1,1,114,0,0.578634," ","integrate(sec(d*x+c)^10*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{63 i \, a \tan\left(d x + c\right)^{10} + 70 \, a \tan\left(d x + c\right)^{9} + 315 i \, a \tan\left(d x + c\right)^{8} + 360 \, a \tan\left(d x + c\right)^{7} + 630 i \, a \tan\left(d x + c\right)^{6} + 756 \, a \tan\left(d x + c\right)^{5} + 630 i \, a \tan\left(d x + c\right)^{4} + 840 \, a \tan\left(d x + c\right)^{3} + 315 i \, a \tan\left(d x + c\right)^{2} + 630 \, a \tan\left(d x + c\right)}{630 \, d}"," ",0,"1/630*(63*I*a*tan(d*x + c)^10 + 70*a*tan(d*x + c)^9 + 315*I*a*tan(d*x + c)^8 + 360*a*tan(d*x + c)^7 + 630*I*a*tan(d*x + c)^6 + 756*a*tan(d*x + c)^5 + 630*I*a*tan(d*x + c)^4 + 840*a*tan(d*x + c)^3 + 315*I*a*tan(d*x + c)^2 + 630*a*tan(d*x + c))/d","A",0
2,1,92,0,0.568184," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{35 i \, a \tan\left(d x + c\right)^{8} + 40 \, a \tan\left(d x + c\right)^{7} + 140 i \, a \tan\left(d x + c\right)^{6} + 168 \, a \tan\left(d x + c\right)^{5} + 210 i \, a \tan\left(d x + c\right)^{4} + 280 \, a \tan\left(d x + c\right)^{3} + 140 i \, a \tan\left(d x + c\right)^{2} + 280 \, a \tan\left(d x + c\right)}{280 \, d}"," ",0,"1/280*(35*I*a*tan(d*x + c)^8 + 40*a*tan(d*x + c)^7 + 140*I*a*tan(d*x + c)^6 + 168*a*tan(d*x + c)^5 + 210*I*a*tan(d*x + c)^4 + 280*a*tan(d*x + c)^3 + 140*I*a*tan(d*x + c)^2 + 280*a*tan(d*x + c))/d","A",0
3,1,70,0,0.480306," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{5 i \, a \tan\left(d x + c\right)^{6} + 6 \, a \tan\left(d x + c\right)^{5} + 15 i \, a \tan\left(d x + c\right)^{4} + 20 \, a \tan\left(d x + c\right)^{3} + 15 i \, a \tan\left(d x + c\right)^{2} + 30 \, a \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(5*I*a*tan(d*x + c)^6 + 6*a*tan(d*x + c)^5 + 15*I*a*tan(d*x + c)^4 + 20*a*tan(d*x + c)^3 + 15*I*a*tan(d*x + c)^2 + 30*a*tan(d*x + c))/d","A",0
4,1,48,0,0.604595," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 i \, a \tan\left(d x + c\right)^{4} + 4 \, a \tan\left(d x + c\right)^{3} + 6 i \, a \tan\left(d x + c\right)^{2} + 12 \, a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*I*a*tan(d*x + c)^4 + 4*a*tan(d*x + c)^3 + 6*I*a*tan(d*x + c)^2 + 12*a*tan(d*x + c))/d","A",0
5,1,21,0,0.460231," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{2 \, a d}"," ",0,"-1/2*I*(I*a*tan(d*x + c) + a)^2/(a*d)","A",0
6,1,17,0,0.312587," ","integrate(a+I*a*tan(d*x+c),x, algorithm=""maxima"")","a x + \frac{i \, a \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a*x + I*a*log(sec(d*x + c))/d","A",0
7,1,38,0,0.480918," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} a + \frac{a \tan\left(d x + c\right) - i \, a}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*((d*x + c)*a + (a*tan(d*x + c) - I*a)/(tan(d*x + c)^2 + 1))/d","A",0
8,1,61,0,0.915152," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(d x + c\right)} a + \frac{3 \, a \tan\left(d x + c\right)^{3} + 5 \, a \tan\left(d x + c\right) - 2 i \, a}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*(3*(d*x + c)*a + (3*a*tan(d*x + c)^3 + 5*a*tan(d*x + c) - 2*I*a)/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
9,1,82,0,0.850325," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{15 \, {\left(d x + c\right)} a + \frac{15 \, a \tan\left(d x + c\right)^{5} + 40 \, a \tan\left(d x + c\right)^{3} + 33 \, a \tan\left(d x + c\right) - 8 i \, a}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"1/48*(15*(d*x + c)*a + (15*a*tan(d*x + c)^5 + 40*a*tan(d*x + c)^3 + 33*a*tan(d*x + c) - 8*I*a)/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1))/d","A",0
