1,1,84,0,0.321190," ","integrate(cos(d*x+c)^5*(a+a*cos(d*x+c)),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)} a - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{960 \, d}"," ",0,"1/960*(64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a)/d","A",0
2,1,69,0,0.787880," ","integrate(cos(d*x+c)^4*(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a)/d","A",0
3,1,57,0,0.297171," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*a - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a)/d","A",0
4,1,46,0,0.297230," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a}{12 \, d}"," ",0,"-1/12*(4*(sin(d*x + c)^3 - 3*sin(d*x + c))*a - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a)/d","A",0
5,1,34,0,0.294930," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a + 4 \, a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a + 4*a*sin(d*x + c))/d","A",0
6,1,15,0,0.377201," ","integrate(a+a*cos(d*x+c),x, algorithm=""maxima"")","a x + \frac{a \sin\left(d x + c\right)}{d}"," ",0,"a*x + a*sin(d*x + c)/d","A",0
7,1,28,0,0.299295," ","integrate((a+a*cos(d*x+c))*sec(d*x+c),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} a + a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right)}{d}"," ",0,"((d*x + c)*a + a*log(sec(d*x + c) + tan(d*x + c)))/d","A",0
8,1,38,0,2.227763," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{a {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*a*tan(d*x + c))/d","A",0
9,1,58,0,0.502740," ","integrate((a+a*cos(d*x+c))*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)} - 4 \, a \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 4*a*tan(d*x + c))/d","A",0
10,1,70,0,0.443181," ","integrate((a+a*cos(d*x+c))*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 \, a {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*a - 3*a*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
11,1,95,0,0.973055," ","integrate((a+a*cos(d*x+c))*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 - 3 \, a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*a - 3*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
12,1,107,0,0.305541," ","integrate((a+a*cos(d*x+c))*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 - 15 \, a {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a - 15*a*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
13,1,121,0,0.301699," ","integrate(cos(d*x+c)^4*(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{128 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{2} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{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^{2}}{960 \, d}"," ",0,"1/960*(128*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^2 + 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2)/d","A",0
14,1,95,0,1.128185," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{2} - 80 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{240 \, d}"," ",0,"1/240*(16*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2 - 80*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2)/d","A",0
15,1,83,0,0.484840," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{96 \, d}"," ",0,"-1/96*(64*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2 - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2)/d","A",0
16,1,61,0,0.466294," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 6 \, a^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2 - 6*a^2*sin(d*x + c))/d","A",0
17,1,45,0,0.297077," ","integrate((a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{4 \, d} + \frac{2 \, a^{2} \sin\left(d x + c\right)}{d}"," ",0,"a^2*x + 1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2/d + 2*a^2*sin(d*x + c)/d","A",0
18,1,43,0,0.297667," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} a^{2} + a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + a^{2} \sin\left(d x + c\right)}{d}"," ",0,"(2*(d*x + c)*a^2 + a^2*log(sec(d*x + c) + tan(d*x + c)) + a^2*sin(d*x + c))/d","A",0
19,1,49,0,0.988545," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} a^{2} + a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + a^{2} \tan\left(d x + c\right)}{d}"," ",0,"((d*x + c)*a^2 + a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + a^2*tan(d*x + c))/d","A",0
20,1,88,0,0.451978," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^3,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 2 \, a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 8 \, a^{2} \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 2*a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 8*a^2*tan(d*x + c))/d","A",0
21,1,85,0,0.348285," ","integrate((a+a*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^{2} - 3 \, a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{2} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 - 3*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*a^2*tan(d*x + c))/d","A",0
22,1,145,0,0.308089," ","integrate((a+a*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^{2} - 3 \, a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 - 3*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
23,1,143,0,1.974712," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{192 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{3} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} + 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{960 \, d}"," ",0,"1/960*(192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^3 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^3 - 320*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3 + 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3)/d","A",0
24,1,117,0,0.634446," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} + 45 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{480 \, d}"," ",0,"1/480*(32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3 + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3)/d","A",0
25,1,94,0,0.837616," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} - {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 32 \, a^{3} \sin\left(d x + c\right)}{32 \, d}"," ",0,"-1/32*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3 - (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 - 32*a^3*sin(d*x + c))/d","A",0
26,1,70,0,0.356659," ","integrate((a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x - \frac{{\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3}}{3 \, d} + \frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{4 \, d} + \frac{3 \, a^{3} \sin\left(d x + c\right)}{d}"," ",0,"a^3*x - 1/3*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3/d + 3/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3/d + 3*a^3*sin(d*x + c)/d","A",0
27,1,67,0,1.050349," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 12 \, {\left(d x + c\right)} a^{3} + 4 \, a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, a^{3} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 + 12*(d*x + c)*a^3 + 4*a^3*log(sec(d*x + c) + tan(d*x + c)) + 12*a^3*sin(d*x + c))/d","A",0
28,1,64,0,1.004123," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a^{3} + 3 \, a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, a^{3} \sin\left(d x + c\right) + 2 \, a^{3} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(6*(d*x + c)*a^3 + 3*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*a^3*sin(d*x + c) + 2*a^3*tan(d*x + c))/d","A",0
29,1,99,0,1.110803," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} a^{3} - 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^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*a^3 - 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^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*a^3*tan(d*x + c))/d","A",0
30,1,111,0,0.307971," ","integrate((a+a*cos(d*x+c))^3*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} - 9 \, a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 36 \, a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 - 9*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*a^3*tan(d*x + c))/d","A",0
31,1,156,0,1.099580," ","integrate((a+a*cos(d*x+c))^3*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^{3} - a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 16 \, a^{3} \tan\left(d x + c\right)}{16 \, d}"," ",0,"1/16*(16*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 - a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 16*a^3*tan(d*x + c))/d","A",0
32,1,179,0,1.025234," ","integrate((a+a*cos(d*x+c))^3*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^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} - 45 \, a^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 - 45*a^3*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
33,1,165,0,1.754085," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{256 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{4} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} + 180 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{960 \, d}"," ",0,"1/960*(256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^4 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^4 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 + 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4 + 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4)/d","A",0
34,1,128,0,0.301624," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{4} - 240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 120 \, a^{4} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(8*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^4 - 240*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4 + 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 + 120*a^4*sin(d*x + c))/d","A",0
35,1,106,0,0.738908," ","integrate((a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","a^{4} x - \frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4}}{3 \, d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{32 \, d} + \frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{2 \, d} + \frac{4 \, a^{4} \sin\left(d x + c\right)}{d}"," ",0,"a^4*x - 4/3*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4/d + 3/2*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4/d + 4*a^4*sin(d*x + c)/d","A",0
36,1,89,0,1.522661," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 12 \, {\left(d x + c\right)} a^{4} - 3 \, a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - 18 \, a^{4} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*((sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 - 12*(d*x + c)*a^4 - 3*a^4*log(sec(d*x + c) + tan(d*x + c)) - 18*a^4*sin(d*x + c))/d","A",0
37,1,85,0,0.673250," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 24 \, {\left(d x + c\right)} a^{4} + 8 \, a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 16 \, a^{4} \sin\left(d x + c\right) + 4 \, a^{4} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 + 24*(d*x + c)*a^4 + 8*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 16*a^4*sin(d*x + c) + 4*a^4*tan(d*x + c))/d","A",0
38,1,110,0,0.660900," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{16 \, {\left(d x + c\right)} a^{4} - a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, a^{4} \sin\left(d x + c\right) + 16 \, a^{4} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(16*(d*x + c)*a^4 - a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 12*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*a^4*sin(d*x + c) + 16*a^4*tan(d*x + c))/d","A",0
39,1,120,0,1.855385," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4} + 3 \, {\left(d x + c\right)} a^{4} - 3 \, a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, a^{4} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 18 \, a^{4} \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 + 3*(d*x + c)*a^4 - 3*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*a^4*tan(d*x + c))/d","A",0
40,1,182,0,1.012903," ","integrate((a+a*cos(d*x+c))^4*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^{4} - 3 \, a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 24 \, 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^{4} \tan\left(d x + c\right)}{48 \, d}"," ",0,"1/48*(64*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 - 3*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 72*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 24*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 192*a^4*tan(d*x + c))/d","B",0
41,1,190,0,1.957371," ","integrate((a+a*cos(d*x+c))^4*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^{4} + 120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4} - 15 \, a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 60 \, a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 60 \, a^{4} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(4*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^4 + 120*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 - 15*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 60*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 60*a^4*tan(d*x + c))/d","A",0
42,1,270,0,1.369548," ","integrate((a+a*cos(d*x+c))^4*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^{4} + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4} - 5 \, a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"1/480*(128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^4 + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 - 5*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 180*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","B",0
43,1,217,0,1.239649," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{109 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{115 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{75 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{12 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{12 \, d}"," ",0,"-1/12*((21*sin(d*x + c)/(cos(d*x + c) + 1) + 109*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 115*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 75*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 12*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","A",0
44,1,176,0,1.554813," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{3 \, d}"," ",0,"1/3*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 3*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","A",0
45,1,133,0,1.333994," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-((sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","A",0
46,1,92,0,2.251124," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 2*sin(d*x + c)/((a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
47,1,49,0,1.222797," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","A",0
48,1,23,0,1.117654," ","integrate(1/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{\sin\left(d x + c\right)}{a d {\left(\cos\left(d x + c\right) + 1\right)}}"," ",0,"sin(d*x + c)/(a*d*(cos(d*x + c) + 1))","A",0
49,1,75,0,1.118960," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","A",0
50,1,119,0,0.490389," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{{\left(a - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{d}"," ",0,"-(log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a - 2*sin(d*x + c)/((a - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
51,1,162,0,0.313202," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{2 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 2*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
52,1,205,0,0.816124," ","integrate(sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a - \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a} + \frac{9 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a} + \frac{6 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{6 \, d}"," ",0,"1/6*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a - 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 9*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a + 9*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a + 6*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
53,1,207,0,1.356723," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{60 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{6 \, d}"," ",0,"1/6*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 60*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","A",0
54,1,164,0,1.351427," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{42 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{6 \, d}"," ",0,"-1/6*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 42*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","A",0
55,1,118,0,1.502134," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}}{6 \, d}"," ",0,"1/6*((15*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 12*sin(d*x + c)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)))/d","A",0
56,1,72,0,1.001026," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{6 \, d}"," ",0,"-1/6*((9*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","A",0
57,1,47,0,0.310448," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{6 \, a^{2} d}"," ",0,"1/6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2*d)","A",0
58,1,46,0,1.100626," ","integrate(1/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{6 \, a^{2} d}"," ",0,"1/6*(3*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2*d)","A",0
59,1,98,0,0.993272," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{6 \, d}"," ",0,"-1/6*((9*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 6*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","A",0
60,1,145,0,0.645639," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}} + \frac{12 \, \sin\left(d x + c\right)}{{\left(a^{2} - \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}}}{6 \, d}"," ",0,"1/6*((15*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2 + 12*sin(d*x + c)/((a^2 - a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)))/d","A",0
61,1,190,0,0.947389," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{2} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{21 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{6 \, d}"," ",0,"-1/6*(6*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^2 - 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (21*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 21*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 21*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","A",0
62,1,234,0,0.950134," ","integrate(sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{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}}}{6 \, d}"," ",0,"1/6*(4*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2 - 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (27*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 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)/d","A",0
63,1,184,0,1.255841," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{780 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{60 \, d}"," ",0,"-1/60*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 780*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","A",0
64,1,137,0,1.228307," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{20 \, d}"," ",0,"1/20*(40*sin(d*x + c)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","A",0
65,1,92,0,0.688556," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{60 \, d}"," ",0,"-1/60*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","A",0
66,1,67,0,1.011253," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{60 \, a^{3} d}"," ",0,"1/60*(15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3*d)","A",0
67,1,47,0,0.481842," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{20 \, a^{3} d}"," ",0,"1/20*(5*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3*d)","A",0
68,1,67,0,0.333274," ","integrate(1/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{60 \, a^{3} d}"," ",0,"1/60*(15*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^3*d)","A",0
69,1,119,0,1.119137," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{60 \, d}"," ",0,"-1/60*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","A",0
70,1,165,0,1.477283," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{40 \, \sin\left(d x + c\right)}{{\left(a^{3} - \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{85 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{20 \, d}"," ",0,"1/20*(40*sin(d*x + c)/((a^3 - a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (85*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 60*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","A",0
71,1,211,0,0.959040," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{60 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} + \frac{390 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{60 \, d}"," ",0,"-1/60*(60*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^3 - 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (465*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 390*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 + 390*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","A",0
72,1,204,0,1.119914," ","integrate(cos(d*x+c)^6/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} + \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{5880 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}}{280 \, d}"," ",0,"-1/280*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) + 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 + 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) - 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 5880*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4)/d","A",0
73,1,158,0,0.811553," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} + \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{6720 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}}{840 \, d}"," ",0,"1/840*(1680*sin(d*x + c)/((a^4 + a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) - 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 6720*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4)/d","A",0
74,1,112,0,1.264133," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{336 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{4}}}{168 \, d}"," ",0,"-1/168*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 336*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^4)/d","A",0
75,1,87,0,0.864467," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{280 \, a^{4} d}"," ",0,"1/280*(35*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^4*d)","A",0
76,1,87,0,0.835037," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{840 \, a^{4} d}"," ",0,"1/840*(105*sin(d*x + c)/(cos(d*x + c) + 1) - 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^4*d)","A",0
77,1,87,0,1.195142," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{840 \, a^{4} d}"," ",0,"1/840*(105*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^4*d)","A",0
78,1,87,0,0.996676," ","integrate(1/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{35 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{280 \, a^{4} d}"," ",0,"1/280*(35*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^4*d)","A",0
79,1,139,0,1.478094," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}}{168 \, d}"," ",0,"-1/168*((315*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 168*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4)/d","A",0
80,1,186,0,1.473820," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{1680 \, \sin\left(d x + c\right)}{{\left(a^{4} - \frac{a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{5145 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{147 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{3360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}}{840 \, d}"," ",0,"1/840*(1680*sin(d*x + c)/((a^4 - a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (5145*sin(d*x + c)/(cos(d*x + c) + 1) + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 147*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 3360*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4)/d","A",0
81,1,231,0,1.103562," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{280 \, {\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{4} - \frac{2 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{3885 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{455 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{4}} - \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{2940 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}}{280 \, d}"," ",0,"-1/280*(280*(7*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^4 - 2*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (3885*sin(d*x + c)/(cos(d*x + c) + 1) + 455*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^4 - 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 2940*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4)/d","A",0
82,1,224,0,2.430137," ","integrate(cos(d*x+c)^7/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","-\frac{\frac{5040 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{11 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{5} + \frac{2 \, a^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{110565 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15750 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3024 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{450 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{156240 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{5}}}{5040 \, d}"," ",0,"-1/5040*(5040*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 11*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^5 + 2*a^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (110565*sin(d*x + c)/(cos(d*x + c) + 1) - 15750*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3024*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 450*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 156240*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^5)/d","A",0
83,1,178,0,0.774289," ","integrate(cos(d*x+c)^6/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{2016 \, \sin\left(d x + c\right)}{{\left(a^{5} + \frac{a^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{8127 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1512 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{72 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{7 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{10080 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{5}}}{1008 \, d}"," ",0,"1/1008*(2016*sin(d*x + c)/((a^5 + a^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (8127*sin(d*x + c)/(cos(d*x + c) + 1) - 1512*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 72*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 10080*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^5)/d","A",0
