c)*B*a*b^2 + 4*(d*x + c)*A*b^3 + (2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^3 - A*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 2*C*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*B*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*A*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*a*b^2*sin(d*x + c) + 4*B*b^3*sin(d*x + c) + 4*B*a^3*tan(d*x + c) + 12*A*a^2*b*tan(d*x + c))/d","A",0
960,1,280,0,0.336366," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + 36 \, {\left(d x + c\right)} C a b^{2} + 12 \, {\left(d x + c\right)} B b^{3} - 3 \, B a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 9 \, A a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, C a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, B a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, A b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, C b^{3} \sin\left(d x + c\right) + 12 \, C a^{3} \tan\left(d x + c\right) + 36 \, B a^{2} b \tan\left(d x + c\right) + 36 \, A a b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + 36*(d*x + c)*C*a*b^2 + 12*(d*x + c)*B*b^3 - 3*B*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 9*A*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 18*C*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*B*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 6*A*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*C*b^3*sin(d*x + c) + 12*C*a^3*tan(d*x + c) + 36*B*a^2*b*tan(d*x + c) + 36*A*a*b^2*tan(d*x + c))/d","A",0
961,1,372,0,0.345801," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} + 48 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} b + 48 \, {\left(d x + c\right)} C b^{3} - 3 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, B a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 36 \, A a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 72 \, C a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, B b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, C a^{2} b \tan\left(d x + c\right) + 144 \, B a b^{2} \tan\left(d x + c\right) + 48 \, A b^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3 + 48*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2*b + 48*(d*x + c)*C*b^3 - 3*A*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*B*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 36*A*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 72*C*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*B*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 144*C*a^2*b*tan(d*x + c) + 144*B*a*b^2*tan(d*x + c) + 48*A*b^3*tan(d*x + c))/d","A",0
962,1,452,0,0.358065," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{3} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} b + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b^{2} - 15 \, B a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 45 \, A a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, C a^{2} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, B a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, 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)} + 120 \, C b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 720 \, C a b^{2} \tan\left(d x + c\right) + 240 \, B b^{3} \tan\left(d x + c\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*a^3 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2*b + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^2 - 15*B*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 45*A*a^2*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 180*C*a^2*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 180*B*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 60*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)) + 120*C*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 720*C*a*b^2*tan(d*x + c) + 240*B*b^3*tan(d*x + c))/d","A",0
963,1,565,0,0.377827," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{3} + 96 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{2} b + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b^{2} + 160 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{3} - 5 \, A a^{3} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, B a^{2} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 90 \, A 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)} - 360 \, C a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, C b^{3} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^3 + 96*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^2*b + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b^2 + 160*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^3 - 5*A*a^3*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*C*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*B*a^2*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 90*A*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)) - 360*C*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 120*B*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*C*b^3*tan(d*x + c))/d","A",0
964,1,498,0,0.369623," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{1680 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 2240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{4} + 6720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} b - 8960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{3} b + 840 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b - 13440 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a^{2} b^{2} + 1260 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b^{2} + 2688 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} C a^{2} b^{2} + 840 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{3} + 1792 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B a b^{3} - 140 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{3} + 448 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} A b^{4} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{4} - 192 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} C b^{4} + 6720 \, A a^{4} \sin\left(d x + c\right)}{6720 \, d}"," ",0,"1/6720*(1680*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 2240*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^4 + 6720*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3*b - 8960*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^3*b + 840*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^3*b - 13440*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a^2*b^2 + 1260*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^2*b^2 + 2688*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a^2*b^2 + 840*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a*b^3 + 1792*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a*b^3 - 140*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*C*a*b^3 + 448*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*A*b^4 - 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*B*b^4 - 192*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*C*b^4 + 6720*A*a^4*sin(d*x + c))/d","A",0
965,1,415,0,0.341653," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\frac{960 \, {\left(d x + c\right)} A a^{4} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{4} + 960 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{3} b - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{3} b + 1440 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} b^{2} - 1920 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a^{2} b^{2} + 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)} C a^{2} b^{2} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A a b^{3} + 120 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{3} + 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)} C a b^{3} + 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{4} + 64 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} B b^{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)} C b^{4} + 960 \, B a^{4} \sin\left(d x + c\right) + 3840 \, A a^{3} b \sin\left(d x + c\right)}{960 \, d}"," ",0,"1/960*(960*(d*x + c)*A*a^4 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^4 + 960*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^3*b - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^3*b + 1440*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2*b^2 - 1920*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^2*b^2 + 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a^2*b^2 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*a*b^3 + 120*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a*b^3 + 256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*a*b^3 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*b^4 + 64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*b^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))*C*b^4 + 960*B*a^4*sin(d*x + c) + 3840*A*a^3*b*sin(d*x + c))/d","A",0
966,1,340,0,0.345185," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\frac{480 \, {\left(d x + c\right)} B a^{4} + 1920 \, {\left(d x + c\right)} A a^{3} b + 480 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b + 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b^{2} - 960 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b^{2} + 480 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a b^{3} - 640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b^{3} + 60 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{3} - 160 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} A b^{4} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{4} + 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)} C b^{4} + 480 \, A a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 480 \, C a^{4} \sin\left(d x + c\right) + 1920 \, B a^{3} b \sin\left(d x + c\right) + 2880 \, A a^{2} b^{2} \sin\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(480*(d*x + c)*B*a^4 + 1920*(d*x + c)*A*a^3*b + 480*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3*b + 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2*b^2 - 960*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b^2 + 480*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a*b^3 - 640*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b^3 + 60*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b^3 - 160*(sin(d*x + c)^3 - 3*sin(d*x + c))*A*b^4 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*b^4 + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^4 + 480*A*a^4*log(sec(d*x + c) + tan(d*x + c)) + 480*C*a^4*sin(d*x + c) + 1920*B*a^3*b*sin(d*x + c) + 2880*A*a^2*b^2*sin(d*x + c))/d","A",0
967,1,305,0,0.346622," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{96 \, {\left(d x + c\right)} C a^{4} + 384 \, {\left(d x + c\right)} B a^{3} b + 576 \, {\left(d x + c\right)} A a^{2} b^{2} + 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{2} b^{2} + 96 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{3} - 128 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b^{3} + 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A b^{4} - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b^{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)} C b^{4} + 48 \, B a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 192 \, A a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 384 \, C a^{3} b \sin\left(d x + c\right) + 576 \, B a^{2} b^{2} \sin\left(d x + c\right) + 384 \, A a b^{3} \sin\left(d x + c\right) + 96 \, A a^{4} \tan\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(96*(d*x + c)*C*a^4 + 384*(d*x + c)*B*a^3*b + 576*(d*x + c)*A*a^2*b^2 + 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^2*b^2 + 96*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b^3 - 128*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b^3 + 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*b^4 - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b^4 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^4 + 48*B*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 192*A*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 384*C*a^3*b*sin(d*x + c) + 576*B*a^2*b^2*sin(d*x + c) + 384*A*a*b^3*sin(d*x + c) + 96*A*a^4*tan(d*x + c))/d","A",0
968,1,311,0,0.361603," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{48 \, {\left(d x + c\right)} C a^{3} b + 72 \, {\left(d x + c\right)} B a^{2} b^{2} + 48 \, {\left(d x + c\right)} A a b^{3} + 12 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{3} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{4} - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{4} - 3 \, A a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, C a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, B a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, A a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 72 \, C a^{2} b^{2} \sin\left(d x + c\right) + 48 \, B a b^{3} \sin\left(d x + c\right) + 12 \, A b^{4} \sin\left(d x + c\right) + 12 \, B a^{4} \tan\left(d x + c\right) + 48 \, A a^{3} b \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(48*(d*x + c)*C*a^3*b + 72*(d*x + c)*B*a^2*b^2 + 48*(d*x + c)*A*a*b^3 + 12*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^3 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^4 - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^4 - 3*A*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*C*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*B*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*A*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 72*C*a^2*b^2*sin(d*x + c) + 48*B*a*b^3*sin(d*x + c) + 12*A*b^4*sin(d*x + c) + 12*B*a^4*tan(d*x + c) + 48*A*a^3*b*tan(d*x + c))/d","A",0
969,1,335,0,0.363571," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{4} + 72 \, {\left(d x + c\right)} C a^{2} b^{2} + 48 \, {\left(d x + c\right)} B a b^{3} + 12 \, {\left(d x + c\right)} A b^{4} + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C b^{4} - 3 \, B a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, A a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, C a^{3} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, B a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C a b^{3} \sin\left(d x + c\right) + 12 \, B b^{4} \sin\left(d x + c\right) + 12 \, C a^{4} \tan\left(d x + c\right) + 48 \, B a^{3} b \tan\left(d x + c\right) + 72 \, A a^{2} b^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^4 + 72*(d*x + c)*C*a^2*b^2 + 48*(d*x + c)*B*a*b^3 + 12*(d*x + c)*A*b^4 + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*b^4 - 3*B*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 12*A*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*C*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*B*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*A*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*C*a*b^3*sin(d*x + c) + 12*B*b^4*sin(d*x + c) + 12*C*a^4*tan(d*x + c) + 48*B*a^3*b*tan(d*x + c) + 72*A*a^2*b^2*tan(d*x + c))/d","A",0
970,1,431,0,0.356787," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{4} + 64 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} b + 192 \, {\left(d x + c\right)} C a b^{3} + 48 \, {\left(d x + c\right)} B b^{4} - 3 \, A a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, C a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 48 \, B a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, A a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 144 \, C a^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 96 \, B a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, A b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, C b^{4} \sin\left(d x + c\right) + 192 \, C a^{3} b \tan\left(d x + c\right) + 288 \, B a^{2} b^{2} \tan\left(d x + c\right) + 192 \, A a b^{3} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^4 + 64*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3*b + 192*(d*x + c)*C*a*b^3 + 48*(d*x + c)*B*b^4 - 3*A*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*C*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 48*B*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 72*A*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 144*C*a^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 96*B*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 24*A*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*C*b^4*sin(d*x + c) + 192*C*a^3*b*tan(d*x + c) + 288*B*a^2*b^2*tan(d*x + c) + 192*A*a*b^3*tan(d*x + c))/d","A",0
971,1,511,0,0.375783," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,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 a^{4} + 80 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{4} + 320 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{3} b + 480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} b^{2} + 240 \, {\left(d x + c\right)} C b^{4} - 15 \, B a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, A 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)} - 240 \, C a^{3} b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 360 \, B a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 240 \, A a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 480 \, C a b^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, B b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 1440 \, C a^{2} b^{2} \tan\left(d x + c\right) + 960 \, B a b^{3} \tan\left(d x + c\right) + 240 \, A b^{4} \tan\left(d x + c\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*a^4 + 80*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^4 + 320*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^3*b + 480*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2*b^2 + 240*(d*x + c)*C*b^4 - 15*B*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*A*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)) - 240*C*a^3*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 360*B*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 240*A*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 480*C*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 120*B*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 1440*C*a^2*b^2*tan(d*x + c) + 960*B*a*b^3*tan(d*x + c) + 240*A*b^4*tan(d*x + c))/d","A",0
972,1,660,0,0.376950," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{4} + 128 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{3} b + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{3} b + 960 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a^{2} b^{2} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a b^{3} - 5 \, A a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, C a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, B 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)} - 180 \, A 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)} - 720 \, C a^{2} b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 480 \, B a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, A b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, C b^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 1920 \, C a b^{3} \tan\left(d x + c\right) + 480 \, B b^{4} \tan\left(d x + c\right)}{480 \, d}"," ",0,"1/480*(32*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^4 + 128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^3*b + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^3*b + 960*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a^2*b^2 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*a*b^3 - 5*A*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 30*C*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*B*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)) - 180*A*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)) - 720*C*a^2*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 480*B*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 120*A*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 240*C*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 1920*C*a*b^3*tan(d*x + c) + 480*B*b^4*tan(d*x + c))/d","A",0
973,1,746,0,0.393482," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^8,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 a^{4} + 224 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} C a^{4} + 896 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} B a^{3} b + 1344 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{2} b^{2} + 6720 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} C a^{2} b^{2} + 4480 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} B a b^{3} + 1120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A b^{4} - 35 \, B a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 140 \, A a^{3} b {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, C a^{3} b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 1260 \, B a^{2} b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, A a b^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 3360 \, C a b^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 840 \, 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)} + 3360 \, C b^{4} \tan\left(d x + c\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*a^4 + 224*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*C*a^4 + 896*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*B*a^3*b + 1344*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^2*b^2 + 6720*(tan(d*x + c)^3 + 3*tan(d*x + c))*C*a^2*b^2 + 4480*(tan(d*x + c)^3 + 3*tan(d*x + c))*B*a*b^3 + 1120*(tan(d*x + c)^3 + 3*tan(d*x + c))*A*b^4 - 35*B*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 140*A*a^3*b*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 840*C*a^3*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 1260*B*a^2*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 840*A*a*b^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 3360*C*a*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 840*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)) + 3360*C*b^4*tan(d*x + c))/d","A",0
974,1,263,0,0.356558," ","integrate((a+b*cos(d*x+c))^3*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{480 \, {\left(d x + c\right)} C a^{5} - 480 \, {\left(d x + c\right)} B a^{4} b + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a^{3} b^{2} - 720 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{2} b^{3} + 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a^{2} b^{3} + 640 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B a b^{4} - 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)} C a b^{4} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{5} - 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)} C b^{5} + 1440 \, C a^{4} b \sin\left(d x + c\right) - 1920 \, B a^{3} b^{2} \sin\left(d x + c\right)}{480 \, d}"," ",0,"-1/480*(480*(d*x + c)*C*a^5 - 480*(d*x + c)*B*a^4*b + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a^3*b^2 - 720*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^2*b^3 + 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a^2*b^3 + 640*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a*b^4 - 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*a*b^4 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*b^5 - 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*C*b^5 + 1440*C*a^4*b*sin(d*x + c) - 1920*B*a^3*b^2*sin(d*x + c))/d","A",0