10,1,103,0,0.926795," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{105 \, {\left(d x + c\right)} a + \frac{105 \, a \tan\left(d x + c\right)^{7} + 385 \, a \tan\left(d x + c\right)^{5} + 511 \, a \tan\left(d x + c\right)^{3} + 279 \, a \tan\left(d x + c\right) - 48 i \, a}{\tan\left(d x + c\right)^{8} + 4 \, \tan\left(d x + c\right)^{6} + 6 \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{2} + 1}}{384 \, d}"," ",0,"1/384*(105*(d*x + c)*a + (105*a*tan(d*x + c)^7 + 385*a*tan(d*x + c)^5 + 511*a*tan(d*x + c)^3 + 279*a*tan(d*x + c) - 48*I*a)/(tan(d*x + c)^8 + 4*tan(d*x + c)^6 + 6*tan(d*x + c)^4 + 4*tan(d*x + c)^2 + 1))/d","A",0
11,1,106,0,0.345079," ","integrate(sec(d*x+c)^7*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{7 \, a {\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)} - \frac{96 i \, a}{\cos\left(d x + c\right)^{7}}}{672 \, d}"," ",0,"-1/672*(7*a*(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)) - 96*I*a/cos(d*x + c)^7)/d","A",0
12,1,86,0,0.316485," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, 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)} - \frac{16 i \, a}{\cos\left(d x + c\right)^{5}}}{80 \, d}"," ",0,"-1/80*(5*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)) - 16*I*a/cos(d*x + c)^5)/d","A",0
13,1,61,0,0.447716," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{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)} - \frac{4 i \, a}{\cos\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(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)) - 4*I*a/cos(d*x + c)^3)/d","A",0
14,1,32,0,0.351735," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + \frac{i \, a}{\cos\left(d x + c\right)}}{d}"," ",0,"(a*log(sec(d*x + c) + tan(d*x + c)) + I*a/cos(d*x + c))/d","A",0
15,1,22,0,0.379208," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right)}{d}"," ",0,"(-I*a*cos(d*x + c) + a*sin(d*x + c))/d","A",0
16,1,36,0,0.317963," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, a \cos\left(d x + c\right)^{3} + {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a}{3 \, d}"," ",0,"-1/3*(I*a*cos(d*x + c)^3 + (sin(d*x + c)^3 - 3*sin(d*x + c))*a)/d","A",0
17,1,49,0,0.331222," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{3 i \, a \cos\left(d x + c\right)^{5} - {\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 \, d}"," ",0,"-1/15*(3*I*a*cos(d*x + c)^5 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a)/d","A",0
18,1,58,0,0.463291," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{5 i \, a \cos\left(d x + c\right)^{7} + {\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 \, d}"," ",0,"-1/35*(5*I*a*cos(d*x + c)^7 + (5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a)/d","A",0
19,1,108,0,0.562960," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{140 \, a^{2} \tan\left(d x + c\right)^{9} - 315 i \, a^{2} \tan\left(d x + c\right)^{8} + 360 \, a^{2} \tan\left(d x + c\right)^{7} - 1260 i \, a^{2} \tan\left(d x + c\right)^{6} - 1890 i \, a^{2} \tan\left(d x + c\right)^{4} - 840 \, a^{2} \tan\left(d x + c\right)^{3} - 1260 i \, a^{2} \tan\left(d x + c\right)^{2} - 1260 \, a^{2} \tan\left(d x + c\right)}{1260 \, d}"," ",0,"-1/1260*(140*a^2*tan(d*x + c)^9 - 315*I*a^2*tan(d*x + c)^8 + 360*a^2*tan(d*x + c)^7 - 1260*I*a^2*tan(d*x + c)^6 - 1890*I*a^2*tan(d*x + c)^4 - 840*a^2*tan(d*x + c)^3 - 1260*I*a^2*tan(d*x + c)^2 - 1260*a^2*tan(d*x + c))/d","A",0
20,1,95,0,0.446977," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{15 \, a^{2} \tan\left(d x + c\right)^{7} - 35 i \, a^{2} \tan\left(d x + c\right)^{6} + 21 \, a^{2} \tan\left(d x + c\right)^{5} - 105 i \, a^{2} \tan\left(d x + c\right)^{4} - 35 \, a^{2} \tan\left(d x + c\right)^{3} - 105 i \, a^{2} \tan\left(d x + c\right)^{2} - 105 \, a^{2} \tan\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(15*a^2*tan(d*x + c)^7 - 35*I*a^2*tan(d*x + c)^6 + 21*a^2*tan(d*x + c)^5 - 105*I*a^2*tan(d*x + c)^4 - 35*a^2*tan(d*x + c)^3 - 105*I*a^2*tan(d*x + c)^2 - 105*a^2*tan(d*x + c))/d","A",0