84,1,132,0,0.699028," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","-\frac{\frac{\frac{9765 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2730 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1008 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{270 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{10080 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{5}}}{5040 \, d}"," ",0,"-1/5040*((9765*sin(d*x + c)/(cos(d*x + c) + 1) - 2730*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1008*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 270*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 10080*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^5)/d","A",0
85,1,107,0,0.991920," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{420 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{180 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{5040 \, a^{5} d}"," ",0,"1/5040*(315*sin(d*x + c)/(cos(d*x + c) + 1) - 420*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 180*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
86,1,87,0,1.904819," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{63 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{42 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{18 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{7 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{1008 \, a^{5} d}"," ",0,"1/1008*(63*sin(d*x + c)/(cos(d*x + c) + 1) - 42*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 18*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
87,1,67,0,0.678213," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{18 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{720 \, a^{5} d}"," ",0,"1/720*(45*sin(d*x + c)/(cos(d*x + c) + 1) - 18*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
88,1,87,0,0.973194," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{63 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{42 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{18 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{7 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{1008 \, a^{5} d}"," ",0,"1/1008*(63*sin(d*x + c)/(cos(d*x + c) + 1) + 42*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 18*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
89,1,107,0,1.012940," ","integrate(1/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{420 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{180 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{5040 \, a^{5} d}"," ",0,"1/5040*(315*sin(d*x + c)/(cos(d*x + c) + 1) + 420*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 180*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^5*d)","A",0
90,1,159,0,0.962286," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","-\frac{\frac{\frac{9765 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2730 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1008 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{270 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{5}} + \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{5}}}{5040 \, d}"," ",0,"-1/5040*((9765*sin(d*x + c)/(cos(d*x + c) + 1) + 2730*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1008*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 270*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 5040*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^5 + 5040*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^5)/d","A",0
91,1,206,0,1.057945," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","\frac{\frac{2016 \, \sin\left(d x + c\right)}{{\left(a^{5} - \frac{a^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{\frac{8127 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1512 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{378 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{72 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{7 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{5}} + \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{5}}}{1008 \, d}"," ",0,"1/1008*(2016*sin(d*x + c)/((a^5 - a^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(cos(d*x + c) + 1)) + (8127*sin(d*x + c)/(cos(d*x + c) + 1) + 1512*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 378*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 72*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 7*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 5040*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^5 + 5040*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^5)/d","A",0
92,1,251,0,0.686402," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^5,x, algorithm=""maxima"")","-\frac{\frac{5040 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{11 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{5} - \frac{2 \, a^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{110565 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{15750 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3024 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{450 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{35 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{5}} - \frac{78120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{5}} + \frac{78120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{5}}}{5040 \, d}"," ",0,"-1/5040*(5040*(9*sin(d*x + c)/(cos(d*x + c) + 1) - 11*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^5 - 2*a^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (110565*sin(d*x + c)/(cos(d*x + c) + 1) + 15750*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3024*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 450*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 35*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^5 - 78120*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^5 + 78120*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^5)/d","A",0
93,1,127,0,0.673057," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^6,x, algorithm=""maxima"")","\frac{\frac{693 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1155 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1386 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{990 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{385 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{63 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{22176 \, a^{6} d}"," ",0,"1/22176*(693*sin(d*x + c)/(cos(d*x + c) + 1) - 1155*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1386*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 990*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 385*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 63*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/(a^6*d)","A",0
94,1,127,0,1.489295," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^6,x, algorithm=""maxima"")","\frac{\frac{1155 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1155 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{462 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{330 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{385 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{105 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{36960 \, a^{6} d}"," ",0,"1/36960*(1155*sin(d*x + c)/(cos(d*x + c) + 1) - 1155*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 462*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 330*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 385*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 105*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/(a^6*d)","A",0
95,1,79,0,1.131838," ","integrate(cos(d*x+c)^4*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(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))*sqrt(a)/d","A",0
96,1,65,0,1.451957," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{140 \, d}"," ",0,"1/140*(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))*sqrt(a)/d","A",0
97,1,51,0,1.396204," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{30 \, d}"," ",0,"1/30*(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))*sqrt(a)/d","A",0
98,1,36,0,1.883125," ","integrate(cos(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)} \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))*sqrt(a)/d","A",0
99,1,20,0,1.637303," ","integrate((a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}"," ",0,"2*sqrt(2)*sqrt(a)*sin(1/2*d*x + 1/2*c)/d","A",0
100,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/2)*sec(d*x+c),x, algorithm=""maxima"")","\int \sqrt{a \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
101,1,1170,0,2.591415," ","integrate((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left({\left(4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\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) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\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) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} \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) - 2 \, {\left(2 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\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) - \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(\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 \, \sqrt{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\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) + \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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)} \sqrt{a}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*((4*sqrt(2)*sin(1/2*d*x + 1/2*c) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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 + (4*sqrt(2)*sin(1/2*d*x + 1/2*c) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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 + 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) - 2*(2*sqrt(2)*sin(3/2*d*x + 3/2*c) - 4*sqrt(2)*sin(1/2*d*x + 1/2*c) + log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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) - 4*(sqrt(2)*cos(2*d*x + 2*c) + sqrt(2))*sin(5/2*d*x + 5/2*c) - 4*sqrt(2)*sin(3/2*d*x + 3/2*c) + 4*sqrt(2)*sin(1/2*d*x + 1/2*c) - log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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))*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
102,1,2642,0,11.912475," ","integrate((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^3,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)} \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))*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
103,1,5115,0,171.931684," ","integrate((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{{\left(15 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} + 135 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 135 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 15 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} + 135 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 135 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 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) + 2 \, {\left(45 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 45 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 60 \, \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 200 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 168 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 12 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{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) + 6 \, {\left(45 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 168 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 12 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 20 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 30 \, {\left(3 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 24 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\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) + 2 \, {\left(45 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 45 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 60 \, \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 200 \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 168 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 12 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 20 \, \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) + 6 \, {\left(45 \, {\left(\sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 8 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right) - 168 \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 12 \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 20 \, \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) + 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 40 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}}{96 \, {\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)} d}"," ",0,"1/96*(15*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*cos(6*d*x + 6*c)^2 + 135*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c)^2 + 135*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c)^2 + 15*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*sin(6*d*x + 6*c)^2 + 135*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c)^2 + 135*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c)^2 - 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) + 2*(45*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c) + 45*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 60*sin(11/2*d*x + 11/2*c) + 200*sin(9/2*d*x + 9/2*c) + 168*sin(7/2*d*x + 7/2*c) + 12*sin(5/2*d*x + 5/2*c) - 20*sin(3/2*d*x + 3/2*c) - 120*sin(1/2*d*x + 1/2*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) + 6*(45*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 168*sin(7/2*d*x + 7/2*c) + 12*sin(5/2*d*x + 5/2*c) - 20*sin(3/2*d*x + 3/2*c) - 120*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c) + 30*(3*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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*sin(3/2*d*x + 3/2*c) - 24*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 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) + 2*(45*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c) + 45*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) - 60*cos(11/2*d*x + 11/2*c) - 200*cos(9/2*d*x + 9/2*c) - 168*cos(7/2*d*x + 7/2*c) - 12*cos(5/2*d*x + 5/2*c) + 20*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) + 6*(45*(sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 8*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c) - 168*cos(7/2*d*x + 7/2*c) - 12*cos(5/2*d*x + 5/2*c) + 20*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) + 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 40*sin(3/2*d*x + 3/2*c) - 120*sin(1/2*d*x + 1/2*c))*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))*d)","B",0
104,1,84,0,1.052780," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(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))*sqrt(a)/d","A",0
105,1,69,0,1.007213," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{420 \, d}"," ",0,"1/420*(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))*sqrt(a)/d","A",0
106,1,53,0,1.127101," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2),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)} \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))*sqrt(a)/d","A",0
107,1,38,0,1.129739," ","integrate((a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\left(\sqrt{2} a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}}{3 \, d}"," ",0,"1/3*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*sqrt(a)/d","A",0
108,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
109,1,1314,0,1.670205," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\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)} \sqrt{a}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"-1/4*(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))*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
110,1,3216,0,3.697136," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{{\left({\left(7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 4 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 12 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 12 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 4 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 12 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 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) + 4 \, {\left(7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 12 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 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) + 2 \, {\left(7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 2 \, {\left(7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 12 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 40 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 2 \, {\left(4 \, a \cos\left(2 \, d x + 2 \, c\right) + 23 \, a\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 6 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 6 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\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(4 \, a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 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) + {\left(7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 7 \, \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 12 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 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) + 8 \, {\left(2 \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + 23 \, a \cos\left(2 \, d x + 2 \, c\right) + 11 \, 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) - 56 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \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*((7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 4*a*sin(5/2*d*x + 5/2*c) - 12*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c)^2 + 4*(7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 12*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c)^2 + (7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 4*a*sin(5/2*d*x + 5/2*c) - 12*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c)^2 - 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) + 4*(7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 12*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c)^2 + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 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) + 2*(7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 2*(7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 12*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 40*a*sin(7/2*d*x + 7/2*c) + 2*(4*a*cos(2*d*x + 2*c) + 23*a)*sin(5/2*d*x + 5/2*c) + 6*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c) + 4*(7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 6*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) - 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*(4*a*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 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) + (7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 7*sqrt(2)*a*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 12*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 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) + 8*(2*a*cos(2*d*x + 2*c)^2 + 2*a*sin(2*d*x + 2*c)^2 + 23*a*cos(2*d*x + 2*c) + 11*a)*sin(5/2*d*x + 5/2*c) + 24*a*sin(3/2*d*x + 3/2*c) - 56*a*sin(1/2*d*x + 1/2*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
111,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,1,111,0,1.218592," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{11088 \, d}"," ",0,"1/11088*(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))*sqrt(a)/d","A",0
113,1,94,0,1.176518," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\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)} \sqrt{a}}{2520 \, d}"," ",0,"1/2520*(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))*sqrt(a)/d","A",0
114,1,77,0,0.970682," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2),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)} \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))*sqrt(a)/d","A",0
115,1,60,0,0.991560," ","integrate((a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}}{30 \, d}"," ",0,"1/30*(3*sqrt(2)*a^2*sin(5/2*d*x + 5/2*c) + 25*sqrt(2)*a^2*sin(3/2*d*x + 3/2*c) + 150*sqrt(2)*a^2*sin(1/2*d*x + 1/2*c))*sqrt(a)/d","A",0
116,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
117,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,1,3667,0,13.576738," ","integrate((a+a*cos(d*x+c))^(5/2)*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)} \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))*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
119,1,6703,0,131.605089," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^4,x, algorithm=""maxima"")","-\frac{{\left(4176 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 2430 \, a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 678 \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 10 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 30 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 78 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 170 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 600 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right)^{2} - 9 \, {\left(75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 30 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 78 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 170 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 600 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} - 45 \, {\left(15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 34 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 10 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 30 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 78 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 170 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 600 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)^{2} - 9 \, {\left(75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 30 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 78 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 170 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 600 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} - 45 \, {\left(15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 34 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - 56 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 600 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{21}{2} \, d x + \frac{21}{2} \, c\right) - 30 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{19}{2} \, d x + \frac{19}{2} \, c\right) - 48 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{17}{2} \, d x + \frac{17}{2} \, c\right) + 80 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{15}{2} \, d x + \frac{15}{2} \, c\right) + 396 \, {\left(a^{2} \sin\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 6 \, {\left(25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 170 \, a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 19 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 200 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 30 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 78 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 170 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 600 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 5 \, {\left(15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 34 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 10 \, {\left(a^{2} \cos\left(4 \, d x + 4 \, c\right) + a^{2} \cos\left(2 \, d x + 2 \, c\right) - 25 \, a^{2}\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 2 \, {\left(15 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 121 \, a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + {\left(78 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 161 \, a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \cos\left(6 \, d x + 6 \, c\right) + 3060 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 4560 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 18 \, {\left(25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 200 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, {\left(15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 34 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(15 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 121 \, a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + {\left(78 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 161 \, a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) - 18 \, {\left(25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 25 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 200 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 10 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{21}{2} \, d x + \frac{21}{2} \, c\right) + 30 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{19}{2} \, d x + \frac{19}{2} \, c\right) + 48 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{17}{2} \, d x + \frac{17}{2} \, c\right) - 80 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{15}{2} \, d x + \frac{15}{2} \, c\right) - 396 \, {\left(a^{2} \cos\left(6 \, d x + 6 \, c\right) + 3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) - 2 \, {\left(90 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 234 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 510 \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 760 \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 696 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 405 \, a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 113 \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 30 \, {\left(a^{2} \sin\left(4 \, d x + 4 \, c\right) + a^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 3 \, {\left(75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 75 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 30 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 78 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 170 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 600 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 15 \, {\left(15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 34 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) - 1020 \, {\left(3 \, a^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 10 \, {\left(9 \, a^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 9 \, a^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, a^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 450 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - 151 \, a^{2} + 18 \, {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right) - 25 \, a^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 6 \, {\left(90 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 234 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 696 \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 405 \, a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 113 \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 15 \, {\left(15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 15 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 34 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 120 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 18 \, {\left(15 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 15 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 242 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 79 \, a^{2}\right)} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 6 \, {\left(117 \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 117 \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 483 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 148 \, a^{2}\right)} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)} \sqrt{a}}{96 \, {\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)} d}"," ",0,"-1/96*(4176*a^2*cos(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 2430*a^2*cos(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) + 678*a^2*cos(3/2*d*x + 3/2*c)*sin(2*d*x + 2*c) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - (75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 10*a^2*sin(9/2*d*x + 9/2*c) + 30*a^2*sin(7/2*d*x + 7/2*c) + 78*a^2*sin(5/2*d*x + 5/2*c) - 170*a^2*sin(3/2*d*x + 3/2*c) - 600*a^2*sin(1/2*d*x + 1/2*c))*cos(6*d*x + 6*c)^2 - 9*(75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 30*a^2*sin(7/2*d*x + 7/2*c) + 78*a^2*sin(5/2*d*x + 5/2*c) - 170*a^2*sin(3/2*d*x + 3/2*c) - 600*a^2*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c)^2 - 45*(15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 34*a^2*sin(3/2*d*x + 3/2*c) - 120*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c)^2 - (75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 10*a^2*sin(9/2*d*x + 9/2*c) + 30*a^2*sin(7/2*d*x + 7/2*c) + 78*a^2*sin(5/2*d*x + 5/2*c) - 170*a^2*sin(3/2*d*x + 3/2*c) - 600*a^2*sin(1/2*d*x + 1/2*c))*sin(6*d*x + 6*c)^2 - 9*(75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 30*a^2*sin(7/2*d*x + 7/2*c) + 78*a^2*sin(5/2*d*x + 5/2*c) - 170*a^2*sin(3/2*d*x + 3/2*c) - 600*a^2*sin(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c)^2 - 45*(15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 34*a^2*sin(3/2*d*x + 3/2*c) - 120*a^2*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c)^2 - 56*a^2*sin(3/2*d*x + 3/2*c) + 600*a^2*sin(1/2*d*x + 1/2*c) + 10*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 3*a^2*sin(2*d*x + 2*c))*cos(21/2*d*x + 21/2*c) - 30*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 3*a^2*sin(2*d*x + 2*c))*cos(19/2*d*x + 19/2*c) - 48*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 3*a^2*sin(2*d*x + 2*c))*cos(17/2*d*x + 17/2*c) + 80*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 3*a^2*sin(2*d*x + 2*c))*cos(15/2*d*x + 15/2*c) + 396*(a^2*sin(6*d*x + 6*c) + 3*a^2*sin(4*d*x + 4*c) + 3*a^2*sin(2*d*x + 2*c))*cos(13/2*d*x + 13/2*c) - 6*(25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 170*a^2*sin(11/2*d*x + 11/2*c) - 19*a^2*sin(3/2*d*x + 3/2*c) - 200*a^2*sin(1/2*d*x + 1/2*c) + (75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 30*a^2*sin(7/2*d*x + 7/2*c) + 78*a^2*sin(5/2*d*x + 5/2*c) - 170*a^2*sin(3/2*d*x + 3/2*c) - 600*a^2*sin(1/2*d*x + 1/2*c))*cos(4*d*x + 4*c) + 5*(15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 34*a^2*sin(3/2*d*x + 3/2*c) - 120*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) - 10*(a^2*cos(4*d*x + 4*c) + a^2*cos(2*d*x + 2*c) - 25*a^2)*sin(9/2*d*x + 9/2*c) + 2*(15*a^2*cos(2*d*x + 2*c) + 121*a^2)*sin(7/2*d*x + 7/2*c) + (78*a^2*cos(2*d*x + 2*c) + 161*a^2)*sin(5/2*d*x + 5/2*c))*cos(6*d*x + 6*c) + 3060*(a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*cos(11/2*d*x + 11/2*c) + 4560*(a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*cos(9/2*d*x + 9/2*c) - 18*(25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*sin(3/2*d*x + 3/2*c) - 200*a^2*sin(1/2*d*x + 1/2*c) + 5*(15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 34*a^2*sin(3/2*d*x + 3/2*c) - 120*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) + 2*(15*a^2*cos(2*d*x + 2*c) + 121*a^2)*sin(7/2*d*x + 7/2*c) + (78*a^2*cos(2*d*x + 2*c) + 161*a^2)*sin(5/2*d*x + 5/2*c))*cos(4*d*x + 4*c) - 18*(25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 25*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 19*a^2*sin(3/2*d*x + 3/2*c) - 200*a^2*sin(1/2*d*x + 1/2*c))*cos(2*d*x + 2*c) - 10*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4*d*x + 4*c) + 3*a^2*cos(2*d*x + 2*c) + a^2)*sin(21/2*d*x + 21/2*c) + 30*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4*d*x + 4*c) + 3*a^2*cos(2*d*x + 2*c) + a^2)*sin(19/2*d*x + 19/2*c) + 48*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4*d*x + 4*c) + 3*a^2*cos(2*d*x + 2*c) + a^2)*sin(17/2*d*x + 17/2*c) - 80*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4*d*x + 4*c) + 3*a^2*cos(2*d*x + 2*c) + a^2)*sin(15/2*d*x + 15/2*c) - 396*(a^2*cos(6*d*x + 6*c) + 3*a^2*cos(4*d*x + 4*c) + 3*a^2*cos(2*d*x + 2*c) + a^2)*sin(13/2*d*x + 13/2*c) - 2*(90*a^2*sin(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 234*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 510*a^2*cos(11/2*d*x + 11/2*c) - 760*a^2*cos(9/2*d*x + 9/2*c) - 696*a^2*cos(7/2*d*x + 7/2*c) - 405*a^2*cos(5/2*d*x + 5/2*c) - 113*a^2*cos(3/2*d*x + 3/2*c) - 30*(a^2*sin(4*d*x + 4*c) + a^2*sin(2*d*x + 2*c))*sin(9/2*d*x + 9/2*c) + 3*(75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 75*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 30*a^2*sin(7/2*d*x + 7/2*c) + 78*a^2*sin(5/2*d*x + 5/2*c) - 170*a^2*sin(3/2*d*x + 3/2*c) - 600*a^2*sin(1/2*d*x + 1/2*c))*sin(4*d*x + 4*c) + 15*(15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 34*a^2*sin(3/2*d*x + 3/2*c) - 120*a^2*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) - 1020*(3*a^2*cos(4*d*x + 4*c) + 3*a^2*cos(2*d*x + 2*c) + a^2)*sin(11/2*d*x + 11/2*c) + 10*(9*a^2*cos(4*d*x + 4*c)^2 + 9*a^2*cos(2*d*x + 2*c)^2 + 9*a^2*sin(4*d*x + 4*c)^2 + 18*a^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*a^2*sin(2*d*x + 2*c)^2 - 450*a^2*cos(2*d*x + 2*c) - 151*a^2 + 18*(a^2*cos(2*d*x + 2*c) - 25*a^2)*cos(4*d*x + 4*c))*sin(9/2*d*x + 9/2*c) - 6*(90*a^2*sin(7/2*d*x + 7/2*c)*sin(2*d*x + 2*c) + 234*a^2*sin(5/2*d*x + 5/2*c)*sin(2*d*x + 2*c) - 696*a^2*cos(7/2*d*x + 7/2*c) - 405*a^2*cos(5/2*d*x + 5/2*c) - 113*a^2*cos(3/2*d*x + 3/2*c) + 15*(15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 15*sqrt(2)*a^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 34*a^2*sin(3/2*d*x + 3/2*c) - 120*a^2*sin(1/2*d*x + 1/2*c))*sin(2*d*x + 2*c))*sin(4*d*x + 4*c) - 18*(15*a^2*cos(2*d*x + 2*c)^2 + 15*a^2*sin(2*d*x + 2*c)^2 + 242*a^2*cos(2*d*x + 2*c) + 79*a^2)*sin(7/2*d*x + 7/2*c) - 6*(117*a^2*cos(2*d*x + 2*c)^2 + 117*a^2*sin(2*d*x + 2*c)^2 + 483*a^2*cos(2*d*x + 2*c) + 148*a^2)*sin(5/2*d*x + 5/2*c))*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))*d)","B",0
120,-1,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,1,77,0,1.065985," ","integrate((a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{{\left(5 \, \sqrt{2} a^{3} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 49 \, \sqrt{2} a^{3} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 245 \, \sqrt{2} a^{3} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 1225 \, \sqrt{2} a^{3} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}}{140 \, d}"," ",0,"1/140*(5*sqrt(2)*a^3*sin(7/2*d*x + 7/2*c) + 49*sqrt(2)*a^3*sin(5/2*d*x + 5/2*c) + 245*sqrt(2)*a^3*sin(3/2*d*x + 3/2*c) + 1225*sqrt(2)*a^3*sin(1/2*d*x + 1/2*c))*sqrt(a)/d","A",0
122,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(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
125,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,1,90,0,1.309227," ","integrate(1/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{2 \, \sqrt{a} d}"," ",0,"1/2*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))/(sqrt(a)*d)","B",0
127,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(a*cos(d*x + c) + a), x)","F",0
128,-1,0,0,0.000000," ","integrate(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
129,-1,0,0,0.000000," ","integrate(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
130,-1,0,0,0.000000," ","integrate(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
131,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate(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
134,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
137,-1,0,0,0.000000," ","integrate(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
138,-1,0,0,0.000000," ","integrate(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
139,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(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
142,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
145,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
147,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
148,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
149,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a \cos\left(d x + c\right) + a}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
150,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
151,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
152,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
153,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
154,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
155,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
156,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
157,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
158,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
159,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
160,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
161,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
162,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
163,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
164,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
165,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
166,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
167,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4*cos(d*x + c)^(3/2), x)","F",0
168,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4*sqrt(cos(d*x + c)), x)","F",0
169,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4/sqrt(cos(d*x + c)), x)","F",0
170,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4/cos(d*x + c)^(3/2), x)","F",0
171,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4/cos(d*x + c)^(5/2), x)","F",0
172,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4/cos(d*x + c)^(7/2), x)","F",0
173,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{4}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4/cos(d*x + c)^(9/2), x)","F",0
174,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a), x)","F",0
175,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
176,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
177,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
178,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
179,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
180,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
181,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(9/2)/(a*cos(d*x + c) + a)^2, x)","F",0
182,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^2, x)","F",0
183,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
184,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
185,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
186,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
187,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
188,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2)), x)","F",0
189,0,0,0,0.000000," ","integrate(cos(d*x+c)^(11/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{11}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(11/2)/(a*cos(d*x + c) + a)^3, x)","F",0
190,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(9/2)/(a*cos(d*x + c) + a)^3, x)","F",0
191,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^3, x)","F",0
192,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^3, x)","F",0
193,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^3, x)","F",0
194,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
195,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-2,0,0,0.000000," ","integrate(1/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
197,-1,0,0,0.000000," ","integrate(1/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
198,1,1921,0,2.014130," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(3 \, d x + 3 \, c\right) - {\left(\cos\left(3 \, d x + 3 \, c\right) - 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 6 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + 15 \, \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)}, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right), \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, d x + 3 \, c\right), \cos\left(3 \, d x + 3 \, c\right)\right)\right) + 1\right)\right) - 1\right)\right)}}{96 \, d}"," ",0,"1/96*(4*(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(3/4)*(cos(3/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(3*d*x + 3*c) - (cos(3*d*x + 3*c) - 1)*sin(3/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)))*sqrt(a) + 6*(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*((sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 5*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) - (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 3*cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - 4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)))*sqrt(a) + 15*sqrt(a)*(arctan2(-(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))) + 1) - arctan2(-(cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) - cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*(cos(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1))) - 1) - arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) + 1) + arctan2((cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)), (cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))^2 + 2*cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))), cos(2/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))) + 1)) - 1)))/d","B",0
199,1,1059,0,1.705550," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}}{16 \, d}"," ",0,"1/16*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))/d","B",0
200,1,791,0,1.840771," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))/d","B",0
201,1,146,0,1.729460," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right)}{d}"," ",0,"sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c))/d","B",0
202,1,98,0,1.326520," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\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)}}{d {\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}}}"," ",0,"2*(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)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2))","B",0
203,1,190,0,1.436451," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\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}}{3 \, d {\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)}}"," ",0,"2/3*(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/(d*(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))","B",0
204,1,237,0,1.110860," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\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}}{15 \, d {\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)}}"," ",0,"2/15*(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/(d*(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))","B",0
205,1,283,0,1.484100," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\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}}{35 \, d {\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)}}"," ",0,"2/35*(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/(d*(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))","B",0
206,1,1942,0,2.066232," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{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}}{96 \, d}"," ",0,"1/96*(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))/d","B",0
207,1,1080,0,1.912534," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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}}{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))/d","B",0
208,1,803,0,1.964761," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}}{4 \, d}"," ",0,"1/4*(2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))/d","B",0
209,1,997,0,1.655322," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/2*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
210,1,125,0,0.731680," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{4 \, {\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)}}{3 \, d {\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}}}"," ",0,"4/3*(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)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2))","A",0
211,1,217,0,1.134766," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{4 \, {\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)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{5 \, d {\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)}}"," ",0,"4/5*(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)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/(d*(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))","B",0
212,1,263,0,1.201717," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{4 \, {\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)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{105 \, d {\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)}}"," ",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)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/(d*(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))","A",0
213,1,7450,0,3.271245," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{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}}{768 \, {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} d}"," ",0,"1/768*(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))/((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
214,1,1964,0,2.230561," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{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}}{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))/d","B",0
215,1,1106,0,1.811535," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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}}{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^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))/d","B",0
216,1,973,0,1.816126," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{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}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/4*(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))/((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
217,1,1395,0,1.541591," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}}{6 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"1/6*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*d)","B",0
218,1,151,0,1.366474," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{8 \, {\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)}}{15 \, d {\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}}}"," ",0,"8/15*(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)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2))","A",0
219,1,243,0,0.853305," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{8 \, {\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)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{21 \, d {\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)}}"," ",0,"8/21*(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)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/(d*(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))","A",0
220,1,289,0,1.155034," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{8 \, {\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)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{315 \, d {\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)}}"," ",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)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/(d*(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))","A",0
221,1,121,0,1.130852," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/4),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{\sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{4}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{4}} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"4*(sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/4)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(1/4))","B",0
222,1,146,0,1.224708," ","integrate((a+a*cos(f*x+e))^(1/2)/cos(f*x+e)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} \arctan\left({\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \sin\left(f x + e\right), {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \cos\left(f x + e\right)\right)}{f}"," ",0,"sqrt(a)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + sin(f*x + e), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + cos(f*x + e))/f","B",0
223,1,420,0,0.858354," ","integrate((a-a*cos(f*x+e))^(1/2)/(-cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{-a} {\left(\log\left(4 \, \sqrt{\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2} + 4 \, \sqrt{\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2} + 8 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 4\right) - \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + \sqrt{\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2}\right)} + 2 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(f x + e\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \sin\left(f x + e\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)}\right)\right)}}{2 \, f}"," ",0,"1/2*sqrt(-a)*(log(4*sqrt(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + 4*sqrt(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + 8*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 4) - log(cos(f*x + e)^2 + sin(f*x + e)^2 + sqrt(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2) + 2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/4)*(cos(f*x + e)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + sin(f*x + e)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))))/f","B",0
224,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
225,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/sqrt(a*cos(d*x + c) + a), x)","F",0
226,-2,0,0,0.000000," ","integrate(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
227,-2,0,0,0.000000," ","integrate(1/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
228,-2,0,0,0.000000," ","integrate(1/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
229,-2,0,0,0.000000," ","integrate(1/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
230,-2,0,0,0.000000," ","integrate(1/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
231,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/sqrt(cos(d*x + c) + 1), x)","F",0
232,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/sqrt(cos(d*x + c) + 1), x)","F",0
233,-2,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(1+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
234,-2,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(1+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
235,-2,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(1+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
236,-2,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(1+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
237,-2,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(1+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
238,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\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(cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
239,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\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(cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
240,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
241,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
242,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
243,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
244,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
245,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
246,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\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(cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
247,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
248,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
249,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
250,-1,0,0,0.000000," ","integrate(1/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
251,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{9}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(9/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
252,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
253,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
254,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(7/2), x)","F",0
255,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(a*cos(d*x + c) + a)^(7/2), x)","F",0
256,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(7/2)*sqrt(cos(d*x + c))), x)","F",0
257,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a)^(9/2), x)","F",0
260,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(9/2), x)","F",0
261,-2,0,0,0.000000," ","integrate(1/cos(x)^(1/2)/(1+cos(x))^(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
262,-2,0,0,0.000000," ","integrate(1/cos(x)^(1/2)/(a+a*cos(x))^(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
263,1,1063,0,1.089654," ","integrate(cos(d*x+c)^(3/2)*(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{-a} + 3 \, \sqrt{-a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}}{16 \, d}"," ",0,"1/16*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(-a) + 3*sqrt(-a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))/d","B",0