975,1,162,0,0.355665," ","integrate((a+b*cos(d*x+c))^2*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{96 \, {\left(d x + c\right)} C a^{4} - 96 \, {\left(d x + c\right)} B a^{3} b - 72 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a b^{3} + 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C a b^{3} + 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B b^{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)} C b^{4} + 192 \, C a^{3} b \sin\left(d x + c\right) - 288 \, B a^{2} b^{2} \sin\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(96*(d*x + c)*C*a^4 - 96*(d*x + c)*B*a^3*b - 72*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a*b^3 + 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*a*b^3 + 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*b^4 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*C*b^4 + 192*C*a^3*b*sin(d*x + c) - 288*B*a^2*b^2*sin(d*x + c))/d","A",0
976,1,125,0,0.348200," ","integrate((a+b*cos(d*x+c))*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""maxima"")","-\frac{12 \, {\left(d x + c\right)} C a^{3} - 12 \, {\left(d x + c\right)} B a^{2} b - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} C a b^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B b^{3} + 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} C b^{3} + 12 \, C a^{2} b \sin\left(d x + c\right) - 24 \, B a b^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(12*(d*x + c)*C*a^3 - 12*(d*x + c)*B*a^2*b - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*C*a*b^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*b^3 + 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*C*b^3 + 12*C*a^2*b*sin(d*x + c) - 24*B*a*b^2*sin(d*x + c))/d","A",0
977,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
978,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
979,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
980,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
981,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
982,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
983,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
984,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
985,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
986,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
987,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
988,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
989,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
990,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
991,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
992,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
993,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
994,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
995,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
996,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
997,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
998,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
999,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1000,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1001,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1002,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1003,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1004,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1005,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1006,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1007,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1008,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1009,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1010,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1011,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1012,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1013,-2,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^5,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1014,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
1015,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*cos(d*x + c), x)","F",0
1016,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a), x)","F",0
1017,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
1018,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
1019,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
1020,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
1021,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
1022,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
1023,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2), x)","F",0
1024,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
1025,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
1026,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
1027,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
1028,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^5, x)","F",0
1029,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
1030,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
1031,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2), x)","F",0
1032,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
1033,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
1034,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
1035,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
1036,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1037,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1038,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)*(b*cos(d*x + c) + a)^(3/2), x)","F",0
1039,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b\right)} \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)*sqrt(b*cos(d*x + c) + a), x)","F",0
1040,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
1041,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
1042,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(b*cos(d*x + c) + a), x)","F",0
1043,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
1044,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
1045,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
1046,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{4}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^4/sqrt(b*cos(d*x + c) + a), x)","F",0
1047,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1048,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1049,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1050,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1051,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1052,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1053,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1054,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1055,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1056,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1057,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1058,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1059,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1060,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(7/2), x)","F",0
1061,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)/sqrt(b*cos(d*x + c) + a), x)","F",0
1062,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1063,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1064,0,0,0,0.000000," ","integrate((a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{C b^{2} \cos\left(d x + c\right)^{2} + B b^{2} \cos\left(d x + c\right) - C a^{2} + B a b}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*b^2*cos(d*x + c)^2 + B*b^2*cos(d*x + c) - C*a^2 + B*a*b)/(b*cos(d*x + c) + a)^(7/2), x)","F",0
1065,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
1066,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1067,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1068,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1069,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
1070,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
1071,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
1072,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
1073,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
1074,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
1075,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
1076,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
1077,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
1078,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(9/2), x)","F",0
1079,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/cos(d*x + c)^(11/2), x)","F",0
1080,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
1081,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
1082,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
1083,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
1084,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
1085,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
1086,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/cos(d*x + c)^(11/2), x)","F",0
1087,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sqrt(cos(d*x + c)), x)","F",0
1088,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/sqrt(cos(d*x + c)), x)","F",0
1089,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(3/2), x)","F",0
1090,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(5/2), x)","F",0
1091,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(7/2), x)","F",0
1092,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(9/2), x)","F",0
1093,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(11/2), x)","F",0
1094,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/cos(d*x + c)^(13/2), x)","F",0
1095,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
1096,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
1097,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
1098,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1099,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1100,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1101,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
1102,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
1103,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
1104,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
1105,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
1106,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1107,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1108,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1109,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1110,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1111,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1112,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1113,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1114,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(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
1115,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1116,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
1117,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
1118,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
1119,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
1120,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
1121,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
1122,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
1123,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
1124,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
1125,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
1126,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(7/2), x)","F",0
1127,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(9/2), x)","F",0
1128,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(11/2), x)","F",0
1129,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
1130,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
1131,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
1132,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
1133,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(7/2), x)","F",0
1134,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(9/2), x)","F",0
1135,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(11/2), x)","F",0
1136,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1137,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1138,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1139,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
1140,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
1141,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(7/2)), x)","F",0
1142,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(9/2)), x)","F",0
1143,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1144,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c)+2*b*cos(d*x+c)^2)/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{2 \, b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) + a}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((2*b*cos(d*x + c)^2 + a*cos(d*x + c) + a)/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
1145,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1146,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1147,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
1148,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
1149,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
1150,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
1151,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1152,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1153,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
1154,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
1155,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
1156,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*cos(d*x + c)^m, x)","F",0
1157,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*cos(d*x + c)^m, x)","F",0
1158,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a), x)","F",0
1159,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*cos(d*x + c)^m/(b*cos(d*x + c) + a)^2, x)","F",0
1160,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1161,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1162,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1163,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1164,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1165,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1166,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1167,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(11/2), x)","F",0
1168,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
1169,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
1170,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
1171,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
1172,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
1173,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
1174,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
1175,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(13/2), x)","F",0
1176,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(11/2), x)","F",0
1177,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
1178,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
1179,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
1180,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
1181,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
1182,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
1183,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(a*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1184,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a), x)","F",0
1185,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
1186,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
1187,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
1188,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1189,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1190,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1191,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1192,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1193,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
1194,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1195,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1196,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
1197,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1198,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1199,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1200,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
1201,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
1202,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
1203,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
1204,1,659,0,0.806443," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{A {\left(\frac{315 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{735 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1302 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1206 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{431 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{107 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{21 \, C {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{55 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{82 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{66 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{31 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{315 \, d}"," ",0,"2/315*(A*(315*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 735*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1302*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1206*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 431*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 107*sqrt(2)*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 21*C*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 55*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 82*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 66*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 31*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
1205,1,567,0,0.856955," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, A {\left(\frac{35 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{70 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{84 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{58 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{35 \, C {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{12 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{105 \, d}"," ",0,"2/105*(3*A*(35*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 70*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 84*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 58*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 35*C*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 12*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
1206,1,474,0,0.747861," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{A {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{15 \, C {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{15 \, d}"," ",0,"2/15*(A*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 17*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 15*C*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 3*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
1207,1,1360,0,1.304827," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} \sqrt{a} \sin\left(\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(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\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} + {\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)} \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(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\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) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\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) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\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)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{4 \, A {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{6 \, d}"," ",0,"1/6*(3*(2*(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)*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)*(cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) + 1)*sin(3/2*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)*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) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 4*A*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
1208,1,890,0,0.941252," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C + \frac{8 \, A {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}}}{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)))*C + 8*A*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)))/d","B",0
1209,1,1207,0,1.493197," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{16 \, A \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C}{16 \, d}"," ",0,"1/16*(16*A*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C)/d","B",0
1210,1,2713,0,1.183513," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A + {\left(4 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(\cos\left(3 \, d x + 3 \, c\right) - 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 15 \, \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)}\right)} C}{96 \, d}"," ",0,"1/96*(24*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A + (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)))*C)/d","B",0