21,1,56,0,0.411048," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, a^{2} \tan\left(d x + c\right)^{5} - 15 i \, a^{2} \tan\left(d x + c\right)^{4} - 30 i \, a^{2} \tan\left(d x + c\right)^{2} - 30 \, a^{2} \tan\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(6*a^2*tan(d*x + c)^5 - 15*I*a^2*tan(d*x + c)^4 - 30*I*a^2*tan(d*x + c)^2 - 30*a^2*tan(d*x + c))/d","A",0
22,1,21,0,0.314322," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{3 \, a d}"," ",0,"-1/3*I*(I*a*tan(d*x + c) + a)^3/(a*d)","A",0
23,1,41,0,0.788594," ","integrate((a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(d x + c - \tan\left(d x + c\right)\right)} a^{2}}{d} + \frac{2 i \, a^{2} \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^2*x + (d*x + c - tan(d*x + c))*a^2/d + 2*I*a^2*log(sec(d*x + c))/d","A",0
24,1,32,0,0.624675," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \tan\left(d x + c\right) - i \, a^{2}}{{\left(\tan\left(d x + c\right)^{2} + 1\right)} d}"," ",0,"(a^2*tan(d*x + c) - I*a^2)/((tan(d*x + c)^2 + 1)*d)","A",0
25,1,67,0,0.629150," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} a^{2} + \frac{a^{2} \tan\left(d x + c\right)^{3} + 3 \, a^{2} \tan\left(d x + c\right) - 2 i \, a^{2}}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{4 \, d}"," ",0,"1/4*((d*x + c)*a^2 + (a^2*tan(d*x + c)^3 + 3*a^2*tan(d*x + c) - 2*I*a^2)/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
26,1,92,0,0.717269," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, {\left(d x + c\right)} a^{2} + \frac{3 \, a^{2} \tan\left(d x + c\right)^{5} + 8 \, a^{2} \tan\left(d x + c\right)^{3} + 9 \, a^{2} \tan\left(d x + c\right) - 4 i \, a^{2}}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1}}{12 \, d}"," ",0,"1/12*(3*(d*x + c)*a^2 + (3*a^2*tan(d*x + c)^5 + 8*a^2*tan(d*x + c)^3 + 9*a^2*tan(d*x + c) - 4*I*a^2)/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1))/d","A",0
27,1,115,0,0.488309," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{15 \, {\left(d x + c\right)} a^{2} + \frac{15 \, a^{2} \tan\left(d x + c\right)^{7} + 55 \, a^{2} \tan\left(d x + c\right)^{5} + 73 \, a^{2} \tan\left(d x + c\right)^{3} + 49 \, a^{2} \tan\left(d x + c\right) - 16 i \, a^{2}}{\tan\left(d x + c\right)^{8} + 4 \, \tan\left(d x + c\right)^{6} + 6 \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{2} + 1}}{64 \, d}"," ",0,"1/64*(15*(d*x + c)*a^2 + (15*a^2*tan(d*x + c)^7 + 55*a^2*tan(d*x + c)^5 + 73*a^2*tan(d*x + c)^3 + 49*a^2*tan(d*x + c) - 16*I*a^2)/(tan(d*x + c)^8 + 4*tan(d*x + c)^6 + 6*tan(d*x + c)^4 + 4*tan(d*x + c)^2 + 1))/d","A",0
28,1,181,0,0.704674," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{5 \, a^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 8 \, \sin\left(d x + c\right)^{3} - 3 \, \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} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 30 \, a^{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)} - \frac{192 i \, a^{2}}{\cos\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(5*a^2*(2*(3*sin(d*x + c)^5 - 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 30*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)) - 192*I*a^2/cos(d*x + c)^5)/d","A",0
29,1,130,0,0.564337," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\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} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} - \frac{32 i \, a^{2}}{\cos\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"-1/48*(3*a^2*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + 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)) - 32*I*a^2/cos(d*x + c)^3)/d","A",0