264,1,795,0,0.977444," ","integrate(cos(d*x+c)^(1/2)*(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{-a} + \sqrt{-a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(-a) + sqrt(-a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))/d","B",0
265,1,148,0,1.052164," ","integrate((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{-a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right)}{d}"," ",0,"sqrt(-a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c))/d","B",0
266,1,82,0,0.626789," ","integrate((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{2} \sqrt{a} - \frac{\sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{d {\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}}}"," ",0,"2*(sqrt(2)*sqrt(a) - sqrt(2)*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2))","B",0
267,1,174,0,0.853775," ","integrate((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{2} \sqrt{a} - \frac{4 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{3 \, d {\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)}}"," ",0,"-2/3*(sqrt(2)*sqrt(a) - 4*sqrt(2)*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sqrt(2)*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/(d*(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))","B",0
268,1,221,0,0.977617," ","integrate((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, \sqrt{2} \sqrt{a} - \frac{17 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{25 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{15 \, \sqrt{2} \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{15 \, d {\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)}}"," ",0,"2/15*(7*sqrt(2)*sqrt(a) - 17*sqrt(2)*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 25*sqrt(2)*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 15*sqrt(2)*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/(d*(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))","B",0
269,1,1305,0,0.754678," ","integrate((1-cos(d*x+c))^(1/2)*cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\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)} \cos\left(\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(\frac{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)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 3 \, \log\left(\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} \cos\left(\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} + \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} \sin\left(\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} + 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}} \cos\left(\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) - 3 \, \log\left(\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} \cos\left(\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} + \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} \sin\left(\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} - 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}} \cos\left(\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) + 3 \, \log\left({\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} \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} + 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) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{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) - 3 \, \log\left({\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} \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} - 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) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{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)}{32 \, d}"," ",0,"1/32*(4*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(((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)*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(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))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 3*log(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + 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)) + 1) - 3*log(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 - 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)) + 1) + 3*log(((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + (cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2)*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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(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) - 3*log(((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + (cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2)*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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(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))/d","B",0
270,1,966,0,1.028212," ","integrate((1-cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(d x + c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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)} - \log\left(\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} \cos\left(\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} + \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} \sin\left(\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} + 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}} \cos\left(\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) + \log\left(\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} \cos\left(\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} + \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} \sin\left(\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} - 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}} \cos\left(\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) - \log\left({\left({\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} \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} + 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(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) + \log\left({\left({\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} \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} - 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(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)}{8 \, d}"," ",0,"1/8*(4*(cos(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) + 1)*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))) - log(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + 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)) + 1) + log(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 - 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)) + 1) - log(((cos(d*x + c)^2 + sin(d*x + c)^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + (cos(d*x + c)^2 + sin(d*x + c)^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2)*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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(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) + log(((cos(d*x + c)^2 + sin(d*x + c)^2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + (cos(d*x + c)^2 + sin(d*x + c)^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2)*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*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(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))/d","B",0
271,1,221,0,1.069321," ","integrate((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \operatorname{arsinh}\left(1\right) + \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{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} {\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)^{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}\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(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)}\right)}{2 \, d}"," ",0,"1/2*(2*arcsinh(1) + log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2) + 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(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)))))/d","B",0
272,1,75,0,0.783235," ","integrate((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{2} - \frac{\sqrt{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{d {\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}}}"," ",0,"2*(sqrt(2) - sqrt(2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2))","B",0
273,1,164,0,0.891086," ","integrate((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{2} - \frac{4 \, \sqrt{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sqrt{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{3 \, d {\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)}}"," ",0,"-2/3*(sqrt(2) - 4*sqrt(2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sqrt(2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/(d*(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))","B",0
274,1,209,0,0.655144," ","integrate((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, \sqrt{2} - \frac{17 \, \sqrt{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{25 \, \sqrt{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{15 \, \sqrt{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{15 \, d {\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)}}"," ",0,"2/15*(7*sqrt(2) - 17*sqrt(2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 25*sqrt(2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 15*sqrt(2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/(d*(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))","B",0
275,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{-a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/sqrt(-a*cos(d*x + c) + a), x)","F",0
276,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{-a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/sqrt(-a*cos(d*x + c) + a), x)","F",0
277,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{-a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(-a*cos(d*x + c) + a), x)","F",0
278,1,209,0,1.358903," ","integrate(1/cos(d*x+c)^(1/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \arctan\left(\frac{2 \, \sqrt{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}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)}{\sqrt{a} {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|}}, \frac{2 \, {\left(\sqrt{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}} \sqrt{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) - \sqrt{-a} {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|} + 2 \, \sqrt{a}\right)}}{a {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|}}\right)}{\sqrt{-a} d}"," ",0,"-sqrt(2)*arctan2(2*sqrt(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)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))/(sqrt(a)*abs(e^(I*d*x + I*c) - 1)), 2*(sqrt(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)*sqrt(a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - sqrt(-a)*abs(e^(I*d*x + I*c) - 1) + 2*sqrt(a))/(a*abs(e^(I*d*x + I*c) - 1)))/(sqrt(-a)*d)","C",0
279,1,351,0,0.997063," ","integrate(1/cos(d*x+c)^(3/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{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) - 2 \, {\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) - \sqrt{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}} \arctan\left(\frac{2 \, \sqrt{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}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)}{\sqrt{a} {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|}}, \frac{2 \, {\left(\sqrt{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}} \sqrt{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) - \sqrt{-a} {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|} + 2 \, \sqrt{a}\right)}}{a {\left| e^{\left(i \, d x + i \, 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}} \sqrt{-a} d}"," ",0,"(2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - 2*(cos(d*x + c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - sqrt(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)*arctan2(2*sqrt(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)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))/(sqrt(a)*abs(e^(I*d*x + I*c) - 1)), 2*(sqrt(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)*sqrt(a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - sqrt(-a)*abs(e^(I*d*x + I*c) - 1) + 2*sqrt(a))/(a*abs(e^(I*d*x + I*c) - 1))))/((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)*d)","C",0
280,1,504,0,1.187443," ","integrate(1/cos(d*x+c)^(5/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{3 \, {\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)} \arctan\left(\frac{2 \, \sqrt{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}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)}{\sqrt{a} {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|}}, \frac{2 \, {\left(\sqrt{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}} \sqrt{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) - \sqrt{-a} {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|} + 2 \, \sqrt{a}\right)}}{a {\left| e^{\left(i \, d x + i \, 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{3}{4}} {\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) + 3\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\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(d x + c\right) - {\left(\cos\left(d x + 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)}}{3 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{-a} d}"," ",0,"-1/3*(3*(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))*arctan2(2*sqrt(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)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))/(sqrt(a)*abs(e^(I*d*x + I*c) - 1)), 2*(sqrt(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)*sqrt(a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - sqrt(-a)*abs(e^(I*d*x + I*c) - 1) + 2*sqrt(a))/(a*abs(e^(I*d*x + I*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)^(3/4)*(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) + 3)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 4*(cos(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(d*x + c) - (cos(d*x + c) - 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sqrt(-a)*d)","C",0
281,1,692,0,0.982546," ","integrate(1/cos(d*x+c)^(7/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{15 \, {\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)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \arctan\left(\frac{2 \, \sqrt{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}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)}{\sqrt{a} {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|}}, \frac{2 \, {\left(\sqrt{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}} \sqrt{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) - \sqrt{-a} {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|} + 2 \, \sqrt{a}\right)}}{a {\left| e^{\left(i \, d x + i \, c\right)} - 1 \right|}}\right) - 26 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + \sin\left(2 \, d x + 2 \, c\right)^{2} \sin\left(d x + c\right) + 2 \, \cos\left(2 \, d x + 2 \, c\right) \sin\left(d x + c\right) + \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) + 24 \, \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) \sin\left(d x + c\right) - 24 \, {\left(\cos\left(d x + c\right) + 1\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) + 2 \, {\left({\left(13 \, \cos\left(d x + c\right) + 15\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(13 \, \cos\left(d x + c\right) + 15\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(13 \, \cos\left(d x + c\right) + 15\right)} \cos\left(2 \, d x + 2 \, c\right) + 13 \, \cos\left(d x + c\right) + 15\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 4 \, \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} {\left(7 \, \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(d x + c\right) - {\left(7 \, \cos\left(d x + c\right) + 5\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)}}{15 \, {\left(\cos\left(2 \, d x + 2 \, 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}} \sqrt{-a} d}"," ",0,"-1/15*(15*(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))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*arctan2(2*sqrt(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)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))/(sqrt(a)*abs(e^(I*d*x + I*c) - 1)), 2*(sqrt(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)*sqrt(a)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - sqrt(-a)*abs(e^(I*d*x + I*c) - 1) + 2*sqrt(a))/(a*abs(e^(I*d*x + I*c) - 1))) - 26*(cos(2*d*x + 2*c)^2*sin(d*x + c) + sin(2*d*x + 2*c)^2*sin(d*x + c) + 2*cos(2*d*x + 2*c)*sin(d*x + c) + sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 24*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - 24*(cos(d*x + c) + 1)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 2*((13*cos(d*x + c) + 15)*cos(2*d*x + 2*c)^2 + (13*cos(d*x + c) + 15)*sin(2*d*x + 2*c)^2 + 2*(13*cos(d*x + c) + 15)*cos(2*d*x + 2*c) + 13*cos(d*x + c) + 15)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*(7*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (7*cos(d*x + c) + 5)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(5/4)*sqrt(-a)*d)","C",0
282,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(1-cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{-\cos\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/sqrt(-cos(d*x + c) + 1), x)","F",0
283,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(1-cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{-\cos\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/sqrt(-cos(d*x + c) + 1), x)","F",0
284,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(1-cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{-\cos\left(d x + c\right) + 1}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(-cos(d*x + c) + 1), x)","F",0
285,1,248,0,0.994967," ","integrate(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} \log\left(\frac{4 \, {\left({\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|}^{2} + 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} {\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)^{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}\right)} - 2 \, {\left(\sqrt{2} {\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|} \sin\left(\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 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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}} + 4\right)}}{{\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|}^{2}}\right)}{2 \, d}"," ",0,"1/2*sqrt(2)*log(4*(abs(I*e^(I*d*x + I*c) - I)^2 + 2*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2) - 2*(sqrt(2)*abs(I*e^(I*d*x + I*c) - I)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 4)/abs(I*e^(I*d*x + I*c) - I)^2)/d","C",0
286,1,400,0,1.020652," ","integrate(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(2 \, \sqrt{2} \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) + 2 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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}} \log\left(\frac{4 \, {\left({\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|}^{2} + 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} {\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)^{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}\right)} - 2 \, {\left(\sqrt{2} {\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|} \sin\left(\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 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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}} + 4\right)}}{{\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|}^{2}}\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}} d}"," ",0,"-1/2*sqrt(2)*(2*sqrt(2)*sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 2*(sqrt(2)*cos(d*x + c) + sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*log(4*(abs(I*e^(I*d*x + I*c) - I)^2 + 2*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2) - 2*(sqrt(2)*abs(I*e^(I*d*x + I*c) - I)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 4)/abs(I*e^(I*d*x + I*c) - I)^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)*d)","C",0
287,1,563,0,1.013656," ","integrate(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\frac{4 \, {\left({\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|}^{2} + 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} {\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)^{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}\right)} - 2 \, {\left(\sqrt{2} {\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|} \sin\left(\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 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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}} + 4\right)}}{{\left| i \, e^{\left(i \, d x + i \, c\right)} - i \right|}^{2}}\right) - 2 \, {\left(\sqrt{2} \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) + {\left(\sqrt{2} \cos\left(d x + c\right) + 3 \, \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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}} - 4 \, {\left(\sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(\sqrt{2} \cos\left(d x + c\right) - \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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}}}{3 \, {\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)} d}"," ",0,"1/3*(3*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*log(4*(abs(I*e^(I*d*x + I*c) - I)^2 + 2*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))^2) - 2*(sqrt(2)*abs(I*e^(I*d*x + I*c) - I)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4) + 4)/abs(I*e^(I*d*x + I*c) - I)^2) - 2*(sqrt(2)*sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (sqrt(2)*cos(d*x + c) + 3*sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*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) - 4*(sqrt(2)*sin(d*x + c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (sqrt(2)*cos(d*x + c) - sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4))/((sqrt(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))*d)","C",0
288,0,0,0,0.000000," ","integrate(cos(d*x+c)^(4/3)*(a+a*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}} \cos\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(1/3)*cos(d*x + c)^(4/3), x)","F",0
289,0,0,0,0.000000," ","integrate(cos(d*x+c)^(4/3)*(a+a*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}} \cos\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(2/3)*cos(d*x + c)^(4/3), x)","F",0
290,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/3)*(a+a*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}} \cos\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(2/3)*cos(d*x + c)^(5/3), x)","F",0
291,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
292,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
293,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
294,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
295,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{a \cos\left(d x + c\right) + a}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
296,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{a \cos\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
297,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{a \cos\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
298,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
299,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
300,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
301,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
302,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
303,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
304,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
305,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
306,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
307,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
308,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
309,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
310,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
311,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4*sec(d*x + c)^(9/2), x)","F",0
312,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4*sec(d*x + c)^(7/2), x)","F",0
313,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4*sec(d*x + c)^(5/2), x)","F",0
314,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{4} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4*sec(d*x + c)^(3/2), x)","F",0
315,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{4} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4*sqrt(sec(d*x + c)), x)","F",0
316,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^4/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{4}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4/sqrt(sec(d*x + c)), x)","F",0
317,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
318,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
319,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
321,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
322,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
323,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
324,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^2, x)","F",0
325,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^2, x)","F",0
326,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^2, x)","F",0
327,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
328,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
329,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
330,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2)), x)","F",0
331,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2)), x)","F",0
332,-1,0,0,0.000000," ","integrate(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
333,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^3, x)","F",0
334,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
335,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
336,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2)), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2)), x)","F",0
339,1,283,0,1.016076," ","integrate(sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\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}}{35 \, d {\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)}}"," ",0,"2/35*(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/(d*(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))","B",0
340,1,237,0,0.980822," ","integrate(sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\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}}{15 \, d {\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)}}"," ",0,"2/15*(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/(d*(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))","B",0