1211,1,7700,0,2.004448," ","integrate((A+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{48 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A + \frac{{\left(2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(60 \, {\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} + 15 \, \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 15 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 60 \, {\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} + 15 \, {\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) + 60 \, {\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} - 31 \, \cos\left(4 \, d x + 4 \, c\right) + 15\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) + 31 \, \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) - 15 \, \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) - 60 \, {\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(15 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 4 \, {\left(15 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(15 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 38 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 31 \, \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(15 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(15 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(15 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 22 \, \cos\left(4 \, d x + 4 \, c\right)^{2} - \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} - 31 \, \cos\left(4 \, d x + 4 \, c\right) + 15\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) + 31 \, \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) - 15 \, \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(15 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(15 \, \cos\left(4 \, d x + 4 \, c\right) - 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 23 \, \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) - 15 \, {\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(15 \, \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(15 \, \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(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)^{3} - 4 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 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) - 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}{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} - 3 \, \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \sin\left(4 \, d x + 4 \, c\right)^{3} - 4 \, {\left(3 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(3 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 6 \, \cos\left(4 \, d x + 4 \, c\right) + 11\right)} \sin\left(4 \, d x + 4 \, c\right) + 32 \, \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) - 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}{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} - 2 \, {\left(6 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 6 \, {\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) + 3 \, \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(64 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 64 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 61 \, \cos\left(4 \, d x + 4 \, c\right) - 3\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) - 3 \, \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(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)^{2} + 4 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 8 \, {\left(2 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 5 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 32 \, \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) - 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) + 3 \, {\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) + 10 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 61 \, \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) + {\left(32 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 32 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 3 \, \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(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)^{3} - 3 \, \cos\left(4 \, d x + 4 \, c\right)^{3} - 4 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 16\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 10 \, \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}{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} - 3 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 3 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 30 \, \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}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 51 \, \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(6 \, \cos\left(4 \, d x + 4 \, c\right)^{3} + 2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 22\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 38 \, \cos\left(4 \, d x + 4 \, c\right)^{2} - {\left(32 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 32 \, \sin\left(4 \, d x + 4 \, c\right)^{2} - 29 \, \cos\left(4 \, d x + 4 \, c\right) - 3\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) - 3 \, \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(16 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 3 \, \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(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)^{2} \sin\left(4 \, d x + 4 \, c\right) - 8 \, {\left({\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 22\right)} \sin\left(4 \, d x + 4 \, c\right) - 16 \, \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) - 6 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 8\right)} \sin\left(4 \, d x + 4 \, c\right) + 29 \, \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) + 3 \, {\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) + 3 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 105 \, {\left({\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left(-{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left(-{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) + 1\right) + {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)}}{768 \, d}"," ",0,"1/768*(48*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A + (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)*((60*(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 + 15*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 15*sin(4*d*x + 4*c)^3 + 60*(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 + 15*(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))) + 60*(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 - 31*cos(4*d*x + 4*c) + 15)*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) + 31*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 15*cos(4*d*x + 4*c))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 60*(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)) - (15*cos(4*d*x + 4*c)^3 + 4*(15*cos(4*d*x + 4*c)^3 + (15*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 - 38*cos(4*d*x + 4*c)^2 + 31*cos(4*d*x + 4*c) - 8)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (15*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 + 4*(15*cos(4*d*x + 4*c)^3 + (15*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 + 22*cos(4*d*x + 4*c)^2 - 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 - 31*cos(4*d*x + 4*c) + 15)*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) + 31*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 15*cos(4*d*x + 4*c))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(15*cos(4*d*x + 4*c)^3 + (15*cos(4*d*x + 4*c) - 8)*sin(4*d*x + 4*c)^2 - 23*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))) - 15*(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*(15*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) + (15*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)*((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)))^3 - 4*(3*sin(4*d*x + 4*c)^3 + 3*(cos(4*d*x + 4*c)^2 - 2*cos(4*d*x + 4*c) + 1)*sin(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)*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 - 3*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) - 3*sin(4*d*x + 4*c)^3 - 4*(3*sin(4*d*x + 4*c)^3 + (3*cos(4*d*x + 4*c)^2 + 6*cos(4*d*x + 4*c) + 11)*sin(4*d*x + 4*c) + 32*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(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)*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 - 2*(6*sin(4*d*x + 4*c)^3 + 6*(cos(4*d*x + 4*c)^2 - cos(4*d*x + 4*c))*sin(4*d*x + 4*c) + 3*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) - (64*cos(4*d*x + 4*c)^2 + 64*sin(4*d*x + 4*c)^2 - 61*cos(4*d*x + 4*c) - 3)*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))) - 3*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(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)))^2 + 4*cos(4*d*x + 4*c)^2 + 8*(2*cos(4*d*x + 4*c)^2 + 5*sin(4*d*x + 4*c)^2 - 32*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(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))) + 3*(cos(4*d*x + 4*c) + 1)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 10*sin(4*d*x + 4*c)^2 - 61*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))) + (32*cos(4*d*x + 4*c)^2 + 32*sin(4*d*x + 4*c)^2 + 3*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)) - (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)))^3 - 3*cos(4*d*x + 4*c)^3 - 4*(3*cos(4*d*x + 4*c)^3 + (3*cos(4*d*x + 4*c) + 16)*sin(4*d*x + 4*c)^2 + 10*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(1/4*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 - 3*(cos(4*d*x + 4*c) + 8)*sin(4*d*x + 4*c)^2 - 4*(3*cos(4*d*x + 4*c)^3 + 3*(cos(4*d*x + 4*c) + 8)*sin(4*d*x + 4*c)^2 + 30*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(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 16*(cos(4*d*x + 4*c)^2 + sin(4*d*x + 4*c)^2 + 2*cos(4*d*x + 4*c) + 1)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 51*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*(6*cos(4*d*x + 4*c)^3 + 2*(3*cos(4*d*x + 4*c) + 22)*sin(4*d*x + 4*c)^2 + 38*cos(4*d*x + 4*c)^2 - (32*cos(4*d*x + 4*c)^2 + 32*sin(4*d*x + 4*c)^2 - 29*cos(4*d*x + 4*c) - 3)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 3*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))) + (16*cos(4*d*x + 4*c)^2 + 16*sin(4*d*x + 4*c)^2 + 3*cos(4*d*x + 4*c))*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2*sin(4*d*x + 4*c) - 8*((3*cos(4*d*x + 4*c) + 22)*sin(4*d*x + 4*c) - 16*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))) - 6*(cos(4*d*x + 4*c) + 8)*sin(4*d*x + 4*c) + 29*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 3*(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))) + 3*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))*C/(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
1212,1,712,0,0.974489," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{7 \, {\left(\frac{165 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{495 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1056 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1254 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{781 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{299 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{46 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{11 \, {\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{455 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{868 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{962 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{653 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{247 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{1155 \, d}"," ",0,"4/1155*(7*(165*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 495*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1056*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1254*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 781*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 299*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 46*sqrt(2)*a^(3/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 11*(105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 455*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 868*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 962*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 653*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 247*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
1213,1,619,0,1.149365," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{{\left(\frac{315 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{840 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1344 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1242 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{517 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{94 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{63 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{32 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{26 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{11 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{315 \, d}"," ",0,"4/315*((315*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 840*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1344*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1242*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 517*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 94*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 63*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 32*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 26*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 11*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
1214,1,527,0,0.664601," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{{\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{245 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{273 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{171 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{35 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{11 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{9 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{105 \, d}"," ",0,"4/105*((105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 245*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 273*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 171*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 35*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 11*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 9*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
1215,1,1700,0,1.491955," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{5 \, {\left(2 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} a^{\frac{3}{2}} \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) + 3 \, {\left({\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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} - 2 \, {\left({\left(6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\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) - 3 \, a \sin\left(4 \, d x + 4 \, c\right) - 7 \, a \sin\left(2 \, d x + 2 \, c\right) - 6 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 7 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\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) + 4 \, a\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 9 \, {\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, 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)} \sqrt{a}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}}} + \frac{24 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{30 \, d}"," ",0,"1/30*(5*(2*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*a^(3/2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 3*((a*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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) - 2*((6*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*a*sin(4*d*x + 4*c) - 7*a*sin(2*d*x + 2*c) - 6*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(5/2*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) + 1)) + (3*a*cos(4*d*x + 4*c) + 7*a*cos(2*d*x + 2*c) + 6*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*a)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 9*(a*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(5/4) + 24*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
1216,1,1393,0,1.386279," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\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}} a^{\frac{3}{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(3 \, a \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + a \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + a \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) - 3 \, {\left(a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(d x + c\right) - a\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a \cos\left(d x + c\right) - a\right)} \cos\left(2 \, d x + 2 \, c\right) + 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({\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{16 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} A}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}}{12 \, d}"," ",0,"1/12*(3*(6*(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^(3/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 2*(3*a*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(2*d*x + 2*c) + (a*cos(2*d*x + 2*c)^2*sin(d*x + c) + a*sin(2*d*x + 2*c)^2*sin(d*x + c) + 2*a*cos(2*d*x + 2*c)*sin(d*x + c) + a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 3*(a*cos(2*d*x + 2*c) + a)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((a*cos(d*x + c) - a)*cos(2*d*x + 2*c)^2 + (a*cos(d*x + c) - a)*sin(2*d*x + 2*c)^2 + 2*(a*cos(d*x + c) - a)*cos(2*d*x + 2*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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 16*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*A/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)))/d","B",0
1217,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1218,1,2746,0,2.010586," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A + {\left(4 \, {\left(a \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(a \cos\left(3 \, d x + 3 \, c\right) - a\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)} {\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}} \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(3 \, a \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) + 11 \, a \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(3 \, a \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) + 5 \, a \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) - 8 \, a\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} + 33 \, {\left(a \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) - a \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) - a \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) + a \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)} \sqrt{a}\right)} C}{96 \, d}"," ",0,"1/96*(24*(2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A + (4*(a*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) - (a*cos(3*d*x + 3*c) - a)*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)))*(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)*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)*((3*a*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 11*a*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)) - (3*a*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 8*a)*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) + 33*(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) - 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) - 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)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a*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))*sqrt(a))*C)/d","B",0
1219,1,7999,0,1.889607," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{16 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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) \sin\left(2 \, d x + 2 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right) - {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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)\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(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) - a \cos\left(2 \, d x + 2 \, c\right) + {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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) + 6 \, 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} + 7 \, {\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)} \sqrt{a}\right)} A + \frac{{\left(2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(4 \, d x + 4 \, c\right)^{3} + 4 \, {\left(a \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + {\left(2 \, a \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) + a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + a\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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 4 \, {\left(a \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} - a \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(8 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 32 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 32 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} - a \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 17 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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(64 \, a \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) + 17 \, a \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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 4 \, {\left(4 \, a \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} + a \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(a \cos\left(4 \, d x + 4 \, c\right)^{3} - 8 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{3} - 10 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 17 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\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(a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{3} - 6 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 15 \, a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\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} + {\left(8 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 32 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} + 32 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} - a \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(16 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 16 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 17 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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(64 \, a \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) + 17 \, a \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)} \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(a \cos\left(4 \, d x + 4 \, c\right)^{3} - 9 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 8 \, a \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(2 \, a \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) + a \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + a\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}{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(a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\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(a \cos\left(4 \, d x + 4 \, c\right) - 8 \, a\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} + 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{1}{4}} {\left({\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + a \sin\left(4 \, d x + 4 \, c\right)^{3} + 80 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\right)} \sin\left(4 \, d x + 4 \, c\right) + 76 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \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) + 4 \, {\left(a \sin\left(4 \, d x + 4 \, c\right)^{3} - 80 \, a \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(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) - 19 \, a\right)} \sin\left(4 \, d x + 4 \, c\right) + 76 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 2 \, {\left(2 \, a \sin\left(4 \, d x + 4 \, c\right)^{3} + a \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(a \cos\left(4 \, d x + 4 \, c\right)^{2} - a \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(152 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 152 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 153 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, {\left(10 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 40 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 153 \, a \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) + 8 \, {\left(5 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 76 \, a \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) - 5 \, a \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(a \cos\left(4 \, d x + 4 \, c\right) + a\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)\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) + {\left(76 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 76 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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(a \cos\left(4 \, d x + 4 \, c\right)^{3} + 80 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} - 56 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{3} - 38 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(a \cos\left(4 \, d x + 4 \, c\right) - 36 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 93 \, a \cos\left(4 \, d x + 4 \, c\right) + 36 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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) - 56 \, a\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(a \cos\left(4 \, d x + 4 \, c\right) - 56 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{3} - 54 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + {\left(a \cos\left(4 \, d x + 4 \, c\right) - 56 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 111 \, a \cos\left(4 \, d x + 4 \, c\right) + 20 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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) + 36 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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) - 56 \, a\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} - a \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) + 2 \, {\left(2 \, a \cos\left(4 \, d x + 4 \, c\right)^{3} - 104 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) - 51 \, a\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) + 112 \, a \cos\left(4 \, d x + 4 \, c\right) + {\left(72 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 72 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - 73 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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)\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(36 \, a \cos\left(4 \, d x + 4 \, c\right)^{2} + 36 \, a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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(160 \, a \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) + 73 \, a \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) + 8 \, {\left(36 \, a \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(a \cos\left(4 \, d x + 4 \, c\right) - 51 \, a\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(a \cos\left(4 \, d x + 4 \, c\right) - 56 \, a\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(a \cos\left(4 \, d x + 4 \, c\right) + a\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)\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} + 75 \, {\left({\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) - 4 \, {\left(4 \, a \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) + a \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(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) - 4 \, {\left(4 \, a \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) + a \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(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) - 4 \, {\left(4 \, a \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) + a \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(a \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a \cos\left(4 \, d x + 4 \, c\right) + a\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} + 4 \, {\left(a \cos\left(4 \, d x + 4 \, c\right)^{2} + a \sin\left(4 \, d x + 4 \, c\right)^{2} - a \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) - 4 \, {\left(4 \, a \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) + a \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{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)}}{256 \, d}"," ",0,"1/256*(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)*((a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a*sin(2*d*x + 2*c) - (a*cos(2*d*x + 2*c) - 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a*cos(2*d*x + 2*c) + (a*cos(2*d*x + 2*c) - 6*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 7*(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))*sqrt(a))*A + (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)*((a*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + a*sin(4*d*x + 4*c)^3 + 4*(a*sin(4*d*x + 4*c)^3 + (a*cos(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*sin(4*d*x + 4*c)^3 + (a*cos(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (2*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*sin(4*d*x + 4*c) - 2*(a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(a*sin(4*d*x + 4*c)^3 + (a*cos(4*d*x + 4*c)^2 - a*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))) + (8*a*cos(4*d*x + 4*c)^2 + 32*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*a*sin(4*d*x + 4*c)^2 + 32*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 - a*cos(4*d*x + 4*c) + 2*(16*a*cos(4*d*x + 4*c)^2 + 16*a*sin(4*d*x + 4*c)^2 - 17*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 17*a*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c)^2 + a*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)) - (a*cos(4*d*x + 4*c)^3 - 8*a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^3 - 10*a*cos(4*d*x + 4*c)^2 + (a*cos(4*d*x + 4*c) - 8*a)*sin(4*d*x + 4*c)^2 + 17*a*cos(4*d*x + 4*c) - 8*a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (a*cos(4*d*x + 4*c) - 8*a)*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^3 - 6*a*cos(4*d*x + 4*c)^2 + (a*cos(4*d*x + 4*c) - 8*a)*sin(4*d*x + 4*c)^2 - 15*a*cos(4*d*x + 4*c) - 8*a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (8*a*cos(4*d*x + 4*c)^2 + 32*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*a*sin(4*d*x + 4*c)^2 + 32*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 - a*cos(4*d*x + 4*c) + 2*(16*a*cos(4*d*x + 4*c)^2 + 16*a*sin(4*d*x + 4*c)^2 - 17*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(64*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 17*a*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(a*cos(4*d*x + 4*c)^3 - 9*a*cos(4*d*x + 4*c)^2 + (a*cos(4*d*x + 4*c) - 8*a)*sin(4*d*x + 4*c)^2 + 8*a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - (2*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*sin(4*d*x + 4*c) - 2*(a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*(a*cos(4*d*x + 4*c) - 8*a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (a*cos(4*d*x + 4*c) - 8*a)*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) + 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)^(1/4)*((a*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + a*sin(4*d*x + 4*c)^3 + 80*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 + 4*(a*sin(4*d*x + 4*c)^3 + (a*cos(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*sin(4*d*x + 4*c) + 76*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*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 + a*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 4*(a*sin(4*d*x + 4*c)^3 - 80*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (a*cos(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) - 19*a)*sin(4*d*x + 4*c) + 76*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*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 + 2*(2*a*sin(4*d*x + 4*c)^3 + a*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 2*(a*cos(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*sin(4*d*x + 4*c) + (152*a*cos(4*d*x + 4*c)^2 + 152*a*sin(4*d*x + 4*c)^2 - 153*a*cos(4*d*x + 4*c) + a)*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*(10*a*cos(4*d*x + 4*c)^2 + 40*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*a*sin(4*d*x + 4*c)^2 - 153*a*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 8*(5*a*cos(4*d*x + 4*c)^2 + 4*a*sin(4*d*x + 4*c)^2 - 76*a*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 5*a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - (a*cos(4*d*x + 4*c) + a)*cos(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))) + (76*a*cos(4*d*x + 4*c)^2 + 76*a*sin(4*d*x + 4*c)^2 - a*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)) - (a*cos(4*d*x + 4*c)^3 + 80*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 - 56*a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^3 - 38*a*cos(4*d*x + 4*c)^2 + (a*cos(4*d*x + 4*c) - 36*a)*sin(4*d*x + 4*c)^2 + 93*a*cos(4*d*x + 4*c) + 36*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 56*a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (a*cos(4*d*x + 4*c) - 56*a)*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^3 - 54*a*cos(4*d*x + 4*c)^2 + (a*cos(4*d*x + 4*c) - 56*a)*sin(4*d*x + 4*c)^2 - 111*a*cos(4*d*x + 4*c) + 20*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 36*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 56*a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 - a*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 2*(2*a*cos(4*d*x + 4*c)^3 - 104*a*cos(4*d*x + 4*c)^2 + 2*(a*cos(4*d*x + 4*c) - 51*a)*sin(4*d*x + 4*c)^2 - a*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 112*a*cos(4*d*x + 4*c) + (72*a*cos(4*d*x + 4*c)^2 + 72*a*sin(4*d*x + 4*c)^2 - 73*a*cos(4*d*x + 4*c) + a)*cos(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))) + (36*a*cos(4*d*x + 4*c)^2 + 36*a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(160*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2*sin(4*d*x + 4*c) + 73*a*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 8*(36*a*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (a*cos(4*d*x + 4*c) - 51*a)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 2*(a*cos(4*d*x + 4*c) - 56*a)*sin(4*d*x + 4*c) - (a*cos(4*d*x + 4*c) + a)*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))))*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) + 75*((a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + a*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*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) - (a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + a*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*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) - (a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + a*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*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) + (a*cos(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - 2*a*cos(4*d*x + 4*c) + a)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + a*sin(4*d*x + 4*c)^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 + 2*a*cos(4*d*x + 4*c) + a)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a*cos(4*d*x + 4*c)^2 + a*sin(4*d*x + 4*c)^2 - a*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a*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))*C/(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
1220,1,4470,0,2.127436," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{80 \, {\left(4 \, {\left(a \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(a \cos\left(3 \, d x + 3 \, c\right) - a\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)} {\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}} \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(3 \, a \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) + 11 \, a \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(3 \, a \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) + 5 \, a \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) - 8 \, a\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} + 33 \, {\left(a \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) - a \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) - a \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) + a \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)} \sqrt{a}\right)} A + {\left(50 \, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(9 \, a \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 8 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 9 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - {\left(9 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 8 \, a \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 9 \, a \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 8 \, a\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(8 \, {\left(a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} \sin\left(5 \, d x + 5 \, c\right) + a \sin\left(5 \, d x + 5 \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(5 \, d x + 5 \, c\right) + a \sin\left(5 \, d x + 5 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 5 \, {\left(9 \, a \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 9 \, a \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 28 \, a \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 124 \, a \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 8 \, {\left({\left(a \cos\left(5 \, d x + 5 \, c\right) - a\right)} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + {\left(a \cos\left(5 \, d x + 5 \, c\right) - a\right)} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + a \cos\left(5 \, d x + 5 \, c\right) + 2 \, {\left(a \cos\left(5 \, d x + 5 \, c\right) - a\right)} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - a\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + 5 \, {\left(9 \, a \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 9 \, a \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 28 \, a \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 68 \, a \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 96 \, a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 1995 \, {\left(a \arctan\left(-{\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{7680 \, d}"," ",0,"1/7680*(80*(4*(a*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) - (a*cos(3*d*x + 3*c) - a)*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)))*(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)*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)*((3*a*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 11*a*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)) - (3*a*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 8*a)*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) + 33*(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) - 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) - 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)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a*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))*sqrt(a))*A + (50*(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(3/4)*((9*a*sin(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 8*a*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 9*a*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*cos(3/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - (9*a*cos(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 8*a*cos(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 9*a*cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 8*a)*sin(3/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)))*sqrt(a) + 6*(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(8*(a*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2*sin(5*d*x + 5*c) + a*sin(5*d*x + 5*c)*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*a*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(5*d*x + 5*c) + a*sin(5*d*x + 5*c))*cos(5/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 5*(9*a*sin(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 9*a*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 28*a*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 124*a*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 8*((a*cos(5*d*x + 5*c) - a)*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + (a*cos(5*d*x + 5*c) - a)*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + a*cos(5*d*x + 5*c) + 2*(a*cos(5*d*x + 5*c) - a)*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - a)*sin(5/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + 5*(9*a*cos(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 9*a*cos(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 28*a*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 68*a*cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 96*a)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)))*sqrt(a) + 1995*(a*arctan2(-(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))) + 1) - a*arctan2(-(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))) - 1) - a*arctan2((cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + 1) + a*arctan2((cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 1))*sqrt(a))*C)/d","B",0
1221,1,763,0,0.931097," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(15/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{{\left(\frac{45045 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{165165 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{414414 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{604890 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{522665 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{289185 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{88980 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{11864 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{143 \, {\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1575 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3654 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5130 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{4595 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2535 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{780 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{45045 \, d}"," ",0,"8/45045*((45045*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 165165*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 414414*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 604890*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 522665*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 289185*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 88980*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 11864*sqrt(2)*a^(5/2)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 143*(315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 1575*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3654*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5130*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 4595*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2535*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 780*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
1222,1,671,0,0.838845," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{{\left(\frac{693 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2310 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4620 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5478 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3575 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{1300 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{200 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{33 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{98 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{196 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{218 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{143 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{52 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{693 \, d}"," ",0,"8/693*((693*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 2310*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4620*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5478*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3575*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 1300*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 200*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 33*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 98*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 196*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 218*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 143*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 52*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
1223,1,579,0,0.998568," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{{\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{945 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1449 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1287 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{572 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{21 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{65 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{113 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{99 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{44 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{315 \, d}"," ",0,"8/315*((315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 945*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1449*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1287*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 572*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 21*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 65*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 113*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 99*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 44*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