30,1,83,0,0.462251," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 4 \, a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + \frac{8 i \, a^{2}}{\cos\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*(a^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 4*a^2*log(sec(d*x + c) + tan(d*x + c)) + 8*I*a^2/cos(d*x + c))/d","A",0
31,1,61,0,0.367642," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 4 i \, a^{2} \cos\left(d x + c\right) - 2 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(a^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 4*I*a^2*cos(d*x + c) - 2*a^2*sin(d*x + c))/d","A",0
32,1,52,0,0.321705," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 i \, a^{2} \cos\left(d x + c\right)^{3} + a^{2} \sin\left(d x + c\right)^{3} + {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2}}{3 \, d}"," ",0,"-1/3*(2*I*a^2*cos(d*x + c)^3 + a^2*sin(d*x + c)^3 + (sin(d*x + c)^3 - 3*sin(d*x + c))*a^2)/d","A",0
33,1,79,0,0.437198," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 i \, a^{2} \cos\left(d x + c\right)^{5} - {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{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)} a^{2}}{15 \, d}"," ",0,"-1/15*(6*I*a^2*cos(d*x + c)^5 - (3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^2 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2)/d","A",0
34,1,98,0,0.425546," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{30 i \, a^{2} \cos\left(d x + c\right)^{7} + {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a^{2} + 3 \, {\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^{2}}{105 \, d}"," ",0,"-1/105*(30*I*a^2*cos(d*x + c)^7 + (15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a^2 + 3*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^2)/d","A",0
35,1,119,0,0.412444," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{70 i \, a^{2} \cos\left(d x + c\right)^{9} - {\left(35 \, \sin\left(d x + c\right)^{9} - 135 \, \sin\left(d x + c\right)^{7} + 189 \, \sin\left(d x + c\right)^{5} - 105 \, \sin\left(d x + c\right)^{3}\right)} a^{2} - {\left(35 \, \sin\left(d x + c\right)^{9} - 180 \, \sin\left(d x + c\right)^{7} + 378 \, \sin\left(d x + c\right)^{5} - 420 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)\right)} a^{2}}{315 \, d}"," ",0,"-1/315*(70*I*a^2*cos(d*x + c)^9 - (35*sin(d*x + c)^9 - 135*sin(d*x + c)^7 + 189*sin(d*x + c)^5 - 105*sin(d*x + c)^3)*a^2 - (35*sin(d*x + c)^9 - 180*sin(d*x + c)^7 + 378*sin(d*x + c)^5 - 420*sin(d*x + c)^3 + 315*sin(d*x + c))*a^2)/d","A",0
36,1,108,0,0.601770," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{-84 i \, a^{3} \tan\left(d x + c\right)^{10} - 280 \, a^{3} \tan\left(d x + c\right)^{9} - 960 \, a^{3} \tan\left(d x + c\right)^{7} + 840 i \, a^{3} \tan\left(d x + c\right)^{6} - 1008 \, a^{3} \tan\left(d x + c\right)^{5} + 1680 i \, a^{3} \tan\left(d x + c\right)^{4} + 1260 i \, a^{3} \tan\left(d x + c\right)^{2} + 840 \, a^{3} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(-84*I*a^3*tan(d*x + c)^10 - 280*a^3*tan(d*x + c)^9 - 960*a^3*tan(d*x + c)^7 + 840*I*a^3*tan(d*x + c)^6 - 1008*a^3*tan(d*x + c)^5 + 1680*I*a^3*tan(d*x + c)^4 + 1260*I*a^3*tan(d*x + c)^2 + 840*a^3*tan(d*x + c))/d","A",0
37,1,108,0,0.376633," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{-105 i \, a^{3} \tan\left(d x + c\right)^{8} - 360 \, a^{3} \tan\left(d x + c\right)^{7} + 140 i \, a^{3} \tan\left(d x + c\right)^{6} - 840 \, a^{3} \tan\left(d x + c\right)^{5} + 1050 i \, a^{3} \tan\left(d x + c\right)^{4} - 280 \, a^{3} \tan\left(d x + c\right)^{3} + 1260 i \, a^{3} \tan\left(d x + c\right)^{2} + 840 \, a^{3} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(-105*I*a^3*tan(d*x + c)^8 - 360*a^3*tan(d*x + c)^7 + 140*I*a^3*tan(d*x + c)^6 - 840*a^3*tan(d*x + c)^5 + 1050*I*a^3*tan(d*x + c)^4 - 280*a^3*tan(d*x + c)^3 + 1260*I*a^3*tan(d*x + c)^2 + 840*a^3*tan(d*x + c))/d","A",0