341,1,190,0,1.123283," ","integrate(sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\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}}{3 \, d {\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)}}"," ",0,"2/3*(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/(d*(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))","B",0
342,1,98,0,1.243285," ","integrate(sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\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)}}{d {\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}}}"," ",0,"2*(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)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2))","B",0
343,1,146,0,1.460355," ","integrate(sec(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \cos\left(d x + c\right)\right)}{d}"," ",0,"sqrt(a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + cos(d*x + c))/d","B",0
344,1,791,0,1.632037," ","integrate((a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + \sqrt{a} {\left(\arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (cos(d*x + c) - 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + sqrt(a)*(arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))/d","B",0
345,1,1059,0,1.640873," ","integrate((a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\cos\left(2 \, d x + 2 \, c\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - \cos\left(2 \, d x + 2 \, c\right) + 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, \sqrt{a} {\left(\arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)}}{16 \, d}"," ",0,"1/16*(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - (cos(2*d*x + 2*c) - 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + ((cos(2*d*x + 2*c) - 2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(2*d*x + 2*c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - cos(2*d*x + 2*c) + 2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*sqrt(a)*(arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1)))/d","B",0
346,1,263,0,1.245281," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{4 \, {\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)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{105 \, d {\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)}}"," ",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)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/(d*(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))","A",0
347,1,217,0,0.961597," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{4 \, {\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)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{5 \, d {\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)}}"," ",0,"4/5*(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)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/(d*(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))","B",0
348,1,125,0,1.008451," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{4 \, {\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)}}{3 \, d {\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}}}"," ",0,"4/3*(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)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2))","A",0
349,1,997,0,1.346332," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 4 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/2*((a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 4*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
350,1,803,0,1.263662," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + 3 \, {\left(a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} + 1\right) - a \arctan\left(-{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} - 1\right) - a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}}{4 \, d}"," ",0,"1/4*(2*(a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - (a*cos(d*x + c) - a)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + 3*(a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) + 1) - a*arctan2(-(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(d*x + c) - cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))) - 1) - a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))/d","B",0
351,1,1080,0,1.567296," ","integrate((a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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}}{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))/d","B",0
352,1,1942,0,1.862655," ","integrate((a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{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}}{96 \, d}"," ",0,"1/96*(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))/d","B",0
353,1,289,0,1.021174," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{8 \, {\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)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{315 \, d {\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)}}"," ",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)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/(d*(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))","A",0
354,1,243,0,1.040171," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{8 \, {\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)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{21 \, d {\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)}}"," ",0,"8/21*(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)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/(d*(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))","A",0
355,1,151,0,0.823102," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{8 \, {\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)}}{15 \, d {\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}}}"," ",0,"8/15*(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)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2))","A",0
356,1,1395,0,1.807965," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{30 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} a^{\frac{5}{2}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(2 \, d x + 2 \, c\right) - 3 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(12 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - a^{2} + 4 \, {\left(3 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, a^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + 3 \, {\left({\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} + 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)}, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} - 1\right) - {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 1\right) + {\left(a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 1\right)\right)} \sqrt{a}}{6 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} d}"," ",0,"1/6*(30*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*a^(5/2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(2*d*x + 2*c) - 3*a^2*sin(2*d*x + 2*c) - 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (12*a^2*sin(2*d*x + 2*c)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3*a^2*cos(2*d*x + 2*c) - a^2 + 4*(3*a^2*cos(2*d*x + 2*c) + 4*a^2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + 3*((a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) + 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))) - 1) - (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) + (a^2*cos(2*d*x + 2*c)^2 + a^2*sin(2*d*x + 2*c)^2 + 2*a^2*cos(2*d*x + 2*c) + a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*d)","B",0
357,1,973,0,1.570301," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{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}}{4 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/4*(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))/((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
358,1,1106,0,1.737221," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(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}}{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^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))/d","B",0
359,1,1964,0,1.708845," ","integrate((a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{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}}{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))/d","B",0
360,1,7450,0,2.144415," ","integrate((a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{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}}{768 \, {\left(4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 2 \, \cos\left(4 \, d x + 4 \, c\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} - \cos\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(4 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) \sin\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} d}"," ",0,"1/768*(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))/((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
361,-2,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(1+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
362,-2,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(1+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
363,-2,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(1+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
364,-2,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(1+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
365,-2,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/2)/(1+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
366,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\cos\left(d x + c\right) + 1} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(cos(d*x + c) + 1)*sec(d*x + c)^(3/2)), x)","F",0
367,-2,0,0,0.000000," ","integrate(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
368,-2,0,0,0.000000," ","integrate(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
369,-2,0,0,0.000000," ","integrate(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
370,-2,0,0,0.000000," ","integrate(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
371,-2,0,0,0.000000," ","integrate(1/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
372,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
373,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
374,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(3/2), x)","F",0
375,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(3/2), x)","F",0
376,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
377,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
378,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
379,-1,0,0,0.000000," ","integrate(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
380,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\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(sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a)^(5/2), x)","F",0
381,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(5/2), x)","F",0
382,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
383,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
384,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
385,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(7/2)), x)","F",0
386,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(a*cos(d*x + c) + a)^(7/2), x)","F",0
389,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(7/2)*sqrt(sec(d*x + c))), x)","F",0
390,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(7/2)*sec(d*x + c)^(3/2)), x)","F",0
391,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(7/2)*sec(d*x + c)^(5/2)), x)","F",0
392,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(7/2)*sec(d*x + c)^(7/2)), x)","F",0
393,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(7/2)*sec(d*x + c)^(9/2)), x)","F",0
394,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(9/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{9}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(9/2)*sec(d*x + c)^(5/2)), x)","F",0
395,0,0,0,0.000000," ","integrate(1/(a+a*cos(d*x+c))^(9/2)/sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{9}{2}} \sec\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((a*cos(d*x + c) + a)^(9/2)*sec(d*x + c)^(7/2)), x)","F",0
396,1,121,0,1.009579," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/4),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{\sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sqrt{2} a^{\frac{3}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{4}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{4}} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{\frac{1}{4}}}"," ",0,"4*(sqrt(2)*a^(3/2)*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(2)*a^(3/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/4)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(1/4))","B",0
397,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+a*cos(d*x+c))^4,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^4*cos(d*x + c)^m, x)","F",0
398,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+a*cos(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^3*cos(d*x + c)^m, x)","F",0
399,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^2*cos(d*x + c)^m, x)","F",0
400,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)*cos(d*x + c)^m, x)","F",0
401,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(a+a*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{m}}{a \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(a*cos(d*x + c) + a), x)","F",0
402,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(a+a*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{m}}{{\left(a \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(a*cos(d*x + c) + a)^2, x)","F",0
403,1,105,0,0.360933," ","integrate(cos(d*x+c)^7*(a+b*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{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)} a + 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)} b}{107520 \, d}"," ",0,"-1/107520*(3072*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a + 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))*b)/d","A",0
404,1,94,0,0.464556," ","integrate(cos(d*x+c)^6*(a+b*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a + 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)} b}{6720 \, d}"," ",0,"-1/6720*(35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a + 192*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*b)/d","A",0
405,1,84,0,0.577581," ","integrate(cos(d*x+c)^5*(a+b*cos(d*x+c)),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)} a - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b}{960 \, d}"," ",0,"1/960*(64*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*b)/d","A",0
406,1,69,0,0.466542," ","integrate(cos(d*x+c)^4*(a+b*cos(d*x+c)),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)} 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)} b}{480 \, d}"," ",0,"1/480*(15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*b)/d","A",0
407,1,57,0,0.898707," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b}{96 \, d}"," ",0,"-1/96*(32*(sin(d*x + c)^3 - 3*sin(d*x + c))*a - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b)/d","A",0
408,1,46,0,0.503761," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a - 4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} b}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a - 4*(sin(d*x + c)^3 - 3*sin(d*x + c))*b)/d","A",0
409,1,34,0,0.654722," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b + 4 \, a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*b + 4*a*sin(d*x + c))/d","A",0
410,1,15,0,0.674348," ","integrate(a+b*cos(d*x+c),x, algorithm=""maxima"")","a x + \frac{b \sin\left(d x + c\right)}{d}"," ",0,"a*x + b*sin(d*x + c)/d","A",0
411,1,28,0,0.322396," ","integrate((a+b*cos(d*x+c))*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)}{d}"," ",0,"((d*x + c)*b + a*log(sec(d*x + c) + tan(d*x + c)))/d","A",0
412,1,38,0,0.701586," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{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*(b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*a*tan(d*x + c))/d","A",0
413,1,58,0,0.342037," ","integrate((a+b*cos(d*x+c))*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)} - 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)) - 4*b*tan(d*x + c))/d","A",0
414,1,70,0,0.532404," ","integrate((a+b*cos(d*x+c))*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 \, 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)))/d","A",0
415,1,95,0,0.634262," ","integrate((a+b*cos(d*x+c))*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)}}{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)))/d","A",0
416,1,107,0,0.692459," ","integrate((a+b*cos(d*x+c))*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 - 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 - 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
417,1,120,0,0.528243," ","integrate(cos(d*x+c)^4*(a+b*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^{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)} a 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)} b^{2}}{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^2 + 128*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a*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))*b^2)/d","A",0
418,1,94,0,0.342762," ","integrate(cos(d*x+c)^3*(a+b*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^{2} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b - 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)} b^{2}}{240 \, d}"," ",0,"-1/240*(80*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a*b - 16*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*b^2)/d","A",0
419,1,82,0,0.833821," ","integrate(cos(d*x+c)^2*(a+b*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^{2} - 64 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + 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)} b^{2}}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2 - 64*(sin(d*x + c)^3 - 3*sin(d*x + c))*a*b + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b^2)/d","A",0
420,1,60,0,0.689100," ","integrate(cos(d*x+c)*(a+b*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)} a b - 2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} b^{2} + 6 \, a^{2} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b - 2*(sin(d*x + c)^3 - 3*sin(d*x + c))*b^2 + 6*a^2*sin(d*x + c))/d","A",0
421,1,44,0,0.773813," ","integrate((a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b^{2}}{4 \, d} + \frac{2 \, a b \sin\left(d x + c\right)}{d}"," ",0,"a^2*x + 1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*b^2/d + 2*a*b*sin(d*x + c)/d","A",0
422,1,42,0,0.600773," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} a b + a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + b^{2} \sin\left(d x + c\right)}{d}"," ",0,"(2*(d*x + c)*a*b + a^2*log(sec(d*x + c) + tan(d*x + c)) + b^2*sin(d*x + c))/d","A",0
423,1,48,0,0.420661," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} b^{2} + a b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + a^{2} \tan\left(d x + c\right)}{d}"," ",0,"((d*x + c)*b^2 + a*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + a^2*tan(d*x + c))/d","A",0
424,1,87,0,0.570227," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^3,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 2 \, b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 8 \, a b \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) - 2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 8*a*b*tan(d*x + c))/d","A",0
425,1,84,0,0.333639," ","integrate((a+b*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^{2} - 3 \, a b {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 6 \, 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^2 - 3*a*b*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)) + 6*b^2*tan(d*x + c))/d","A",0
426,1,144,0,0.672405," ","integrate((a+b*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 b - 3 \, a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, 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 \, d}"," ",0,"1/48*(32*(tan(d*x + c)^3 + 3*tan(d*x + c))*a*b - 3*a^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 12*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)))/d","A",0
427,1,132,0,0.553149," ","integrate((a+b*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^{2} + 40 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} b^{2} - 15 \, a b {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{120 \, d}"," ",0,"1/120*(8*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^2 + 40*(tan(d*x + c)^3 + 3*tan(d*x + c))*b^2 - 15*a*b*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)))/d","A",0
428,1,145,0,0.614020," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","-\frac{320 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b - 192 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a 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)} b^{3}}{960 \, d}"," ",0,"-1/960*(320*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3 - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2*b - 192*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + 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))*b^3)/d","A",0
429,1,119,0,0.666442," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 480 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} b + 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^{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)} b^{3}}{480 \, d}"," ",0,"1/480*(120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 - 480*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2*b + 45*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a*b^2 + 32*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*b^3)/d","A",0
430,1,95,0,0.364278," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b - 32 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a b^{2} + {\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^{3} + 32 \, a^{3} \sin\left(d x + c\right)}{32 \, d}"," ",0,"1/32*(24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2*b - 32*(sin(d*x + c)^3 - 3*sin(d*x + c))*a*b^2 + (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b^3 + 32*a^3*sin(d*x + c))/d","A",0
431,1,72,0,0.613985," ","integrate((a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x + \frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{2}}{4 \, d} - \frac{{\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} b^{3}}{3 \, d} + \frac{3 \, a^{2} b \sin\left(d x + c\right)}{d}"," ",0,"a^3*x + 3/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b^2/d - 1/3*(sin(d*x + c)^3 - 3*sin(d*x + c))*b^3/d + 3*a^2*b*sin(d*x + c)/d","A",0
432,1,69,0,0.344561," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} a^{2} b + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b^{3} + 4 \, a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 12 \, a b^{2} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(12*(d*x + c)*a^2*b + (2*d*x + 2*c + sin(2*d*x + 2*c))*b^3 + 4*a^3*log(sec(d*x + c) + tan(d*x + c)) + 12*a*b^2*sin(d*x + c))/d","A",0
433,1,66,0,0.885662," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a b^{2} + 3 \, a^{2} b {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 2 \, b^{3} \sin\left(d x + c\right) + 2 \, a^{3} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(6*(d*x + c)*a*b^2 + 3*a^2*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 2*b^3*sin(d*x + c) + 2*a^3*tan(d*x + c))/d","A",0
434,1,101,0,0.625334," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} b^{3} - 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 b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{2} b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(4*(d*x + c)*b^3 - 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*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*a^2*b*tan(d*x + c))/d","A",0
435,1,113,0,0.833244," ","integrate((a+b*cos(d*x+c))^3*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} - 9 \, 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)} + 6 \, 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 \, 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^3 - 9*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)) + 6*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 36*a*b^2*tan(d*x + c))/d","A",0
436,1,158,0,0.803118," ","integrate((a+b*cos(d*x+c))^3*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^{2} 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)} - 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)} + 16 \, 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^2*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)) - 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)) + 16*b^3*tan(d*x + c))/d","A",0
437,1,181,0,0.651553," ","integrate((a+b*cos(d*x+c))^3*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^{3} + 240 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a b^{2} - 45 \, 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)} - 60 \, 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 \, d}"," ",0,"1/240*(16*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^3 + 240*(tan(d*x + c)^3 + 3*tan(d*x + c))*a*b^2 - 45*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)) - 60*b^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
438,1,192,0,0.664105," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^4,x, algorithm=""maxima"")","-\frac{560 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} b - 672 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{2} b^{2} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{3} + 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)} b^{4}}{1680 \, d}"," ",0,"-1/1680*(560*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3*b - 672*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2*b^2 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a*b^3 + 48*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*b^4)/d","A",0
439,1,170,0,0.582594," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 1280 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} b + 180 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b^{2} + 256 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a 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)} b^{4}}{960 \, d}"," ",0,"1/960*(240*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 - 1280*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3*b + 180*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2*b^2 + 256*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + 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))*b^4)/d","A",0