1224,1,2343,0,1.232310," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\frac{7 \, {\left(6 \, {\left(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) + 1\right)\right) + 25 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{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{3}{4}} \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}} {\left({\left(15 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 50 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 58 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 20 \, {\left(3 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 11 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(3 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 11 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{7}{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}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left(15 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 50 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 58 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 23 \, a^{2} + 20 \, {\left(3 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 11 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(3 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 11 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{7}{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{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 25 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{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} + 15 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 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)^{4} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 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)^{4} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 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)^{4} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{4} + \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{80 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{56 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{210 \, d}"," ",0,"1/210*(7*(6*(a^2*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 25*(a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(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)^(3/4)*sqrt(a) + 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)*((15*a^2*sin(6*d*x + 6*c) + 50*a^2*sin(4*d*x + 4*c) + 58*a^2*sin(2*d*x + 2*c) - 20*(3*a^2*sin(6*d*x + 6*c) + 10*a^2*sin(4*d*x + 4*c) + 11*a^2*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(3*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 11*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (15*a^2*cos(6*d*x + 6*c) + 50*a^2*cos(4*d*x + 4*c) + 58*a^2*cos(2*d*x + 2*c) + 23*a^2 + 20*(3*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 11*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(3*a^2*sin(6*d*x + 6*c) + 10*a^2*sin(4*d*x + 4*c) + 11*a^2*sin(2*d*x + 2*c))*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 25*(a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 15*((a^2*cos(2*d*x + 2*c)^4 + a^2*sin(2*d*x + 2*c)^4 + 4*a^2*cos(2*d*x + 2*c)^3 + 6*a^2*cos(2*d*x + 2*c)^2 + 4*a^2*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(2*d*x + 2*c)^2 + 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)^4 + a^2*sin(2*d*x + 2*c)^4 + 4*a^2*cos(2*d*x + 2*c)^3 + 6*a^2*cos(2*d*x + 2*c)^2 + 4*a^2*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(2*d*x + 2*c)^2 + 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)^4 + a^2*sin(2*d*x + 2*c)^4 + 4*a^2*cos(2*d*x + 2*c)^3 + 6*a^2*cos(2*d*x + 2*c)^2 + 4*a^2*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(2*d*x + 2*c)^2 + 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)^4 + a^2*sin(2*d*x + 2*c)^4 + 4*a^2*cos(2*d*x + 2*c)^3 + 6*a^2*cos(2*d*x + 2*c)^2 + 4*a^2*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(2*d*x + 2*c)^2 + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*C/(cos(2*d*x + 2*c)^4 + sin(2*d*x + 2*c)^4 + 4*cos(2*d*x + 2*c)^3 + 2*(cos(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + 80*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 56*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
1225,1,1673,0,1.422531," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{5 \, {\left(2 \, {\left(5 \, 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) + 1\right)\right) + 3 \, {\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) - 3 \, {\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{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} \sqrt{a} + 15 \, {\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)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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} + 2 \, {\left({\left(12 \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 24 \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + 35 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) + 12 \, a^{2} \sin\left(d x + c\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) + 1\right)\right) - {\left(12 \, a^{2} \cos\left(5 \, d x + 5 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 24 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + 35 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 12 \, a^{2} \cos\left(d x + c\right) + 20 \, a^{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 27 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}}} + \frac{32 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{28 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} A}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}}{60 \, d}"," ",0,"1/60*(5*(2*(5*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 3*(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)) - 3*((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(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a) + 15*((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))*(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) + 2*((12*a^2*sin(5*d*x + 5*c) + 15*a^2*sin(4*d*x + 4*c) + 24*a^2*sin(3*d*x + 3*c) + 35*a^2*sin(2*d*x + 2*c) + 12*a^2*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (12*a^2*cos(5*d*x + 5*c) + 15*a^2*cos(4*d*x + 4*c) + 24*a^2*cos(3*d*x + 3*c) + 35*a^2*cos(2*d*x + 2*c) + 12*a^2*cos(d*x + c) + 20*a^2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 27*(a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(5/4) + 32*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 28*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*A/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)))/d","B",0
1226,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1227,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1228,1,8555,0,2.408465," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{48 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\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(a^{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) - a^{2} \cos\left(2 \, d x + 2 \, c\right) + 10 \, a^{2} + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 10 \, 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)\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} + 19 \, {\left(a^{2} \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^{2} \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^{2} \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^{2} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A - \frac{{\left(2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 9 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 36 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 36 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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 \, a^{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) + a^{2} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 36 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - a^{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(40 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 40 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 160 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 160 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 2 \, {\left(80 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 80 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 71 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 9 \, a^{2}\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(320 \, a^{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) + 71 \, a^{2} \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}{4} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) - 36 \, {\left(4 \, a^{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} + a^{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 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} + 40 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} + 22 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 71 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 40 \, a^{2}\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 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} + 58 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 89 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 40 \, a^{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)^{2} - {\left(40 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 40 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 160 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 160 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 2 \, {\left(80 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 80 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 71 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 9 \, a^{2}\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(320 \, a^{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) + 71 \, a^{2} \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)} \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 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} + 31 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 40 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2}\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 \, a^{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) + a^{2} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)} \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 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\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 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 40 \, a^{2}\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(5 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} \sin\left(4 \, d x + 4 \, c\right) + 5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 5 \, a^{2} \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) + 192 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{3} + 4 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 5 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 168 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 4 \, {\left(5 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} - 192 \, a^{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) + {\left(5 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 43 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 168 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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} + 2 \, {\left(10 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{3} + 5 \, a^{2} \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) + 10 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - a^{2} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(336 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 336 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 341 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2}\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 \, {\left(24 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 14 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 341 \, a^{2} \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) + 96 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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 \, {\left(12 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 7 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 168 \, a^{2} \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) - 12 \, a^{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) - 5 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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)\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) + {\left(168 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 168 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 5 \, a^{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(5 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} - 120 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 192 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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 \, a^{2} \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 \, {\left(5 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} - 82 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 197 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(5 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 72 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 120 \, a^{2} + 72 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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)\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 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) - 24 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(5 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} - 110 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 235 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) - 24 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 120 \, a^{2} + 48 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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) + 72 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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)\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} + 2 \, {\left(10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{3} - 226 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} - 5 \, a^{2} \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) + 240 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(5 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 108 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + {\left(144 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 144 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 149 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 5 \, a^{2}\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)\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(72 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 72 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 5 \, a^{2} \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(384 \, a^{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)^{2} \sin\left(4 \, d x + 4 \, c\right) + 149 \, a^{2} \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) + 8 \, {\left(72 \, a^{2} \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(5 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) - 108 \, a^{2}\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) + 10 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) - 24 \, a^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) - 5 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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)\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} - 489 \, {\left({\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - a^{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) - 4 \, {\left(4 \, a^{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) + a^{2} \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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - a^{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) - 4 \, {\left(4 \, a^{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) + a^{2} \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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - a^{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) - 4 \, {\left(4 \, a^{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) + a^{2} \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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2}\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(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{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)^{2} + 4 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} - a^{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) - 4 \, {\left(4 \, a^{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) + a^{2} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)}}{768 \, d}"," ",0,"1/768*(48*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a^2*sin(2*d*x + 2*c) - (a^2*cos(2*d*x + 2*c) - 10*a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a^2*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a^2*cos(2*d*x + 2*c) + 10*a^2 + (a^2*cos(2*d*x + 2*c) - 10*a^2)*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)))*sqrt(a) + 19*(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*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*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*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A - (2*(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)*((9*a^2*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 9*a^2*sin(4*d*x + 4*c)^3 + 36*(a^2*sin(4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 36*(a^2*sin(4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*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*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d*x + 4*c) - 2*(a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 36*(a^2*sin(4*d*x + 4*c)^3 + (a^2*cos(4*d*x + 4*c)^2 - a^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))) - (40*a^2*cos(4*d*x + 4*c)^2 + 40*a^2*sin(4*d*x + 4*c)^2 + 9*a^2*cos(4*d*x + 4*c) + 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*(80*a^2*cos(4*d*x + 4*c)^2 + 80*a^2*sin(4*d*x + 4*c)^2 - 71*a^2*cos(4*d*x + 4*c) - 9*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(320*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 71*a^2*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 36*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c)^2 + a^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*a^2*cos(4*d*x + 4*c)^3 + 40*a^2*cos(4*d*x + 4*c)^2 + 4*(9*a^2*cos(4*d*x + 4*c)^3 + 22*a^2*cos(4*d*x + 4*c)^2 - 71*a^2*cos(4*d*x + 4*c) + (9*a^2*cos(4*d*x + 4*c) + 40*a^2)*sin(4*d*x + 4*c)^2 + 40*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + (9*a^2*cos(4*d*x + 4*c) + 40*a^2)*sin(4*d*x + 4*c)^2 + 4*(9*a^2*cos(4*d*x + 4*c)^3 + 58*a^2*cos(4*d*x + 4*c)^2 + 89*a^2*cos(4*d*x + 4*c) + (9*a^2*cos(4*d*x + 4*c) + 40*a^2)*sin(4*d*x + 4*c)^2 + 40*a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 - (40*a^2*cos(4*d*x + 4*c)^2 + 40*a^2*sin(4*d*x + 4*c)^2 + 9*a^2*cos(4*d*x + 4*c) + 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 160*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*(80*a^2*cos(4*d*x + 4*c)^2 + 80*a^2*sin(4*d*x + 4*c)^2 - 71*a^2*cos(4*d*x + 4*c) - 9*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(320*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 71*a^2*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*cos(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(9*a^2*cos(4*d*x + 4*c)^3 + 31*a^2*cos(4*d*x + 4*c)^2 - 40*a^2*cos(4*d*x + 4*c) + (9*a^2*cos(4*d*x + 4*c) + 40*a^2)*sin(4*d*x + 4*c)^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 9*(2*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*sin(4*d*x + 4*c) - 2*(a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*sin(3/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*(9*a^2*cos(4*d*x + 4*c) + 40*a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (9*a^2*cos(4*d*x + 4*c) + 40*a^2)*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)*((5*a^2*cos(4*d*x + 4*c)^2*sin(4*d*x + 4*c) + 5*a^2*sin(4*d*x + 4*c)^3 + 5*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 192*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 + 4*(5*a^2*sin(4*d*x + 4*c)^3 + 5*(a^2*cos(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(4*d*x + 4*c) + 168*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*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 + 4*(5*a^2*sin(4*d*x + 4*c)^3 - 192*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (5*a^2*cos(4*d*x + 4*c)^2 + 10*a^2*cos(4*d*x + 4*c) - 43*a^2)*sin(4*d*x + 4*c) + 168*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*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 + 2*(10*a^2*sin(4*d*x + 4*c)^3 + 5*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 10*(a^2*cos(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*sin(4*d*x + 4*c) + (336*a^2*cos(4*d*x + 4*c)^2 + 336*a^2*sin(4*d*x + 4*c)^2 - 341*a^2*cos(4*d*x + 4*c) + 5*a^2)*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*(24*a^2*cos(4*d*x + 4*c)^2 + 14*a^2*sin(4*d*x + 4*c)^2 - 341*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 96*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 8*(12*a^2*cos(4*d*x + 4*c)^2 + 7*a^2*sin(4*d*x + 4*c)^2 - 168*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 12*a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 5*(a^2*cos(4*d*x + 4*c) + a^2)*cos(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))) + (168*a^2*cos(4*d*x + 4*c)^2 + 168*a^2*sin(4*d*x + 4*c)^2 - 5*a^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)) - (5*a^2*cos(4*d*x + 4*c)^3 - 120*a^2*cos(4*d*x + 4*c)^2 + 192*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^3 - 5*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 4*(5*a^2*cos(4*d*x + 4*c)^3 - 82*a^2*cos(4*d*x + 4*c)^2 + 197*a^2*cos(4*d*x + 4*c) + (5*a^2*cos(4*d*x + 4*c) - 72*a^2)*sin(4*d*x + 4*c)^2 - 120*a^2 + 72*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(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*(a^2*cos(4*d*x + 4*c) - 24*a^2)*sin(4*d*x + 4*c)^2 + 4*(5*a^2*cos(4*d*x + 4*c)^3 - 110*a^2*cos(4*d*x + 4*c)^2 - 235*a^2*cos(4*d*x + 4*c) + 5*(a^2*cos(4*d*x + 4*c) - 24*a^2)*sin(4*d*x + 4*c)^2 - 120*a^2 + 48*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 72*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(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 + 2*(10*a^2*cos(4*d*x + 4*c)^3 - 226*a^2*cos(4*d*x + 4*c)^2 - 5*a^2*sin(4*d*x + 4*c)*sin(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 240*a^2*cos(4*d*x + 4*c) + 2*(5*a^2*cos(4*d*x + 4*c) - 108*a^2)*sin(4*d*x + 4*c)^2 + (144*a^2*cos(4*d*x + 4*c)^2 + 144*a^2*sin(4*d*x + 4*c)^2 - 149*a^2*cos(4*d*x + 4*c) + 5*a^2)*cos(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))) + (72*a^2*cos(4*d*x + 4*c)^2 + 72*a^2*sin(4*d*x + 4*c)^2 - 5*a^2*cos(4*d*x + 4*c))*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 2*(384*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2*sin(4*d*x + 4*c) + 149*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + 8*(72*a^2*cos(1/4*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + (5*a^2*cos(4*d*x + 4*c) - 108*a^2)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 10*(a^2*cos(4*d*x + 4*c) - 24*a^2)*sin(4*d*x + 4*c) - 5*(a^2*cos(4*d*x + 4*c) + a^2)*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))))*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) - 489*((a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*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) - (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*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) - (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*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) + (a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - 2*a^2*cos(4*d*x + 4*c) + a^2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 + 2*a^2*cos(4*d*x + 4*c) + a^2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 4*(a^2*cos(4*d*x + 4*c)^2 + a^2*sin(4*d*x + 4*c)^2 - a^2*cos(4*d*x + 4*c))*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 4*(4*a^2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))*sin(4*d*x + 4*c) + a^2*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))*C/(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