38,1,82,0,0.525418," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{-10 i \, a^{3} \tan\left(d x + c\right)^{6} - 36 \, a^{3} \tan\left(d x + c\right)^{5} + 30 i \, a^{3} \tan\left(d x + c\right)^{4} - 40 \, a^{3} \tan\left(d x + c\right)^{3} + 90 i \, a^{3} \tan\left(d x + c\right)^{2} + 60 \, a^{3} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(-10*I*a^3*tan(d*x + c)^6 - 36*a^3*tan(d*x + c)^5 + 30*I*a^3*tan(d*x + c)^4 - 40*a^3*tan(d*x + c)^3 + 90*I*a^3*tan(d*x + c)^2 + 60*a^3*tan(d*x + c))/d","A",0
39,1,21,0,0.496185," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{4 \, a d}"," ",0,"-1/4*I*(I*a*tan(d*x + c) + a)^4/(a*d)","A",0
40,1,76,0,0.678738," ","integrate((a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x + \frac{3 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3}}{d} + \frac{i \, a^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{2 \, d} + \frac{3 i \, a^{3} \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^3*x + 3*(d*x + c - tan(d*x + c))*a^3/d + 1/2*I*a^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d + 3*I*a^3*log(sec(d*x + c))/d","A",0
41,1,62,0,0.570645," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c\right)} a^{3} + i \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - \frac{4 \, {\left(a^{3} \tan\left(d x + c\right) - i \, a^{3}\right)}}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)*a^3 + I*a^3*log(tan(d*x + c)^2 + 1) - 4*(a^3*tan(d*x + c) - I*a^3)/(tan(d*x + c)^2 + 1))/d","A",0
42,1,57,0,0.496325," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 i \, a^{3} \tan\left(d x + c\right)^{2} + 8 \, a^{3} \tan\left(d x + c\right) - 4 i \, a^{3}}{8 \, {\left(\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1\right)} d}"," ",0,"1/8*(4*I*a^3*tan(d*x + c)^2 + 8*a^3*tan(d*x + c) - 4*I*a^3)/((tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1)*d)","B",0
43,1,105,0,0.635544," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a^{3} + \frac{6 \, a^{3} \tan\left(d x + c\right)^{5} + 16 \, a^{3} \tan\left(d x + c\right)^{3} + 12 i \, a^{3} \tan\left(d x + c\right)^{2} + 42 \, a^{3} \tan\left(d x + c\right) - 20 i \, a^{3}}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"1/48*(6*(d*x + c)*a^3 + (6*a^3*tan(d*x + c)^5 + 16*a^3*tan(d*x + c)^3 + 12*I*a^3*tan(d*x + c)^2 + 42*a^3*tan(d*x + c) - 20*I*a^3)/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1))/d","A",0
44,1,128,0,0.523646," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{60 \, {\left(d x + c\right)} a^{3} + \frac{60 \, a^{3} \tan\left(d x + c\right)^{7} + 220 \, a^{3} \tan\left(d x + c\right)^{5} + 292 \, a^{3} \tan\left(d x + c\right)^{3} + 64 i \, a^{3} \tan\left(d x + c\right)^{2} + 324 \, a^{3} \tan\left(d x + c\right) - 128 i \, a^{3}}{\tan\left(d x + c\right)^{8} + 4 \, \tan\left(d x + c\right)^{6} + 6 \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{2} + 1}}{384 \, d}"," ",0,"1/384*(60*(d*x + c)*a^3 + (60*a^3*tan(d*x + c)^7 + 220*a^3*tan(d*x + c)^5 + 292*a^3*tan(d*x + c)^3 + 64*I*a^3*tan(d*x + c)^2 + 324*a^3*tan(d*x + c) - 128*I*a^3)/(tan(d*x + c)^8 + 4*tan(d*x + c)^6 + 6*tan(d*x + c)^4 + 4*tan(d*x + c)^2 + 1))/d","A",0