440,1,133,0,0.673630," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4,x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} b - 240 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2} b^{2} + 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{3} + 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)} b^{4} + 120 \, a^{4} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3*b - 240*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^2*b^2 + 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a*b^3 + 8*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*b^4 + 120*a^4*sin(d*x + c))/d","A",0
441,1,111,0,0.697122," ","integrate((a+b*cos(d*x+c))^4,x, algorithm=""maxima"")","a^{4} x + \frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b^{2}}{2 \, d} - \frac{4 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a b^{3}}{3 \, d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b^{4}}{32 \, d} + \frac{4 \, a^{3} b \sin\left(d x + c\right)}{d}"," ",0,"a^4*x + 3/2*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2*b^2/d - 4/3*(sin(d*x + c)^3 - 3*sin(d*x + c))*a*b^3/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b^4/d + 4*a^3*b*sin(d*x + c)/d","A",0
442,1,95,0,0.680672," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} a^{3} b + 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{3} - {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} b^{4} + 3 \, a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + 18 \, a^{2} b^{2} \sin\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(12*(d*x + c)*a^3*b + 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b^3 - (sin(d*x + c)^3 - 3*sin(d*x + c))*b^4 + 3*a^4*log(sec(d*x + c) + tan(d*x + c)) + 18*a^2*b^2*sin(d*x + c))/d","A",0
443,1,90,0,0.631799," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^2,x, algorithm=""maxima"")","\frac{24 \, {\left(d x + c\right)} a^{2} b^{2} + {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b^{4} + 8 \, 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)} + 16 \, a b^{3} \sin\left(d x + c\right) + 4 \, a^{4} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(24*(d*x + c)*a^2*b^2 + (2*d*x + 2*c + sin(2*d*x + 2*c))*b^4 + 8*a^3*b*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 16*a*b^3*sin(d*x + c) + 4*a^4*tan(d*x + c))/d","A",0
444,1,115,0,0.858251," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^3,x, algorithm=""maxima"")","\frac{16 \, {\left(d x + c\right)} a b^{3} - 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^{2} b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, b^{4} \sin\left(d x + c\right) + 16 \, a^{3} b \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(16*(d*x + c)*a*b^3 - 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^2*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*b^4*sin(d*x + c) + 16*a^3*b*tan(d*x + c))/d","A",0
445,1,125,0,0.631046," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^4,x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{4} + 3 \, {\left(d x + c\right)} b^{4} - 3 \, 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)} + 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)} + 18 \, a^{2} b^{2} \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 3*tan(d*x + c))*a^4 + 3*(d*x + c)*b^4 - 3*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)) + 6*a*b^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 18*a^2*b^2*tan(d*x + c))/d","A",0
446,1,187,0,0.978225," ","integrate((a+b*cos(d*x+c))^4*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^{3} b - 3 \, a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 72 \, a^{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)} + 24 \, b^{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 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^3*b - 3*a^4*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 72*a^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)) + 24*b^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 192*a*b^3*tan(d*x + c))/d","A",0
447,1,195,0,1.201350," ","integrate((a+b*cos(d*x+c))^4*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^{4} + 120 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} b^{2} - 15 \, 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 \, 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)} + 60 \, 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^4 + 120*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2*b^2 - 15*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*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)) + 60*b^4*tan(d*x + c))/d","A",0
448,1,275,0,0.761616," ","integrate((a+b*cos(d*x+c))^4*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^{3} b + 640 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a b^{3} - 5 \, a^{4} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 180 \, a^{2} b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} - 5 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 120 \, b^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"1/480*(128*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^3*b + 640*(tan(d*x + c)^3 + 3*tan(d*x + c))*a*b^3 - 5*a^4*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 180*a^2*b^2*(2*(3*sin(d*x + c)^3 - 5*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 120*b^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) - log(sin(d*x + c) + 1) + log(sin(d*x + c) - 1)))/d","A",0
449,-2,0,0,0.000000," ","integrate(cos(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
450,-2,0,0,0.000000," ","integrate(cos(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
451,-2,0,0,0.000000," ","integrate(cos(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
452,-2,0,0,0.000000," ","integrate(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
453,-2,0,0,0.000000," ","integrate(cos(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
454,-2,0,0,0.000000," ","integrate(1/(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
455,-2,0,0,0.000000," ","integrate(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
456,-2,0,0,0.000000," ","integrate(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
457,-2,0,0,0.000000," ","integrate(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
458,-2,0,0,0.000000," ","integrate(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
459,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(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
460,-2,0,0,0.000000," ","integrate(cos(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
461,-2,0,0,0.000000," ","integrate(cos(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
462,-2,0,0,0.000000," ","integrate(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
463,-2,0,0,0.000000," ","integrate(cos(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
464,-2,0,0,0.000000," ","integrate(1/(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
465,-2,0,0,0.000000," ","integrate(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
466,-2,0,0,0.000000," ","integrate(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
467,-2,0,0,0.000000," ","integrate(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
468,-2,0,0,0.000000," ","integrate(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
469,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(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
470,-2,0,0,0.000000," ","integrate(cos(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
471,-2,0,0,0.000000," ","integrate(cos(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
472,-2,0,0,0.000000," ","integrate(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
473,-2,0,0,0.000000," ","integrate(cos(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
474,-2,0,0,0.000000," ","integrate(1/(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
475,-2,0,0,0.000000," ","integrate(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
476,-2,0,0,0.000000," ","integrate(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
477,-2,0,0,0.000000," ","integrate(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
478,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(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
479,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(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
480,-2,0,0,0.000000," ","integrate(cos(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
481,-2,0,0,0.000000," ","integrate(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
482,-2,0,0,0.000000," ","integrate(cos(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
483,-2,0,0,0.000000," ","integrate(1/(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
484,-2,0,0,0.000000," ","integrate(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
485,-2,0,0,0.000000," ","integrate(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
486,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
487,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
488,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*cos(d*x + c), x)","F",0
489,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a), x)","F",0
490,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
491,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
492,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
493,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
494,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
495,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
496,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2), x)","F",0
497,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
498,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
499,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
500,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
501,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
502,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
503,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2), x)","F",0
504,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
505,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
506,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
507,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
508,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(7/2), x)","F",0
509,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(4*cos(d*x + c) + 3)*cos(d*x + c)^3, x)","F",0
510,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(4*cos(d*x + c) + 3)*cos(d*x + c)^2, x)","F",0
511,0,0,0,0.000000," ","integrate(cos(d*x+c)*(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(4*cos(d*x + c) + 3)*cos(d*x + c), x)","F",0
512,0,0,0,0.000000," ","integrate((3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(d x + c\right) + 3}\,{d x}"," ",0,"integrate(sqrt(4*cos(d*x + c) + 3), x)","F",0
513,0,0,0,0.000000," ","integrate(sec(d*x+c)*(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(4*cos(d*x + c) + 3)*sec(d*x + c), x)","F",0
514,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(4*cos(d*x + c) + 3)*sec(d*x + c)^2, x)","F",0
515,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(4*cos(d*x + c) + 3)*sec(d*x + c)^3, x)","F",0
516,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c)^3, x)","F",0
517,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c)^2, x)","F",0
518,0,0,0,0.000000," ","integrate(cos(d*x+c)*(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c), x)","F",0
519,0,0,0,0.000000," ","integrate((3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-4 \, \cos\left(d x + c\right) + 3}\,{d x}"," ",0,"integrate(sqrt(-4*cos(d*x + c) + 3), x)","F",0
520,0,0,0,0.000000," ","integrate(sec(d*x+c)*(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c), x)","F",0
521,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c)^2, x)","F",0
522,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c)^3, x)","F",0
523,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
524,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
525,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
526,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*cos(d*x + c) + a), x)","F",0
527,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
528,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
529,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
530,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(b*cos(d*x + c) + a)^(3/2), x)","F",0
531,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
532,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
533,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
534,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(-3/2), x)","F",0
535,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
536,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*cos(d*x + c) + a)^(3/2), x)","F",0
537,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(b*cos(d*x + c) + a)^(3/2), x)","F",0
538,0,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{5}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^5/(b*cos(d*x + c) + a)^(5/2), x)","F",0
539,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(b*cos(d*x + c) + a)^(5/2), x)","F",0
540,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/(b*cos(d*x + c) + a)^(5/2), x)","F",0
541,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
542,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
543,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(-5/2), x)","F",0
544,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
545,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*cos(d*x + c) + a)^(5/2), x)","F",0
546,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(-7/2), x)","F",0
547,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/sqrt(4*cos(d*x + c) + 3), x)","F",0
548,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(4*cos(d*x + c) + 3), x)","F",0
549,0,0,0,0.000000," ","integrate(cos(d*x+c)/(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(4*cos(d*x + c) + 3), x)","F",0
550,0,0,0,0.000000," ","integrate(1/(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(1/sqrt(4*cos(d*x + c) + 3), x)","F",0
551,0,0,0,0.000000," ","integrate(sec(d*x+c)/(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(4*cos(d*x + c) + 3), x)","F",0
552,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(4*cos(d*x + c) + 3), x)","F",0
553,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(3+4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(4*cos(d*x + c) + 3), x)","F",0
554,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3}}{\sqrt{-4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/sqrt(-4*cos(d*x + c) + 3), x)","F",0
555,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{-4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(-4*cos(d*x + c) + 3), x)","F",0
556,0,0,0,0.000000," ","integrate(cos(d*x+c)/(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{-4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(-4*cos(d*x + c) + 3), x)","F",0
557,0,0,0,0.000000," ","integrate(1/(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(1/sqrt(-4*cos(d*x + c) + 3), x)","F",0
558,0,0,0,0.000000," ","integrate(sec(d*x+c)/(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{-4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(-4*cos(d*x + c) + 3), x)","F",0
559,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{-4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(-4*cos(d*x + c) + 3), x)","F",0
560,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(3-4*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{-4 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(-4*cos(d*x + c) + 3), x)","F",0
561,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(5/2), x)","F",0
562,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^(3/2), x)","F",0
563,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(cos(d*x + c)), x)","F",0
564,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/sqrt(cos(d*x + c)), x)","F",0
565,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/cos(d*x + c)^(3/2), x)","F",0
566,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/cos(d*x + c)^(5/2), x)","F",0
567,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/cos(d*x + c)^(7/2), x)","F",0
568,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*cos(d*x + c)^(5/2), x)","F",0
569,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2), x)","F",0
570,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c)), x)","F",0
571,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/sqrt(cos(d*x + c)), x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/cos(d*x + c)^(3/2), x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/cos(d*x + c)^(5/2), x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/cos(d*x + c)^(7/2), x)","F",0
575,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*cos(d*x + c)^(3/2), x)","F",0
576,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*sqrt(cos(d*x + c)), x)","F",0
577,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/sqrt(cos(d*x + c)), x)","F",0
578,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/cos(d*x + c)^(3/2), x)","F",0
579,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/cos(d*x + c)^(5/2), x)","F",0
580,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/cos(d*x + c)^(7/2), x)","F",0
581,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/cos(d*x + c)^(9/2), x)","F",0
582,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
583,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
584,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
585,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
586,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
587,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
588,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/2)/(b*cos(d*x + c) + a)^2, x)","F",0
589,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^2, x)","F",0
590,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
591,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
592,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*sqrt(cos(d*x + c))), x)","F",0
593,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*cos(d*x + c)^(3/2)), x)","F",0
594,-1,0,0,0.000000," ","integrate(1/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
595,0,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{9}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(9/2)/(b*cos(d*x + c) + a)^3, x)","F",0
596,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/2)/(b*cos(d*x + c) + a)^3, x)","F",0
597,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^3, x)","F",0
598,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^3, x)","F",0
599,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^3, x)","F",0
600,-1,0,0,0.000000," ","integrate(1/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
601,-2,0,0,0.000000," ","integrate(1/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
602,-1,0,0,0.000000," ","integrate(1/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
603,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
604,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
605,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
606,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
607,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
608,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
609,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
610,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2), x)","F",0
611,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
613,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(3/2), x)","F",0
614,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
615,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(7/2), x)","F",0
616,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(9/2), x)","F",0
617,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(11/2), x)","F",0
618,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c)), x)","F",0
619,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)/sqrt(cos(d*x + c)), x)","F",0
620,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(3/2), x)","F",0
621,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(5/2), x)","F",0
622,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(7/2), x)","F",0
623,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(9/2), x)","F",0
624,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(11/2), x)","F",0
625,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(5/2)/cos(d*x + c)^(13/2), x)","F",0
626,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
627,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
628,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))), x)","F",0
629,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)), x)","F",0
630,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)), x)","F",0
631,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\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(cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
632,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\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(cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
633,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
634,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c))), x)","F",0
635,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(3/2)), x)","F",0
636,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(5/2)), x)","F",0
637,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(3/2)*cos(d*x + c)^(7/2)), x)","F",0
638,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\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(cos(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
639,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\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(cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
640,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
641,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^(5/2)*sqrt(cos(d*x + c))), x)","F",0
642,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(3/2)), x)","F",0
643,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(5/2)*cos(d*x + c)^(5/2)), x)","F",0
644,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{3 \, \cos\left(d x + c\right) + 2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))), x)","F",0
645,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{3 \, \cos\left(d x + c\right) - 2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(3*cos(d*x + c) - 2)*sqrt(cos(d*x + c))), x)","F",0
646,0,0,0,0.000000," ","integrate(1/(2-3*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-3 \, \cos\left(d x + c\right) + 2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))), x)","F",0
647,0,0,0,0.000000," ","integrate(1/(-2-3*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-3 \, \cos\left(d x + c\right) - 2} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*cos(d*x + c) - 2)*sqrt(cos(d*x + c))), x)","F",0
648,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{2 \, \cos\left(d x + c\right) + 3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*cos(d*x + c) + 3)*sqrt(cos(d*x + c))), x)","F",0
649,0,0,0,0.000000," ","integrate(1/(3-2*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-2 \, \cos\left(d x + c\right) + 3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-2*cos(d*x + c) + 3)*sqrt(cos(d*x + c))), x)","F",0
650,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{2 \, \cos\left(d x + c\right) - 3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*cos(d*x + c) - 3)*sqrt(cos(d*x + c))), x)","F",0
651,0,0,0,0.000000," ","integrate(1/(-3-2*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-2 \, \cos\left(d x + c\right) - 3} \sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-2*cos(d*x + c) - 3)*sqrt(cos(d*x + c))), x)","F",0
652,0,0,0,0.000000," ","integrate(1/(-cos(d*x+c))^(1/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(d x + c\right)} \sqrt{3 \, \cos\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-cos(d*x + c))*sqrt(3*cos(d*x + c) + 2)), x)","F",0
653,0,0,0,0.000000," ","integrate(1/(-cos(d*x+c))^(1/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(d x + c\right)} \sqrt{3 \, \cos\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-cos(d*x + c))*sqrt(3*cos(d*x + c) - 2)), x)","F",0
654,0,0,0,0.000000," ","integrate(1/(2-3*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(d x + c\right)} \sqrt{-3 \, \cos\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-cos(d*x + c))*sqrt(-3*cos(d*x + c) + 2)), x)","F",0
655,0,0,0,0.000000," ","integrate(1/(-2-3*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(d x + c\right)} \sqrt{-3 \, \cos\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-cos(d*x + c))*sqrt(-3*cos(d*x + c) - 2)), x)","F",0
656,0,0,0,0.000000," ","integrate(1/(-cos(d*x+c))^(1/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(d x + c\right)} \sqrt{2 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(1/(sqrt(-cos(d*x + c))*sqrt(2*cos(d*x + c) + 3)), x)","F",0
657,0,0,0,0.000000," ","integrate(1/(3-2*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(d x + c\right)} \sqrt{-2 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(1/(sqrt(-cos(d*x + c))*sqrt(-2*cos(d*x + c) + 3)), x)","F",0
658,0,0,0,0.000000," ","integrate(1/(-cos(d*x+c))^(1/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(d x + c\right)} \sqrt{2 \, \cos\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(1/(sqrt(-cos(d*x + c))*sqrt(2*cos(d*x + c) - 3)), x)","F",0
659,0,0,0,0.000000," ","integrate(1/(-3-2*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(d x + c\right)} \sqrt{-2 \, \cos\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(1/(sqrt(-cos(d*x + c))*sqrt(-2*cos(d*x + c) - 3)), x)","F",0
660,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{3 \, \cos\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(3*cos(d*x + c) + 2), x)","F",0
661,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{3 \, \cos\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(3*cos(d*x + c) - 2), x)","F",0
662,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(2-3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{-3 \, \cos\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(-3*cos(d*x + c) + 2), x)","F",0
663,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(-2-3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{-3 \, \cos\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(-3*cos(d*x + c) - 2), x)","F",0
664,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{2 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(2*cos(d*x + c) + 3), x)","F",0
665,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(3-2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{-2 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(-2*cos(d*x + c) + 3), x)","F",0
666,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{2 \, \cos\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(2*cos(d*x + c) - 3), x)","F",0