1229,1,4556,0,1.989164," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{80 \, {\left(4 \, {\left(a^{2} \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(a^{2} \cos\left(3 \, d x + 3 \, c\right) - a^{2}\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)} {\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}} \sqrt{a} + 30 \, {\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(a^{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) + 5 \, a^{2} \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(a^{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) + 3 \, a^{2} \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 \, a^{2}\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} + 75 \, {\left(a^{2} \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) - a^{2} \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) - a^{2} \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) + a^{2} \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)} \sqrt{a}\right)} A + {\left(10 \, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(15 \, a^{2} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 88 \, a^{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 15 \, a^{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - {\left(15 \, a^{2} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 88 \, a^{2} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 15 \, a^{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 88 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(8 \, {\left(a^{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} \sin\left(5 \, d x + 5 \, c\right) + a^{2} \sin\left(5 \, d x + 5 \, c\right) \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, a^{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(5 \, d x + 5 \, c\right) + a^{2} \sin\left(5 \, d x + 5 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + 5 \, {\left(5 \, a^{2} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 5 \, a^{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 80 \, a^{2} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 288 \, a^{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 8 \, {\left(a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(a^{2} \cos\left(5 \, d x + 5 \, c\right) - a^{2}\right)} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + {\left(a^{2} \cos\left(5 \, d x + 5 \, c\right) - a^{2}\right)} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} - a^{2} + 2 \, {\left(a^{2} \cos\left(5 \, d x + 5 \, c\right) - a^{2}\right)} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 5 \, {\left(5 \, a^{2} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 5 \, a^{2} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 80 \, a^{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 128 \, a^{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - 208 \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 4245 \, {\left(a^{2} \arctan\left(-{\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - a^{2} \arctan\left(-{\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) - \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - a^{2} \arctan\left({\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) + 1\right) + a^{2} \arctan\left({\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right), \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(5 \, d x + 5 \, c\right), \cos\left(5 \, d x + 5 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{7680 \, d}"," ",0,"1/7680*(80*(4*(a^2*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) - (a^2*cos(3*d*x + 3*c) - a^2)*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)))*(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)*sqrt(a) + 30*(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)*((a^2*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a^2*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)) - (a^2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 3*a^2*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 4*a^2)*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) + 75*(a^2*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) - a^2*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) - a^2*arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a^2*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))*sqrt(a))*A + (10*(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(3/4)*((15*a^2*sin(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 88*a^2*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 15*a^2*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*cos(3/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - (15*a^2*cos(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 88*a^2*cos(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 15*a^2*cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 88*a^2)*sin(3/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)))*sqrt(a) + 6*(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(8*(a^2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2*sin(5*d*x + 5*c) + a^2*sin(5*d*x + 5*c)*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*a^2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(5*d*x + 5*c) + a^2*sin(5*d*x + 5*c))*cos(5/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + 5*(5*a^2*sin(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 5*a^2*sin(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 80*a^2*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 288*a^2*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 8*(a^2*cos(5*d*x + 5*c) + (a^2*cos(5*d*x + 5*c) - a^2)*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + (a^2*cos(5*d*x + 5*c) - a^2)*sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 - a^2 + 2*(a^2*cos(5*d*x + 5*c) - a^2)*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))))*sin(5/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 5*(5*a^2*cos(4/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 5*a^2*cos(3/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 80*a^2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 128*a^2*cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - 208*a^2)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)))*sqrt(a) + 4245*(a^2*arctan2(-(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))) + 1) - a^2*arctan2(-(cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))*sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) - cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*(cos(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + sin(1/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1))) - 1) - a^2*arctan2((cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) + 1) + a^2*arctan2((cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)), (cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c)))^2 + 2*cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))), cos(2/5*arctan2(sin(5*d*x + 5*c), cos(5*d*x + 5*c))) + 1)) - 1))*sqrt(a))*C)/d","B",0
1230,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1231,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)/(a+a*cos(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
1232,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(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
1233,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(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
1234,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(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
1235,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(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
1236,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(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
1237,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(1/2)/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
1238,-2,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*cos(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
1239,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1240,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1241,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1242,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1243,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1244,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
1245,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
1246,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1247,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1248,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1249,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1250,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
1251,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
1252,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
1253,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(9/2), x)","F",0
1254,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(7/2), x)","F",0
1255,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(5/2), x)","F",0
1256,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sec(d*x + c)^(3/2), x)","F",0
1257,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
1258,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/sqrt(sec(d*x + c)), x)","F",0
1259,0,0,0,0.000000," ","integrate((B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right)}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c))/sec(d*x + c)^(3/2), x)","F",0
1260,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2), x)","F",0
1261,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2), x)","F",0
1262,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2), x)","F",0
1263,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c)), x)","F",0
1264,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sqrt(sec(d*x + c)), x)","F",0
1265,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/sec(d*x + c)^(3/2), x)","F",0
1266,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1267,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1268,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1269,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1270,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1271,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1272,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1273,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(11/2), x)","F",0
1274,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
1275,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
1276,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
1277,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
1278,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
1279,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
1280,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
1281,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(13/2), x)","F",0
1282,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(11/2), x)","F",0
1283,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
1284,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
1285,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
1286,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
1287,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
1288,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
1289,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1290,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(a*cos(d*x + c) + a), x)","F",0
1291,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
1292,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
1293,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
1294,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1295,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1296,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1297,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
1300,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1301,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1302,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
1303,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1304,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1305,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1306,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
1307,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
1308,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
1309,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
1310,1,986,0,0.773143," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{A {\left(\frac{315 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{735 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1302 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1206 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{431 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{107 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{9 \, B {\left(\frac{35 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{105 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{154 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{142 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{67 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{9 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{21 \, C {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{55 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{82 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{66 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{31 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{315 \, d}"," ",0,"2/315*(A*(315*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 735*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1302*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1206*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 431*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 107*sqrt(2)*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 9*B*(35*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 105*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 154*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 142*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 67*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 9*sqrt(2)*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 21*C*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 55*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 82*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 66*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 31*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
1311,1,848,0,0.712997," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, A {\left(\frac{35 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{70 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{84 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{58 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{7 \, B {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{42 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{24 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{35 \, C {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{12 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{105 \, d}"," ",0,"2/105*(3*A*(35*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 70*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 84*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 58*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 7*B*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 42*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 24*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 7*sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 35*C*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 12*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + sqrt(2)*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
1312,1,709,0,0.662882," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{A {\left(\frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{5 \, B {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{15 \, C {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{15 \, d}"," ",0,"2/15*(A*(15*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 17*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 5*B*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 15*C*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 3*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - sqrt(2)*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
1313,1,1547,0,1.014070," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} \sqrt{a} \sin\left(\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(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) + 1\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} + {\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)} \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(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\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) - {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\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) + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\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)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{4 \, A {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{12 \, B {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{6 \, d}"," ",0,"1/6*(3*(2*(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)*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)*(cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) + 1)*sin(3/2*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)*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) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 4*A*(3*sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + 12*B*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sqrt(2)*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
1314,1,1695,0,1.060293," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, B \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)} + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C + \frac{8 \, A {\left(\frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}}}{4 \, d}"," ",0,"1/4*(2*B*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(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)) + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C + 8*A*(sqrt(2)*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)))/d","B",0
1315,1,1996,0,0.931890," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{16 \, A \sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right) + 4 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} B + {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} C}{16 \, d}"," ",0,"1/16*(16*A*sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c)) + 4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*B + (2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*C)/d","B",0
1316,1,3770,0,1.171900," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} A + 6 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}\right)} B + {\left(4 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(\cos\left(3 \, d x + 3 \, c\right) - 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 15 \, \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)}\right)} C}{96 \, d}"," ",0,"1/96*(24*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*A + 6*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))*B + (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)))*C)/d","B",0
1317,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1318,1,1065,0,0.686311," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{21 \, {\left(\frac{165 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{495 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1056 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1254 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{781 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{299 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{46 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{11 \, {\left(\frac{315 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1155 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2184 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2586 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{1759 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{611 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{94 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{33 \, {\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{455 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{868 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{962 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{653 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{247 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{3465 \, d}"," ",0,"4/3465*(21*(165*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 495*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1056*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1254*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 781*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 299*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 46*sqrt(2)*a^(3/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 11*(315*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 1155*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2184*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2586*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 1759*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 611*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 94*sqrt(2)*a^(3/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 33*(105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 455*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 868*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 962*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 653*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 247*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