45,1,155,0,0.749577," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{45 \, a^{3} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\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^{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)} - \frac{240 i \, a^{3}}{\cos\left(d x + c\right)^{3}} - \frac{16 i \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} a^{3}}{\cos\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"-1/240*(45*a^3*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + 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)) - 240*I*a^3/cos(d*x + c)^3 - 16*I*(5*cos(d*x + c)^2 - 3)*a^3/cos(d*x + c)^5)/d","A",0
46,1,109,0,0.418736," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{9 \, a^{3} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 12 \, a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + \frac{36 i \, a^{3}}{\cos\left(d x + c\right)} + \frac{4 i \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{3}}{\cos\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"1/12*(9*a^3*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 12*a^3*log(sec(d*x + c) + tan(d*x + c)) + 36*I*a^3/cos(d*x + c) + 4*I*(3*cos(d*x + c)^2 - 1)*a^3/cos(d*x + c)^3)/d","A",0
47,1,82,0,0.560134," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 i \, a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + 3 \, a^{3} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 6 i \, a^{3} \cos\left(d x + c\right) - 2 \, a^{3} \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*I*a^3*(1/cos(d*x + c) + cos(d*x + c)) + 3*a^3*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 6*I*a^3*cos(d*x + c) - 2*a^3*sin(d*x + c))/d","A",0
48,1,75,0,0.487940," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 i \, a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \sin\left(d x + c\right)^{3} + i \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{3} + {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3}}{3 \, d}"," ",0,"-1/3*(3*I*a^3*cos(d*x + c)^3 + 3*a^3*sin(d*x + c)^3 + I*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^3 + (sin(d*x + c)^3 - 3*sin(d*x + c))*a^3)/d","B",0
49,1,105,0,0.681241," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{9 i \, a^{3} \cos\left(d x + c\right)^{5} + i \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{3} - 3 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{3} - {\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}}{15 \, d}"," ",0,"-1/15*(9*I*a^3*cos(d*x + c)^5 + I*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^3 - 3*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^3 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^3)/d","A",0
50,1,123,0,0.395313," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{15 i \, a^{3} \cos\left(d x + c\right)^{7} + i \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{3} + {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a^{3} + {\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^{3}}{35 \, d}"," ",0,"-1/35*(15*I*a^3*cos(d*x + c)^7 + I*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^3 + (15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a^3 + (5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^3)/d","A",0
51,1,145,0,0.529290," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{105 i \, a^{3} \cos\left(d x + c\right)^{9} + 5 i \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{3} - 3 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 135 \, \sin\left(d x + c\right)^{7} + 189 \, \sin\left(d x + c\right)^{5} - 105 \, \sin\left(d x + c\right)^{3}\right)} a^{3} - {\left(35 \, \sin\left(d x + c\right)^{9} - 180 \, \sin\left(d x + c\right)^{7} + 378 \, \sin\left(d x + c\right)^{5} - 420 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)\right)} a^{3}}{315 \, d}"," ",0,"-1/315*(105*I*a^3*cos(d*x + c)^9 + 5*I*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^3 - 3*(35*sin(d*x + c)^9 - 135*sin(d*x + c)^7 + 189*sin(d*x + c)^5 - 105*sin(d*x + c)^3)*a^3 - (35*sin(d*x + c)^9 - 180*sin(d*x + c)^7 + 378*sin(d*x + c)^5 - 420*sin(d*x + c)^3 + 315*sin(d*x + c))*a^3)/d","A",0