667,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(-3-2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{-2 \, \cos\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(cos(d*x + c))/sqrt(-2*cos(d*x + c) - 3), x)","F",0
668,0,0,0,0.000000," ","integrate((-cos(d*x+c))^(1/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{3 \, \cos\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(-cos(d*x + c))/sqrt(3*cos(d*x + c) + 2), x)","F",0
669,0,0,0,0.000000," ","integrate((-cos(d*x+c))^(1/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{3 \, \cos\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(-cos(d*x + c))/sqrt(3*cos(d*x + c) - 2), x)","F",0
670,0,0,0,0.000000," ","integrate((-cos(d*x+c))^(1/2)/(2-3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{-3 \, \cos\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(-cos(d*x + c))/sqrt(-3*cos(d*x + c) + 2), x)","F",0
671,0,0,0,0.000000," ","integrate((-cos(d*x+c))^(1/2)/(-2-3*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{-3 \, \cos\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(-cos(d*x + c))/sqrt(-3*cos(d*x + c) - 2), x)","F",0
672,0,0,0,0.000000," ","integrate((-cos(d*x+c))^(1/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{2 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(-cos(d*x + c))/sqrt(2*cos(d*x + c) + 3), x)","F",0
673,0,0,0,0.000000," ","integrate((-cos(d*x+c))^(1/2)/(3-2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{-2 \, \cos\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(-cos(d*x + c))/sqrt(-2*cos(d*x + c) + 3), x)","F",0
674,0,0,0,0.000000," ","integrate((-cos(d*x+c))^(1/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{2 \, \cos\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(-cos(d*x + c))/sqrt(2*cos(d*x + c) - 3), x)","F",0
675,0,0,0,0.000000," ","integrate((-cos(d*x+c))^(1/2)/(-3-2*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{-2 \, \cos\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(-cos(d*x + c))/sqrt(-2*cos(d*x + c) - 3), x)","F",0
676,0,0,0,0.000000," ","integrate(cos(d*x+c)^(2/3)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{2}{3}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(2/3)/(b*cos(d*x + c) + a), x)","F",0
677,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/3)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{1}{3}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^(1/3)/(b*cos(d*x + c) + a), x)","F",0
678,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/3)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*cos(d*x + c)^(1/3)), x)","F",0
679,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(2/3)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*cos(d*x + c)^(2/3)), x)","F",0
680,0,0,0,0.000000," ","integrate(cos(d*x+c)^(7/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{7}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(7/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
681,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{5}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(5/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
682,0,0,0,0.000000," ","integrate(cos(d*x+c)^(4/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{4}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(4/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
683,0,0,0,0.000000," ","integrate(cos(d*x+c)^(2/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{2}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(2/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
684,0,0,0,0.000000," ","integrate(cos(d*x+c)^(1/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{\frac{1}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^(1/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
685,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(1/3)), x)","F",0
686,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(2/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(2/3)), x)","F",0
687,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(4/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(4/3)), x)","F",0
688,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/3)), x)","F",0
689,0,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(7/3)), x)","F",0
690,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(7/2), x)","F",0
691,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2), x)","F",0
692,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2), x)","F",0
693,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(sec(d*x + c)), x)","F",0
694,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/sqrt(sec(d*x + c)), x)","F",0
695,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/sec(d*x + c)^(3/2), x)","F",0
696,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/sec(d*x + c)^(5/2), x)","F",0
697,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*sec(d*x + c)^(9/2), x)","F",0
698,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*sec(d*x + c)^(7/2), x)","F",0
699,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2), x)","F",0
700,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2), x)","F",0
701,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c)), x)","F",0
702,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/sqrt(sec(d*x + c)), x)","F",0
703,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/sec(d*x + c)^(3/2), x)","F",0
704,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2/sec(d*x + c)^(5/2), x)","F",0
705,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*sec(d*x + c)^(9/2), x)","F",0
706,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*sec(d*x + c)^(7/2), x)","F",0
707,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2), x)","F",0
708,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2), x)","F",0
709,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c)), x)","F",0
710,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/sqrt(sec(d*x + c)), x)","F",0
711,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3/sec(d*x + c)^(3/2), x)","F",0
712,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a), x)","F",0
713,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
714,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
715,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
716,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
717,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
718,-1,0,0,0.000000," ","integrate(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
719,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^2, x)","F",0
720,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^2, x)","F",0
721,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*sqrt(sec(d*x + c))), x)","F",0
722,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(3/2)), x)","F",0
723,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^2*sec(d*x + c)^(5/2)), x)","F",0
724,-1,0,0,0.000000," ","integrate(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
725,-1,0,0,0.000000," ","integrate(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
726,-1,0,0,0.000000," ","integrate(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
727,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^3*sqrt(sec(d*x + c))), x)","F",0
728,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(3/2)), x)","F",0
729,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^3*sec(d*x + c)^(5/2)), x)","F",0
730,0,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
731,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
732,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
733,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
734,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
735,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \cos\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
736,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(9/2), x)","F",0
737,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(7/2), x)","F",0
738,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2), x)","F",0
739,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
740,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
741,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
742,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
743,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(11/2), x)","F",0
744,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(9/2), x)","F",0
745,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(7/2), x)","F",0
746,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2), x)","F",0
747,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int {\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((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2), x)","F",0
748,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c)), x)","F",0
749,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^(5/2)/sqrt(sec(d*x + c)), x)","F",0
750,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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((b*cos(d*x + c) + a)^(5/2)/sec(d*x + c)^(3/2), x)","F",0
751,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
752,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
753,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
754,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
755,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
756,0,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
757,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
758,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(3/2), x)","F",0
759,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(3/2), x)","F",0
760,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c))), x)","F",0
761,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2)), x)","F",0
762,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2)), x)","F",0
763,0,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(5/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
764,0,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\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(sec(d*x + c)^(3/2)/(b*cos(d*x + c) + a)^(5/2), x)","F",0
765,0,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(d x + c\right)}}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(sec(d*x + c))/(b*cos(d*x + c) + a)^(5/2), x)","F",0
766,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*cos(d*x + c) + a)^(5/2)*sqrt(sec(d*x + c))), x)","F",0
767,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(3/2)), x)","F",0
768,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\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(1/((b*cos(d*x + c) + a)^(5/2)*sec(d*x + c)^(5/2)), x)","F",0
769,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^4,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{4} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^4*cos(d*x + c)^m, x)","F",0
770,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*cos(d*x + c)^m, x)","F",0
771,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*cos(d*x + c)^m, x)","F",0
772,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)*cos(d*x + c)^m, x)","F",0
773,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(b*cos(d*x + c) + a), x)","F",0
774,0,0,0,0.000000," ","integrate(cos(d*x+c)^m/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{m}}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cos(d*x + c)^m/(b*cos(d*x + c) + a)^2, x)","F",0
775,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^m,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{3} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^3*sec(d*x + c)^m, x)","F",0
776,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^m,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)}^{2} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)^2*sec(d*x + c)^m, x)","F",0
777,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)^m,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c) + a)*sec(d*x + c)^m, x)","F",0
778,-2,0,0,0.000000," ","integrate((1-cos(x))^(1/2)/(a-cos(x))^(1/2),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(a-1>0)', see `assume?` for more details)Is a-1 zero or nonzero?","F(-2)",0
779,-2,0,0,0.000000," ","integrate(((1-cos(x))/(a-cos(x)))^(1/2),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(a-1>0)', see `assume?` for more details)Is a-1 zero or nonzero?","F(-2)",0
780,1,45,0,0.318462," ","integrate((a+a*cos(d*x+c))*(-1/2*B+B*cos(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a - 2 \, {\left(d x + c\right)} B a + 2 \, B a \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B*a - 2*(d*x + c)*B*a + 2*B*a*sin(d*x + c))/d","A",0
781,1,144,0,0.344644," ","integrate((a+a*cos(d*x+c))^4*(-4/5*B+B*cos(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\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} - 28 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} B 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)} B a^{4} - 6 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B a^{4} - 24 \, {\left(d x + c\right)} B a^{4} - 66 \, B a^{4} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(2*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*B*a^4 - 28*(sin(d*x + c)^3 - 3*sin(d*x + c))*B*a^4 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*B*a^4 - 6*(2*d*x + 2*c + sin(2*d*x + 2*c))*B*a^4 - 24*(d*x + c)*B*a^4 - 66*B*a^4*sin(d*x + c))/d","B",0
782,1,143,0,0.632707," ","integrate((a+a*cos(d*x+c))^n*(-B*n/(1+n)+B*cos(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} B a^{n} \sin\left(-{\left(d x + c\right)} {\left(n + 1\right)} + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right)\right) - {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{n} B a^{n} \sin\left(-{\left(d x + c\right)} {\left(n - 1\right)} + 2 \, n \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right)\right)}{2 \cdot 2^{n} d {\left(n + 1\right)}}"," ",0,"-1/2*((cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*B*a^n*sin(-(d*x + c)*(n + 1) + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1)) - (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^n*B*a^n*sin(-(d*x + c)*(n - 1) + 2*n*arctan2(sin(d*x + c), cos(d*x + c) + 1)))/(2^n*d*(n + 1))","B",0
783,1,115,0,0.336558," ","integrate((-3/2*B+B*cos(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{2 \, 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}}}{40 \, d}"," ",0,"-1/40*(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 - 2*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","B",0
784,1,92,0,0.535386," ","integrate((a+a*cos(d*x+c))^(3/2)*(-3/5*B+B*cos(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)} B \sqrt{a} - 2 \, {\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}}{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))*B*sqrt(a) - 2*(sqrt(2)*a*sin(3/2*d*x + 3/2*c) + 9*sqrt(2)*a*sin(1/2*d*x + 1/2*c))*B*sqrt(a))/d","B",0
785,-1,0,0,0.000000," ","integrate((B+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
786,-1,0,0,0.000000," ","integrate((-5/3*B+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
787,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(2/3), x)","F",0
788,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(1/3), x)","F",0
789,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(a*cos(d*x + c) + a)^(1/3), x)","F",0
790,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(a*cos(d*x + c) + a)^(2/3), x)","F",0
791,-2,0,0,0.000000," ","integrate((b*B/a+B*cos(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
792,-2,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(b+a*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*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
793,1,52,0,0.428692," ","integrate((3+cos(d*x+c))/(2-cos(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) - 3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)\right)}}{3 \, d}"," ",0,"2/3*(5*sqrt(3)*arctan(sqrt(3)*sin(d*x + c)/(cos(d*x + c) + 1)) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
794,0,0,0,0.000000," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B b \cos\left(d x + c\right) + B a}{\sqrt{b \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*b*cos(d*x + c) + B*a)/sqrt(b*cos(d*x + c) + a), x)","F",0
795,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(2/3), x)","F",0
796,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(1/3), x)","F",0
797,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(1/3), x)","F",0
798,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(2/3), x)","F",0
799,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*cos(d*x + c)^2, x)","F",0
800,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*cos(d*x + c), x)","F",0
801,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c)), x)","F",0
802,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c), x)","F",0
803,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^2, x)","F",0
804,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^3, x)","F",0
805,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^4, x)","F",0
806,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(3/2)*cos(d*x + c), x)","F",0
807,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(3/2), x)","F",0
808,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(3/2)*sec(d*x + c), x)","F",0
809,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(3/2)*sec(d*x + c)^2, x)","F",0
810,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(3/2)*sec(d*x + c)^3, x)","F",0
811,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(3/2)*sec(d*x + c)^4, x)","F",0
812,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(3/2)*sec(d*x + c)^5, x)","F",0
813,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(5/2), x)","F",0
814,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(5/2)*sec(d*x + c), x)","F",0
815,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(5/2)*sec(d*x + c)^2, x)","F",0
816,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(5/2)*sec(d*x + c)^3, x)","F",0
817,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(5/2)*sec(d*x + c)^4, x)","F",0
818,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(5/2)*sec(d*x + c)^5, x)","F",0
819,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(5/2)*sec(d*x + c)^6, x)","F",0
820,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^3/sqrt(b*cos(d*x + c)), x)","F",0
821,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^2/sqrt(b*cos(d*x + c)), x)","F",0
822,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)/sqrt(b*cos(d*x + c)), x)","F",0
823,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/sqrt(b*cos(d*x + c)), x)","F",0
824,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)/sqrt(b*cos(d*x + c)), x)","F",0
825,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^2/sqrt(b*cos(d*x + c)), x)","F",0
826,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^3/sqrt(b*cos(d*x + c)), x)","F",0
827,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{4}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^4/(b*cos(d*x + c))^(3/2), x)","F",0
828,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^3/(b*cos(d*x + c))^(3/2), x)","F",0
829,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c))^(3/2), x)","F",0
830,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c))^(3/2), x)","F",0
831,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c))^(3/2), x)","F",0
832,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c))^(3/2), x)","F",0
833,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^2/(b*cos(d*x + c))^(3/2), x)","F",0
834,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{5}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^5/(b*cos(d*x + c))^(5/2), x)","F",0
835,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{4}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^4/(b*cos(d*x + c))^(5/2), x)","F",0
836,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^3/(b*cos(d*x + c))^(5/2), x)","F",0
837,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c))^(5/2), x)","F",0
838,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c))^(5/2), x)","F",0
839,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c))^(5/2), x)","F",0
840,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c))^(5/2), x)","F",0
841,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\left(b \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c))^(7/2), x)","F",0
842,1,93,0,0.714305," ","integrate(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)\right)} B \sqrt{b} + 8 \, A \sqrt{b} {\left(\sin\left(3 \, d x + 3 \, c\right) + 9 \, \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)}}{96 \, d}"," ",0,"1/96*(3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*B*sqrt(b) + 8*A*sqrt(b)*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))))/d","A",0
843,1,68,0,0.727778," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{b} + B \sqrt{b} {\left(\sin\left(3 \, d x + 3 \, c\right) + 9 \, \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)}}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*sqrt(b) + B*sqrt(b)*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c)))))/d","A",0
844,1,40,0,0.651979," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B \sqrt{b} + 4 \, A \sqrt{b} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B*sqrt(b) + 4*A*sqrt(b)*sin(d*x + c))/d","A",0
845,1,40,0,0.601602," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, A \sqrt{b} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + B \sqrt{b} \sin\left(d x + c\right)}{d}"," ",0,"(2*A*sqrt(b)*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + B*sqrt(b)*sin(d*x + c))/d","A",0
846,1,92,0,0.587361," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{A \sqrt{b} {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)} + 4 \, B \sqrt{b} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{2 \, d}"," ",0,"1/2*(A*sqrt(b)*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1)) + 4*B*sqrt(b)*arctan(sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
847,1,120,0,0.650932," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{B \sqrt{b} {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)} + \frac{4 \, A \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{2 \, d}"," ",0,"1/2*(B*sqrt(b)*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1)) + 4*A*sqrt(b)*sin(2*d*x + 2*c)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","A",0
848,1,716,0,0.708586," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, 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)\right)\right)\right)} A \sqrt{b}}{2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{8 \, B \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{\cos\left(2 \, d 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*((4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A*sqrt(b)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1) - 8*B*sqrt(b)*sin(2*d*x + 2*c)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","B",0
849,1,957,0,0.715610," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\frac{16 \, {\left({\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 9 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{b}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{3 \, {\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, 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)\right)\right)\right)} B \sqrt{b}}{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}}{12 \, d}"," ",0,"1/12*(16*((3*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 3*(3*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) - 3*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 9*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*A*sqrt(b)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) - 3*(4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(b)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
850,1,100,0,0.748205," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, {\left(b \sin\left(3 \, d x + 3 \, c\right) + 9 \, b \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)} A \sqrt{b} + 3 \, {\left(12 \, {\left(d x + c\right)} b + b \sin\left(4 \, d x + 4 \, c\right) + 8 \, b \sin\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)} B \sqrt{b}}{96 \, d}"," ",0,"1/96*(8*(b*sin(3*d*x + 3*c) + 9*b*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*A*sqrt(b) + 3*(12*(d*x + c)*b + b*sin(4*d*x + 4*c) + 8*b*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*B*sqrt(b))/d","A",0
851,1,74,0,1.070748," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, {\left(d x + c\right)} b + b \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{b} + {\left(b \sin\left(3 \, d x + 3 \, c\right) + 9 \, b \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)} B \sqrt{b}}{12 \, d}"," ",0,"1/12*(3*(2*(d*x + c)*b + b*sin(2*d*x + 2*c))*A*sqrt(b) + (b*sin(3*d*x + 3*c) + 9*b*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*B*sqrt(b))/d","A",0
852,1,43,0,1.013680," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{4 \, A b^{\frac{3}{2}} \sin\left(d x + c\right) + {\left(2 \, {\left(d x + c\right)} b + b \sin\left(2 \, d x + 2 \, c\right)\right)} B \sqrt{b}}{4 \, d}"," ",0,"1/4*(4*A*b^(3/2)*sin(d*x + c) + (2*(d*x + c)*b + b*sin(2*d*x + 2*c))*B*sqrt(b))/d","A",0
853,1,40,0,1.144079," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, A b^{\frac{3}{2}} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + B b^{\frac{3}{2}} \sin\left(d x + c\right)}{d}"," ",0,"(2*A*b^(3/2)*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + B*b^(3/2)*sin(d*x + c))/d","A",0
854,1,95,0,1.254008," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{4 \, B b^{\frac{3}{2}} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + {\left(b \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - b \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)} A \sqrt{b}}{2 \, d}"," ",0,"1/2*(4*B*b^(3/2)*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + (b*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - b*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))*A*sqrt(b))/d","A",0
855,1,123,0,1.130433," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{{\left(b \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - b \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)} B \sqrt{b} + \frac{4 \, A b^{\frac{3}{2}} \sin\left(2 \, d x + 2 \, c\right)}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1}}{2 \, d}"," ",0,"1/2*((b*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - b*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))*B*sqrt(b) + 4*A*b^(3/2)*sin(2*d*x + 2*c)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1))/d","A",0