1319,1,926,0,0.648860," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{{\left(\frac{315 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{840 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1344 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1242 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{517 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{94 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{3 \, {\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{350 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{518 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{444 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{209 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{63 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{32 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{26 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{11 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{315 \, d}"," ",0,"4/315*((315*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 840*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1344*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1242*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 517*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 94*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 3*(105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 350*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 518*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 444*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 209*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 38*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 63*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 32*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 26*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 11*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
1320,1,788,0,0.646216," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{{\left(\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{245 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{273 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{171 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{38 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{21 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{17 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{9 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{35 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{11 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{9 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{105 \, d}"," ",0,"4/105*((105*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 245*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 273*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 171*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 38*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 21*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 15*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 17*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 9*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 35*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 11*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 9*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
1321,1,1915,0,0.813122," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{5 \, {\left(2 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} a^{\frac{3}{2}} \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) + 3 \, {\left({\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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} - 2 \, {\left({\left(6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\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) - 3 \, a \sin\left(4 \, d x + 4 \, c\right) - 7 \, a \sin\left(2 \, d x + 2 \, c\right) - 6 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(3 \, a \cos\left(4 \, d x + 4 \, c\right) + 7 \, a \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(a \cos\left(4 \, d x + 4 \, c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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) + 6 \, {\left(a \sin\left(4 \, d x + 4 \, c\right) + 2 \, a \sin\left(2 \, d x + 2 \, c\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) + 4 \, a\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 9 \, {\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, 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)} \sqrt{a}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}}} + \frac{24 \, {\left(\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{40 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{8 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{30 \, d}"," ",0,"1/30*(5*(2*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*a^(3/2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 3*((a*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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) - 2*((6*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 3*a*sin(4*d*x + 4*c) - 7*a*sin(2*d*x + 2*c) - 6*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*sin(5/2*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) + 1)) + (3*a*cos(4*d*x + 4*c) + 7*a*cos(2*d*x + 2*c) + 6*(a*cos(4*d*x + 4*c) + 2*a*cos(2*d*x + 2*c) + a)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6*(a*sin(4*d*x + 4*c) + 2*a*sin(2*d*x + 2*c))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*a)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 9*(a*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(5/4) + 24*(5*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + 40*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 8*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*sqrt(2)*a^(3/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
1322,1,2726,0,0.921206," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{\frac{6 \, {\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}} a^{\frac{3}{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(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) \sin\left(2 \, d x + 2 \, c\right) - a \sin\left(2 \, d x + 2 \, c\right) - 2 \, {\left(a \cos\left(2 \, d x + 2 \, c\right) + a\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(2 \, a \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) + a \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a \cos\left(2 \, d x + 2 \, c\right) + 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) + a\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} + {\left({\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} B}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{3 \, {\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}} a^{\frac{3}{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(3 \, a \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + a \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + 2 \, a \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + a \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) - 3 \, {\left(a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(d x + c\right) - a\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a \cos\left(d x + c\right) - a\right)} \cos\left(2 \, d x + 2 \, c\right) + 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({\left(a \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\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 \cos\left(2 \, d x + 2 \, c\right)^{2} + a \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \cos\left(2 \, d x + 2 \, c\right) + a\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{16 \, {\left(\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)} A}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}}{12 \, d}"," ",0,"1/12*(6*(6*(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^(3/2)*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)*((2*a*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - a*sin(2*d*x + 2*c) - 2*(a*cos(2*d*x + 2*c) + a)*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)) + (2*a*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a*cos(2*d*x + 2*c) + 2*(a*cos(2*d*x + 2*c) + a)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + a)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + ((a*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*B/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 3*(6*(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^(3/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 2*(3*a*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(2*d*x + 2*c) + (a*cos(2*d*x + 2*c)^2*sin(d*x + c) + a*sin(2*d*x + 2*c)^2*sin(d*x + c) + 2*a*cos(2*d*x + 2*c)*sin(d*x + c) + a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 3*(a*cos(2*d*x + 2*c) + a)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - ((a*cos(d*x + c) - a)*cos(2*d*x + 2*c)^2 + (a*cos(d*x + c) - a)*sin(2*d*x + 2*c)^2 + 2*(a*cos(d*x + c) - a)*cos(2*d*x + 2*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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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*cos(2*d*x + 2*c)^2 + a*sin(2*d*x + 2*c)^2 + 2*a*cos(2*d*x + 2*c) + 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))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + 16*(3*sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*sqrt(2)*a^(3/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)*A/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)))/d","B",0
1323,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1324,1,3824,0,1.277408," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} A + 6 \, {\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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) \sin\left(2 \, d x + 2 \, c\right) + a \sin\left(2 \, d x + 2 \, c\right) - {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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)\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(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) - a \cos\left(2 \, d x + 2 \, c\right) + {\left(a \cos\left(2 \, d x + 2 \, c\right) - 6 \, 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) + 6 \, 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} + 7 \, {\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)} \sqrt{a}\right)} B + {\left(4 \, {\left(a \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(a \cos\left(3 \, d x + 3 \, c\right) - a\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)} {\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}} \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(3 \, a \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) + 11 \, a \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(3 \, a \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) + 5 \, a \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) - 8 \, a\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} + 33 \, {\left(a \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) - a \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) - a \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) + a \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)} \sqrt{a}\right)} C}{96 \, d}"," ",0,"1/96*(24*(2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*A + 6*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) + a*sin(2*d*x + 2*c) - (a*cos(2*d*x + 2*c) - 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (a*sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a*cos(2*d*x + 2*c) + (a*cos(2*d*x + 2*c) - 6*a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 6*a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 7*(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))*sqrt(a))*B + (4*(a*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) - (a*cos(3*d*x + 3*c) - a)*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)))*(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)*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)*((3*a*sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 11*a*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)) - (3*a*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*a*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 8*a)*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) + 33*(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) - 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) - 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)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + a*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))*sqrt(a))*C)/d","B",0
1325,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1326,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1327,1,1142,0,0.628264," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(15/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{{\left(\frac{45045 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{165165 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{414414 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{604890 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{522665 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{289185 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{88980 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{11864 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{65 \, {\left(\frac{693 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3003 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6930 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{10098 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9053 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{4875 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{1500 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{200 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}} + \frac{143 \, {\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1575 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3654 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5130 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{4595 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2535 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{780 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(\frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{\sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}\right)}}{45045 \, d}"," ",0,"8/45045*((45045*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 165165*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 414414*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 604890*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 522665*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 289185*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 88980*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 11864*sqrt(2)*a^(5/2)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 65*(693*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 3003*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6930*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 10098*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9053*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 4875*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 1500*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 200*sqrt(2)*a^(5/2)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)) + 143*(315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 1575*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3654*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5130*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 4595*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2535*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 780*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)))/d","B",0
1328,1,1005,0,0.612215," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{5 \, {\left(\frac{693 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2310 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4620 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5478 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3575 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{1300 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{200 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{11 \, {\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1260 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2394 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2736 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{1859 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{676 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}} + \frac{165 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{98 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{196 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{218 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{143 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{52 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(\frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{\sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}\right)}}{3465 \, d}"," ",0,"8/3465*(5*(693*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 2310*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4620*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5478*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3575*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 1300*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 200*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 11*(315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 1260*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2394*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2736*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 1859*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 676*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 104*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)) + 165*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 98*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 196*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 218*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 143*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 52*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)))/d","B",0
1329,1,866,0,0.614305," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{{\left(\frac{315 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{945 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1449 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1287 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{572 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{104 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{15 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{119 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{99 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{44 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}} + \frac{21 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{65 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{113 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{99 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{44 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} C {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \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}} + 1\right)}}\right)}}{315 \, d}"," ",0,"8/315*((315*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 945*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1449*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1287*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 572*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 104*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 15*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 119*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 99*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 44*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)) + 21*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 65*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 113*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 99*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 44*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*C*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)))/d","B",0