52,1,246,0,0.509673," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{5 \, a^{4} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} + 8 \, \sin\left(d x + c\right)^{3} - 3 \, \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} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 180 \, a^{4} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 120 \, a^{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)} - \frac{640 i \, a^{4}}{\cos\left(d x + c\right)^{3}} - \frac{128 i \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} a^{4}}{\cos\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(5*a^4*(2*(3*sin(d*x + c)^5 + 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) + 180*a^4*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + 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)) - 640*I*a^4/cos(d*x + c)^3 - 128*I*(5*cos(d*x + c)^2 - 3)*a^4/cos(d*x + c)^5)/d","A",0
53,1,180,0,0.472831," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, a^{4} {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 72 \, a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 48 \, a^{4} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + \frac{192 i \, a^{4}}{\cos\left(d x + c\right)} + \frac{64 i \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{4}}{\cos\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(3*a^4*(2*(5*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1)) + 72*a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 48*a^4*log(sec(d*x + c) + tan(d*x + c)) + 192*I*a^4/cos(d*x + c) + 64*I*(3*cos(d*x + c)^2 - 1)*a^4/cos(d*x + c)^3)/d","A",0
54,1,137,0,0.450847," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{a^{4} {\left(\frac{2 \, \sin\left(d x + c\right)}{\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) - 4 \, \sin\left(d x + c\right)\right)} + 16 i \, a^{4} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\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) - 2 \, \sin\left(d x + c\right)\right)} + 16 i \, a^{4} \cos\left(d x + c\right) - 4 \, a^{4} \sin\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(a^4*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)) + 16*I*a^4*(1/cos(d*x + c) + cos(d*x + c)) + 12*a^4*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 16*I*a^4*cos(d*x + c) - 4*a^4*sin(d*x + c))/d","A",0
55,1,121,0,0.420398," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{8 i \, a^{4} \cos\left(d x + c\right)^{3} + 12 \, a^{4} \sin\left(d x + c\right)^{3} + 8 i \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{4} + {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a^{4} + 2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{4}}{6 \, d}"," ",0,"-1/6*(8*I*a^4*cos(d*x + c)^3 + 12*a^4*sin(d*x + c)^3 + 8*I*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^4 + (2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a^4 + 2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^4)/d","A",0
56,1,118,0,0.401307," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{12 i \, a^{4} \cos\left(d x + c\right)^{5} - 3 \, a^{4} \sin\left(d x + c\right)^{5} + 4 i \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{4} - 6 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{4} - {\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{4}}{15 \, d}"," ",0,"-1/15*(12*I*a^4*cos(d*x + c)^5 - 3*a^4*sin(d*x + c)^5 + 4*I*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^4 - 6*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^4 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^4)/d","B",0