856,1,747,0,1.270964," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\frac{8 \, B b^{\frac{3}{2}} \sin\left(2 \, d x + 2 \, c\right)}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{{\left(4 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \log\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \log\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(b \cos\left(4 \, d x + 4 \, c\right) + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(b \cos\left(4 \, d x + 4 \, c\right) + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} A \sqrt{b}}{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}}{4 \, d}"," ",0,"1/4*(8*B*b^(3/2)*sin(2*d*x + 2*c)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - (4*(b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(b*cos(4*d*x + 4*c) + 2*b*cos(2*d*x + 2*c) + b)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(b*cos(4*d*x + 4*c) + 2*b*cos(2*d*x + 2*c) + b)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A*sqrt(b)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
857,1,992,0,1.131735," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","-\frac{\frac{16 \, {\left(3 \, b \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(6 \, d x + 6 \, c\right) - 3 \, {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} A \sqrt{b}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{3 \, {\left(4 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) + 2 \, b \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \log\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \log\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(b \cos\left(4 \, d x + 4 \, c\right) + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4 \, {\left(b \cos\left(4 \, d x + 4 \, c\right) + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} B \sqrt{b}}{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}}{12 \, d}"," ",0,"-1/12*(16*(3*b*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) + 9*b*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) - (3*b*cos(2*d*x + 2*c) + b)*sin(6*d*x + 6*c) - 3*(3*b*cos(2*d*x + 2*c) + b)*sin(4*d*x + 4*c))*A*sqrt(b)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) + 3*(4*(b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(b*sin(4*d*x + 4*c) + 2*b*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(b*cos(4*d*x + 4*c) + 2*b*cos(2*d*x + 2*c) + b)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(b*cos(4*d*x + 4*c) + 2*b*cos(2*d*x + 2*c) + b)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(b)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
858,1,110,0,0.655043," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, {\left(b^{2} \sin\left(3 \, d x + 3 \, c\right) + 9 \, b^{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)} A \sqrt{b} + 3 \, {\left(12 \, {\left(d x + c\right)} b^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right) + 8 \, b^{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)\right)} B \sqrt{b}}{96 \, d}"," ",0,"1/96*(8*(b^2*sin(3*d*x + 3*c) + 9*b^2*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*A*sqrt(b) + 3*(12*(d*x + c)*b^2 + b^2*sin(4*d*x + 4*c) + 8*b^2*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))))*B*sqrt(b))/d","A",0
859,1,82,0,0.663601," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, {\left(d x + c\right)} b^{2} + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} A \sqrt{b} + {\left(b^{2} \sin\left(3 \, d x + 3 \, c\right) + 9 \, b^{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)} B \sqrt{b}}{12 \, d}"," ",0,"1/12*(3*(2*(d*x + c)*b^2 + b^2*sin(2*d*x + 2*c))*A*sqrt(b) + (b^2*sin(3*d*x + 3*c) + 9*b^2*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))*B*sqrt(b))/d","A",0
860,1,47,0,0.646091," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{4 \, A b^{\frac{5}{2}} \sin\left(d x + c\right) + {\left(2 \, {\left(d x + c\right)} b^{2} + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} B \sqrt{b}}{4 \, d}"," ",0,"1/4*(4*A*b^(5/2)*sin(d*x + c) + (2*(d*x + c)*b^2 + b^2*sin(2*d*x + 2*c))*B*sqrt(b))/d","A",0
861,1,40,0,0.583045," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, A b^{\frac{5}{2}} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + B b^{\frac{5}{2}} \sin\left(d x + c\right)}{d}"," ",0,"(2*A*b^(5/2)*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + B*b^(5/2)*sin(d*x + c))/d","A",0
862,1,99,0,0.589438," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{4 \, B b^{\frac{5}{2}} \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) + {\left(b^{2} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - b^{2} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)} A \sqrt{b}}{2 \, d}"," ",0,"1/2*(4*B*b^(5/2)*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) + (b^2*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - b^2*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))*A*sqrt(b))/d","A",0
863,1,127,0,0.647285," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\frac{4 \, A b^{\frac{5}{2}} \sin\left(2 \, d x + 2 \, c\right)}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + {\left(b^{2} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - b^{2} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)} B \sqrt{b}}{2 \, d}"," ",0,"1/2*(4*A*b^(5/2)*sin(2*d*x + 2*c)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) + (b^2*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - b^2*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))*B*sqrt(b))/d","A",0
864,1,803,0,0.696410," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{\frac{8 \, B b^{\frac{5}{2}} \sin\left(2 \, d x + 2 \, c\right)}{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} - \frac{{\left(4 \, {\left(b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \log\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \log\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{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) + 4 \, {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{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)} A \sqrt{b}}{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}}{4 \, d}"," ",0,"1/4*(8*B*b^(5/2)*sin(2*d*x + 2*c)/(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1) - (4*(b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(b^2*cos(4*d*x + 4*c) + 2*b^2*cos(2*d*x + 2*c) + b^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(b^2*cos(4*d*x + 4*c) + 2*b^2*cos(2*d*x + 2*c) + b^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A*sqrt(b)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
865,1,1060,0,0.701283," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x, algorithm=""maxima"")","-\frac{\frac{16 \, {\left(3 \, b^{2} \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - {\left(3 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) - 3 \, {\left(3 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \sin\left(4 \, d x + 4 \, c\right)\right)} A \sqrt{b}}{2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1} + \frac{3 \, {\left(4 \, {\left(b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(b^{2} \sin\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \log\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \log\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)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{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) + 4 \, {\left(b^{2} \cos\left(4 \, d x + 4 \, c\right) + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{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)} B \sqrt{b}}{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}}{12 \, d}"," ",0,"-1/12*(16*(3*b^2*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) + 9*b^2*cos(4*d*x + 4*c)*sin(2*d*x + 2*c) - (3*b^2*cos(2*d*x + 2*c) + b^2)*sin(6*d*x + 6*c) - 3*(3*b^2*cos(2*d*x + 2*c) + b^2)*sin(4*d*x + 4*c))*A*sqrt(b)/(2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1) + 3*(4*(b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(b^2*sin(4*d*x + 4*c) + 2*b^2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(b^2*cos(4*d*x + 4*c) + 2*b^2*cos(2*d*x + 2*c) + b^2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(b^2*cos(4*d*x + 4*c) + 2*b^2*cos(2*d*x + 2*c) + b^2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B*sqrt(b)/(2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1))/d","B",0
866,1,68,0,0.669045," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A}{\sqrt{b}} + \frac{B {\left(\sin\left(3 \, d x + 3 \, c\right) + 9 \, \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)}}{\sqrt{b}}}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A/sqrt(b) + B*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))/sqrt(b))/d","A",0
867,1,40,0,0.664316," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B}{\sqrt{b}} + \frac{4 \, A \sin\left(d x + c\right)}{\sqrt{b}}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B/sqrt(b) + 4*A*sin(d*x + c)/sqrt(b))/d","A",0
868,1,40,0,0.593727," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, A \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{\sqrt{b}} + \frac{B \sin\left(d x + c\right)}{\sqrt{b}}}{d}"," ",0,"(2*A*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/sqrt(b) + B*sin(d*x + c)/sqrt(b))/d","A",0
869,1,92,0,0.592006," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{A {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)}}{\sqrt{b}} + \frac{4 \, B \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{\sqrt{b}}}{2 \, d}"," ",0,"1/2*(A*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/sqrt(b) + 4*B*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/sqrt(b))/d","A",0
870,1,125,0,0.671731," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{B {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)}}{\sqrt{b}} + \frac{4 \, A \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b}}{2 \, d}"," ",0,"1/2*(B*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/sqrt(b) + 4*A*sqrt(b)*sin(2*d*x + 2*c)/(b*cos(2*d*x + 2*c)^2 + b*sin(2*d*x + 2*c)^2 + 2*b*cos(2*d*x + 2*c) + b))/d","B",0
871,1,722,0,0.710005," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{8 \, B \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b \cos\left(2 \, d x + 2 \, c\right) + b} - \frac{{\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, 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)\right)\right)\right)} A}{{\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{b}}}{4 \, d}"," ",0,"1/4*(8*B*sqrt(b)*sin(2*d*x + 2*c)/(b*cos(2*d*x + 2*c)^2 + b*sin(2*d*x + 2*c)^2 + 2*b*cos(2*d*x + 2*c) + b) - (4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*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)*sqrt(b)))/d","B",0
872,1,957,0,0.705096," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{16 \, {\left({\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 9 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} A}{{\left(2 \, {\left(3 \, \cos\left(4 \, d x + 4 \, c\right) + 3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + \cos\left(6 \, d x + 6 \, c\right)^{2} + 6 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 9 \, \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 6 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{b}} - \frac{3 \, {\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, 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)\right)\right)\right)} B}{{\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sqrt{b}}}{12 \, d}"," ",0,"1/12*(16*((3*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 3*(3*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) - 3*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 9*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*A/((2*(3*cos(4*d*x + 4*c) + 3*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + cos(6*d*x + 6*c)^2 + 6*(3*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 9*cos(4*d*x + 4*c)^2 + 9*cos(2*d*x + 2*c)^2 + 6*(sin(4*d*x + 4*c) + sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + sin(6*d*x + 6*c)^2 + 9*sin(4*d*x + 4*c)^2 + 18*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c) + 1)*sqrt(b)) - 3*(4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B/((2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*sqrt(b)))/d","B",0
873,1,68,0,0.693794," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A}{b^{\frac{3}{2}}} + \frac{B {\left(\sin\left(3 \, d x + 3 \, c\right) + 9 \, \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)}}{b^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A/b^(3/2) + B*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))/b^(3/2))/d","A",0
874,1,40,0,0.678361," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B}{b^{\frac{3}{2}}} + \frac{4 \, A \sin\left(d x + c\right)}{b^{\frac{3}{2}}}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B/b^(3/2) + 4*A*sin(d*x + c)/b^(3/2))/d","A",0
875,1,40,0,0.598188," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{2 \, A \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{b^{\frac{3}{2}}} + \frac{B \sin\left(d x + c\right)}{b^{\frac{3}{2}}}}{d}"," ",0,"(2*A*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/b^(3/2) + B*sin(d*x + c)/b^(3/2))/d","A",0
876,1,92,0,0.601101," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{A {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)}}{b^{\frac{3}{2}}} + \frac{4 \, B \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{b^{\frac{3}{2}}}}{2 \, d}"," ",0,"1/2*(A*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/b^(3/2) + 4*B*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/b^(3/2))/d","A",0
877,1,133,0,0.673631," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{4 \, A \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}} + \frac{B {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)}}{b^{\frac{3}{2}}}}{2 \, d}"," ",0,"1/2*(4*A*sqrt(b)*sin(2*d*x + 2*c)/(b^2*cos(2*d*x + 2*c)^2 + b^2*sin(2*d*x + 2*c)^2 + 2*b^2*cos(2*d*x + 2*c) + b^2) + B*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/b^(3/2))/d","B",0
878,1,739,0,0.703451," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{8 \, B \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}} - \frac{{\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, 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)\right)\right)\right)} A}{{\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sqrt{b}}}{4 \, d}"," ",0,"1/4*(8*B*sqrt(b)*sin(2*d*x + 2*c)/(b^2*cos(2*d*x + 2*c)^2 + b^2*sin(2*d*x + 2*c)^2 + 2*b^2*cos(2*d*x + 2*c) + b^2) - (4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A/((b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*sqrt(b)))/d","B",0
879,1,983,0,0.715989," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\frac{16 \, {\left({\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 9 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} A}{{\left(b \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(3 \, b \cos\left(4 \, d x + 4 \, c\right) + 3 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, b \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(b \sin\left(4 \, d x + 4 \, c\right) + b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right) + b\right)} \sqrt{b}} - \frac{3 \, {\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, 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)\right)\right)\right)} B}{{\left(b \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \cos\left(2 \, d x + 2 \, c\right)^{2} + b \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(2 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, b \cos\left(2 \, d x + 2 \, c\right) + b\right)} \sqrt{b}}}{12 \, d}"," ",0,"1/12*(16*((3*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 3*(3*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) - 3*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 9*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*A/((b*cos(6*d*x + 6*c)^2 + 9*b*cos(4*d*x + 4*c)^2 + 9*b*cos(2*d*x + 2*c)^2 + b*sin(6*d*x + 6*c)^2 + 9*b*sin(4*d*x + 4*c)^2 + 18*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*b*sin(2*d*x + 2*c)^2 + 2*(3*b*cos(4*d*x + 4*c) + 3*b*cos(2*d*x + 2*c) + b)*cos(6*d*x + 6*c) + 6*(3*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 6*b*cos(2*d*x + 2*c) + 6*(b*sin(4*d*x + 4*c) + b*sin(2*d*x + 2*c))*sin(6*d*x + 6*c) + b)*sqrt(b)) - 3*(4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B/((b*cos(4*d*x + 4*c)^2 + 4*b*cos(2*d*x + 2*c)^2 + b*sin(4*d*x + 4*c)^2 + 4*b*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b*sin(2*d*x + 2*c)^2 + 2*(2*b*cos(2*d*x + 2*c) + b)*cos(4*d*x + 4*c) + 4*b*cos(2*d*x + 2*c) + b)*sqrt(b)))/d","B",0
880,1,68,0,0.669324," ","integrate(cos(d*x+c)^(9/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A}{b^{\frac{5}{2}}} + \frac{B {\left(\sin\left(3 \, d x + 3 \, c\right) + 9 \, \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)}}{b^{\frac{5}{2}}}}{12 \, d}"," ",0,"1/12*(3*(2*d*x + 2*c + sin(2*d*x + 2*c))*A/b^(5/2) + B*(sin(3*d*x + 3*c) + 9*sin(1/3*arctan2(sin(3*d*x + 3*c), cos(3*d*x + 3*c))))/b^(5/2))/d","A",0
881,1,40,0,0.675584," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} B}{b^{\frac{5}{2}}} + \frac{4 \, A \sin\left(d x + c\right)}{b^{\frac{5}{2}}}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*B/b^(5/2) + 4*A*sin(d*x + c)/b^(5/2))/d","A",0
882,1,40,0,0.597964," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{2 \, A \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{b^{\frac{5}{2}}} + \frac{B \sin\left(d x + c\right)}{b^{\frac{5}{2}}}}{d}"," ",0,"(2*A*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/b^(5/2) + B*sin(d*x + c)/b^(5/2))/d","A",0
883,1,92,0,0.604327," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{A {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)}}{b^{\frac{5}{2}}} + \frac{4 \, B \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{b^{\frac{5}{2}}}}{2 \, d}"," ",0,"1/2*(A*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/b^(5/2) + 4*B*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/b^(5/2))/d","A",0
884,1,133,0,0.656557," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{4 \, A \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3}} + \frac{B {\left(\log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)\right)}}{b^{\frac{5}{2}}}}{2 \, d}"," ",0,"1/2*(4*A*sqrt(b)*sin(2*d*x + 2*c)/(b^3*cos(2*d*x + 2*c)^2 + b^3*sin(2*d*x + 2*c)^2 + 2*b^3*cos(2*d*x + 2*c) + b^3) + B*(log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/b^(5/2))/d","B",0
885,1,757,0,0.693226," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{8 \, B \sqrt{b} \sin\left(2 \, d x + 2 \, c\right)}{b^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, b^{3} \cos\left(2 \, d x + 2 \, c\right) + b^{3}} - \frac{{\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, 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)\right)\right)\right)} A}{{\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sqrt{b}}}{4 \, d}"," ",0,"1/4*(8*B*sqrt(b)*sin(2*d*x + 2*c)/(b^3*cos(2*d*x + 2*c)^2 + b^3*sin(2*d*x + 2*c)^2 + 2*b^3*cos(2*d*x + 2*c) + b^3) - (4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*A/((b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*sqrt(b)))/d","B",0
886,1,1033,0,0.705439," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{16 \, {\left({\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(3 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) - 3 \, \cos\left(6 \, d x + 6 \, c\right) \sin\left(2 \, d x + 2 \, c\right) - 9 \, \cos\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right)\right)} A}{{\left(b^{2} \cos\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 9 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(6 \, d x + 6 \, c\right)^{2} + 9 \, b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 18 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 9 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(3 \, b^{2} \cos\left(4 \, d x + 4 \, c\right) + 3 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + 6 \, {\left(3 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(b^{2} \sin\left(4 \, d x + 4 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(6 \, d x + 6 \, c\right)\right)} \sqrt{b}} - \frac{3 \, {\left(4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 4 \, {\left(\sin\left(4 \, d x + 4 \, c\right) + 2 \, \sin\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \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)\right)\right) + 4 \, {\left(\cos\left(4 \, d x + 4 \, c\right) + 2 \, \cos\left(2 \, d x + 2 \, 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)\right)\right)\right)} B}{{\left(b^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + b^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, b^{2} \sin\left(4 \, d x + 4 \, c\right) \sin\left(2 \, d x + 2 \, c\right) + 4 \, b^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2} + 2 \, {\left(2 \, b^{2} \cos\left(2 \, d x + 2 \, c\right) + b^{2}\right)} \cos\left(4 \, d x + 4 \, c\right)\right)} \sqrt{b}}}{12 \, d}"," ",0,"1/12*(16*((3*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 3*(3*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) - 3*cos(6*d*x + 6*c)*sin(2*d*x + 2*c) - 9*cos(4*d*x + 4*c)*sin(2*d*x + 2*c))*A/((b^2*cos(6*d*x + 6*c)^2 + 9*b^2*cos(4*d*x + 4*c)^2 + 9*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(6*d*x + 6*c)^2 + 9*b^2*sin(4*d*x + 4*c)^2 + 18*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 9*b^2*sin(2*d*x + 2*c)^2 + 6*b^2*cos(2*d*x + 2*c) + b^2 + 2*(3*b^2*cos(4*d*x + 4*c) + 3*b^2*cos(2*d*x + 2*c) + b^2)*cos(6*d*x + 6*c) + 6*(3*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c) + 6*(b^2*sin(4*d*x + 4*c) + b^2*sin(2*d*x + 2*c))*sin(6*d*x + 6*c))*sqrt(b)) - 3*(4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 4*(sin(4*d*x + 4*c) + 2*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2*(2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + cos(4*d*x + 4*c)^2 + 4*cos(2*d*x + 2*c)^2 + sin(4*d*x + 4*c)^2 + 4*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*sin(2*d*x + 2*c)^2 + 4*cos(2*d*x + 2*c) + 1)*log(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4*(cos(4*d*x + 4*c) + 2*cos(2*d*x + 2*c) + 1)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*B/((b^2*cos(4*d*x + 4*c)^2 + 4*b^2*cos(2*d*x + 2*c)^2 + b^2*sin(4*d*x + 4*c)^2 + 4*b^2*sin(4*d*x + 4*c)*sin(2*d*x + 2*c) + 4*b^2*sin(2*d*x + 2*c)^2 + 4*b^2*cos(2*d*x + 2*c) + b^2 + 2*(2*b^2*cos(2*d*x + 2*c) + b^2)*cos(4*d*x + 4*c))*sqrt(b)))/d","B",0
887,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*cos(d*x + c)^2, x)","F",0
888,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*cos(d*x + c), x)","F",0
889,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3), x)","F",0
890,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c), x)","F",0
891,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c)^2, x)","F",0
892,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c)^3, x)","F",0
893,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(4/3)*cos(d*x + c)^2, x)","F",0
894,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(4/3)*cos(d*x + c), x)","F",0
895,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(4/3), x)","F",0
896,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(4/3)*sec(d*x + c), x)","F",0
897,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(4/3)*sec(d*x + c)^2, x)","F",0
898,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(4/3)*sec(d*x + c)^3, x)","F",0
899,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c))^(2/3), x)","F",0
900,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c))^(2/3), x)","F",0
901,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c))^(2/3), x)","F",0
902,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c))^(2/3), x)","F",0
903,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^2/(b*cos(d*x + c))^(2/3), x)","F",0
904,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^3/(b*cos(d*x + c))^(2/3), x)","F",0
905,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^2/(b*cos(d*x + c))^(4/3), x)","F",0
906,0,0,0,0.000000," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)/(b*cos(d*x + c))^(4/3), x)","F",0
907,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{B \cos\left(d x + c\right) + A}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)/(b*cos(d*x + c))^(4/3), x)","F",0
908,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)/(b*cos(d*x + c))^(4/3), x)","F",0
909,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{2}}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^2/(b*cos(d*x + c))^(4/3), x)","F",0
910,0,0,0,0.000000," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{3}}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*sec(d*x + c)^3/(b*cos(d*x + c))^(4/3), x)","F",0
911,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*cos(d*x + c)^m, x)","F",0
912,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*cos(d*x + c)^2, x)","F",0
913,0,0,0,0.000000," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*cos(d*x + c), x)","F",0
914,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n, x)","F",0
915,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sec(d*x + c), x)","F",0
916,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sec(d*x + c)^2, x)","F",0
917,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sec(d*x + c)^3, x)","F",0
918,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sec(d*x + c)^4, x)","F",0
919,0,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*cos(d*x + c)^(5/2), x)","F",0
920,0,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*cos(d*x + c)^(3/2), x)","F",0
921,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sqrt{\cos\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sqrt(cos(d*x + c)), x)","F",0
922,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\sqrt{\cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/sqrt(cos(d*x + c)), x)","F",0
923,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/cos(d*x + c)^(3/2), x)","F",0
924,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/cos(d*x + c)^(5/2), x)","F",0
925,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/cos(d*x + c)^(7/2), x)","F",0
926,0,0,0,0.000000," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/cos(d*x + c)^(9/2), x)","F",0
927,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(4/3)*cos(d*x + c)^m, x)","F",0
928,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)*cos(d*x + c)^m, x)","F",0
929,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*cos(d*x + c)^m, x)","F",0
930,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{\left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^m/(b*cos(d*x + c))^(1/3), x)","F",0
931,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{\left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^m/(b*cos(d*x + c))^(2/3), x)","F",0
932,0,0,0,0.000000," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x, algorithm=""maxima"")","\int \frac{{\left(B \cos\left(d x + c\right) + A\right)} \cos\left(d x + c\right)^{m}}{\left(b \cos\left(d x + c\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((B*cos(d*x + c) + A)*cos(d*x + c)^m/(b*cos(d*x + c))^(4/3), x)","F",0