1330,1,2584,0,0.935564," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\frac{7 \, {\left(6 \, {\left(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) + 1\right)\right) + 25 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{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{3}{4}} \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}} {\left({\left(15 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 50 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 58 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 20 \, {\left(3 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 11 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(3 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 11 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{7}{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}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left(15 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 50 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 58 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 23 \, a^{2} + 20 \, {\left(3 \, a^{2} \cos\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 11 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 20 \, {\left(3 \, a^{2} \sin\left(6 \, d x + 6 \, c\right) + 10 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 11 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{7}{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{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 25 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{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} + 15 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 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)^{4} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 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)^{4} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 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)^{4} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + 6 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}\right)} C}{\cos\left(2 \, d x + 2 \, c\right)^{4} + \sin\left(2 \, d x + 2 \, c\right)^{4} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{80 \, {\left(\frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{56 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} A {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{2 \, \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}} + 1\right)}} + \frac{112 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{50 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} B {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(\frac{2 \, \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}} + 1\right)}}}{210 \, d}"," ",0,"1/210*(7*(6*(a^2*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 25*(a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(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)^(3/4)*sqrt(a) + 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)*((15*a^2*sin(6*d*x + 6*c) + 50*a^2*sin(4*d*x + 4*c) + 58*a^2*sin(2*d*x + 2*c) - 20*(3*a^2*sin(6*d*x + 6*c) + 10*a^2*sin(4*d*x + 4*c) + 11*a^2*sin(2*d*x + 2*c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(3*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 11*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (15*a^2*cos(6*d*x + 6*c) + 50*a^2*cos(4*d*x + 4*c) + 58*a^2*cos(2*d*x + 2*c) + 23*a^2 + 20*(3*a^2*cos(6*d*x + 6*c) + 10*a^2*cos(4*d*x + 4*c) + 11*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 20*(3*a^2*sin(6*d*x + 6*c) + 10*a^2*sin(4*d*x + 4*c) + 11*a^2*sin(2*d*x + 2*c))*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 25*(a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 15*((a^2*cos(2*d*x + 2*c)^4 + a^2*sin(2*d*x + 2*c)^4 + 4*a^2*cos(2*d*x + 2*c)^3 + 6*a^2*cos(2*d*x + 2*c)^2 + 4*a^2*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(2*d*x + 2*c)^2 + 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)^4 + a^2*sin(2*d*x + 2*c)^4 + 4*a^2*cos(2*d*x + 2*c)^3 + 6*a^2*cos(2*d*x + 2*c)^2 + 4*a^2*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(2*d*x + 2*c)^2 + 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)^4 + a^2*sin(2*d*x + 2*c)^4 + 4*a^2*cos(2*d*x + 2*c)^3 + 6*a^2*cos(2*d*x + 2*c)^2 + 4*a^2*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(2*d*x + 2*c)^2 + 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)^4 + a^2*sin(2*d*x + 2*c)^4 + 4*a^2*cos(2*d*x + 2*c)^3 + 6*a^2*cos(2*d*x + 2*c)^2 + 4*a^2*cos(2*d*x + 2*c) + 2*(a^2*cos(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(2*d*x + 2*c)^2 + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))*C/(cos(2*d*x + 2*c)^4 + sin(2*d*x + 2*c)^4 + 4*cos(2*d*x + 2*c)^3 + 2*(cos(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) + 80*(21*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 56*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*A*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)) + 112*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 50*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*sqrt(2)*a^(5/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*B*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)))/d","B",0
1331,1,3231,0,1.050045," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\frac{10 \, {\left(10 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} a^{\frac{5}{2}} \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) + 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)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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} + 2 \, {\left({\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, a^{2} \sin\left(2 \, d x + 2 \, c\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) + 4 \, {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\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)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 7 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, 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) + 4 \, {\left(3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 7 \, a^{2} \sin\left(2 \, d x + 2 \, c\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)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 15 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} B}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}}} + \frac{5 \, {\left(2 \, {\left(5 \, 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) + 1\right)\right) + 3 \, {\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) - 3 \, {\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{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} \sqrt{a} + 15 \, {\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)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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} + 2 \, {\left({\left(12 \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + 15 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 24 \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + 35 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) + 12 \, a^{2} \sin\left(d x + c\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) + 1\right)\right) - {\left(12 \, a^{2} \cos\left(5 \, d x + 5 \, c\right) + 15 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 24 \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + 35 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 12 \, a^{2} \cos\left(d x + c\right) + 20 \, a^{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 27 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}\right)} C}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}}} + \frac{32 \, {\left(\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{28 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)} A}{{\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}}{60 \, d}"," ",0,"1/60*(10*(10*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*a^(5/2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 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))*(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) + 2*((3*a^2*sin(4*d*x + 4*c) + 7*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*sin(4*d*x + 4*c) + 7*a^2*sin(2*d*x + 2*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(3*a^2*cos(4*d*x + 4*c) + 7*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(5/2*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) + 1)) - (3*a^2*cos(4*d*x + 4*c) + 7*a^2*cos(2*d*x + 2*c) + 4*a^2 + 4*(3*a^2*cos(4*d*x + 4*c) + 7*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(3*a^2*sin(4*d*x + 4*c) + 7*a^2*sin(2*d*x + 2*c))*sin(5/2*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) + 1)) + 15*(a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*B/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(5/4) + 5*(2*(5*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 3*(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)) - 3*((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(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(a) + 15*((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))*(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) + 2*((12*a^2*sin(5*d*x + 5*c) + 15*a^2*sin(4*d*x + 4*c) + 24*a^2*sin(3*d*x + 3*c) + 35*a^2*sin(2*d*x + 2*c) + 12*a^2*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (12*a^2*cos(5*d*x + 5*c) + 15*a^2*cos(4*d*x + 4*c) + 24*a^2*cos(3*d*x + 3*c) + 35*a^2*cos(2*d*x + 2*c) + 12*a^2*cos(d*x + c) + 20*a^2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 27*(a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))*C/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(5/4) + 32*(15*sqrt(2)*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sqrt(2)*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 28*sqrt(2)*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8*sqrt(2)*a^(5/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)*A/((sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)))/d","B",0
1332,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1333,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1334,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1335,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1336,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1337,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)/(a+a*cos(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
1338,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(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
1339,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(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
1340,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(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
1341,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(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
1342,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(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
1343,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2)/(a+a*cos(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
1344,-2,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+a*cos(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
1345,-2,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(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
1346,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1347,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1348,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1349,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1350,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
1351,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
1352,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
1353,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1354,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1355,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1356,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
1357,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
1358,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
1359,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
1360,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1361,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1362,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1363,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1364,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1365,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1366,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1367,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(11/2), x)","F",0
1368,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
1369,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
1370,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
1371,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
1372,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
1373,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
1374,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
1375,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(11/2), x)","F",0
1376,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
1377,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
1378,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
1379,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
1380,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
1381,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
1382,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1383,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(13/2), x)","F",0
1384,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(11/2), x)","F",0
1385,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(9/2), x)","F",0
1386,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(7/2), x)","F",0
1387,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(5/2), x)","F",0
1388,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(3/2), x)","F",0
1389,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
1390,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
1391,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(b*cos(d*x + c) + a), x)","F",0
1392,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
1393,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
1394,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
1395,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1396,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1397,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1398,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1399,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1400,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
1401,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1402,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1403,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
1404,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1405,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1406,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1407,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
1408,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
1409,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1410,-1,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1411,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
1412,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1413,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1414,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1415,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1416,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1417,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1418,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1419,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(11/2), x)","F",0
1420,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(9/2), x)","F",0
1421,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(7/2), x)","F",0
1422,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2), x)","F",0
1423,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
1424,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
1425,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
1426,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(13/2), x)","F",0
1427,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(11/2), x)","F",0
1428,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(9/2), x)","F",0
1429,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(7/2), x)","F",0
1430,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2), x)","F",0
1431,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
1432,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
1433,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*(b*cos(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
1434,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(9/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1435,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1436,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1437,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1438,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1439,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1440,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(7/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1441,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1442,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1443,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1444,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
1445,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
1446,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1447,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1448,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1449,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
1450,0,0,0,0.000000," ","integrate((A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + A)/((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
1451,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1452,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1453,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1454,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1455,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1456,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1457,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1458,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(11/2), x)","F",0
1459,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
1460,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
1461,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
1462,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
1463,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
1464,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
1465,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
1466,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(11/2), x)","F",0
1467,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
1468,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
1469,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
1470,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
1471,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
1472,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
1473,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
1474,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(13/2), x)","F",0
1475,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(11/2), x)","F",0
1476,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(9/2), x)","F",0
1477,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(7/2), x)","F",0
1478,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(5/2), x)","F",0
1479,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sec(d*x + c)^(3/2), x)","F",0
1480,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
1481,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
1482,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1483,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
1484,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
1485,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
1486,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1487,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1488,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
1489,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1490,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1491,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1492,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
1493,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
1494,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1495,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1496,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1497,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1498,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1499,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1500,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1501,-1,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1502,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
1503,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
1504,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
1505,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
1506,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
1507,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
1508,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
1509,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
1510,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(11/2), x)","F",0
1511,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(9/2), x)","F",0
1512,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(7/2), x)","F",0
1513,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2), x)","F",0
1514,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
1515,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
1516,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
1517,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(13/2), x)","F",0
1518,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(11/2), x)","F",0
1519,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(9/2), x)","F",0
1520,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(7/2), x)","F",0
1521,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2), x)","F",0
1522,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
1523,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
1524,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
1525,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(9/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1526,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1527,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1528,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
1529,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1530,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
1531,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
1532,0,0,0,0.000000," ","integrate((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B b \cos\left(d x + c\right)^{2} + A a + {\left(B a + A b\right)} \cos\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c)^2 + A*a + (B*a + A*b)*cos(d*x + c))*sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
1533,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(7/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1534,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
1535,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
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1540,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
1541,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \cos\left(d x + c\right)^{2} + B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*cos(d*x + c)^2 + B*cos(d*x + c) + A)*sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