57,1,149,0,0.648360," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{20 i \, a^{4} \cos\left(d x + c\right)^{7} + 4 i \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{4} + 2 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a^{4} + {\left(5 \, \sin\left(d x + c\right)^{7} - 7 \, \sin\left(d x + c\right)^{5}\right)} a^{4} + {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} a^{4}}{35 \, d}"," ",0,"-1/35*(20*I*a^4*cos(d*x + c)^7 + 4*I*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^4 + 2*(15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a^4 + (5*sin(d*x + c)^7 - 7*sin(d*x + c)^5)*a^4 + (5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^4)/d","A",0
58,1,181,0,0.490904," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{140 i \, a^{4} \cos\left(d x + c\right)^{9} + 20 i \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{4} - {\left(35 \, \sin\left(d x + c\right)^{9} - 90 \, \sin\left(d x + c\right)^{7} + 63 \, \sin\left(d x + c\right)^{5}\right)} a^{4} - 6 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 135 \, \sin\left(d x + c\right)^{7} + 189 \, \sin\left(d x + c\right)^{5} - 105 \, \sin\left(d x + c\right)^{3}\right)} a^{4} - {\left(35 \, \sin\left(d x + c\right)^{9} - 180 \, \sin\left(d x + c\right)^{7} + 378 \, \sin\left(d x + c\right)^{5} - 420 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)\right)} a^{4}}{315 \, d}"," ",0,"-1/315*(140*I*a^4*cos(d*x + c)^9 + 20*I*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^4 - (35*sin(d*x + c)^9 - 90*sin(d*x + c)^7 + 63*sin(d*x + c)^5)*a^4 - 6*(35*sin(d*x + c)^9 - 135*sin(d*x + c)^7 + 189*sin(d*x + c)^5 - 105*sin(d*x + c)^3)*a^4 - (35*sin(d*x + c)^9 - 180*sin(d*x + c)^7 + 378*sin(d*x + c)^5 - 420*sin(d*x + c)^3 + 315*sin(d*x + c))*a^4)/d","A",0
59,1,160,0,0.456002," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{2310 i \, a^{5} \tan\left(d x + c\right)^{12} + 12600 \, a^{5} \tan\left(d x + c\right)^{11} - 19404 i \, a^{5} \tan\left(d x + c\right)^{10} + 15400 \, a^{5} \tan\left(d x + c\right)^{9} - 76230 i \, a^{5} \tan\left(d x + c\right)^{8} - 55440 \, a^{5} \tan\left(d x + c\right)^{7} - 64680 i \, a^{5} \tan\left(d x + c\right)^{6} - 121968 \, a^{5} \tan\left(d x + c\right)^{5} + 34650 i \, a^{5} \tan\left(d x + c\right)^{4} - 64680 \, a^{5} \tan\left(d x + c\right)^{3} + 69300 i \, a^{5} \tan\left(d x + c\right)^{2} + 27720 \, a^{5} \tan\left(d x + c\right)}{27720 \, d}"," ",0,"1/27720*(2310*I*a^5*tan(d*x + c)^12 + 12600*a^5*tan(d*x + c)^11 - 19404*I*a^5*tan(d*x + c)^10 + 15400*a^5*tan(d*x + c)^9 - 76230*I*a^5*tan(d*x + c)^8 - 55440*a^5*tan(d*x + c)^7 - 64680*I*a^5*tan(d*x + c)^6 - 121968*a^5*tan(d*x + c)^5 + 34650*I*a^5*tan(d*x + c)^4 - 64680*a^5*tan(d*x + c)^3 + 69300*I*a^5*tan(d*x + c)^2 + 27720*a^5*tan(d*x + c))/d","A",0
60,1,108,0,0.499821," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{126 i \, a^{5} \tan\left(d x + c\right)^{10} + 700 \, a^{5} \tan\left(d x + c\right)^{9} - 1260 i \, a^{5} \tan\left(d x + c\right)^{8} - 2940 i \, a^{5} \tan\left(d x + c\right)^{6} - 3528 \, a^{5} \tan\left(d x + c\right)^{5} - 3360 \, a^{5} \tan\left(d x + c\right)^{3} + 3150 i \, a^{5} \tan\left(d x + c\right)^{2} + 1260 \, a^{5} \tan\left(d x + c\right)}{1260 \, d}"," ",0,"1/1260*(126*I*a^5*tan(d*x + c)^10 + 700*a^5*tan(d*x + c)^9 - 1260*I*a^5*tan(d*x + c)^8 - 2940*I*a^5*tan(d*x + c)^6 - 3528*a^5*tan(d*x + c)^5 - 3360*a^5*tan(d*x + c)^3 + 3150*I*a^5*tan(d*x + c)^2 + 1260*a^5*tan(d*x + c))/d","A",0
61,1,108,0,0.349710," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{21 i \, a^{5} \tan\left(d x + c\right)^{8} + 120 \, a^{5} \tan\left(d x + c\right)^{7} - 252 i \, a^{5} \tan\left(d x + c\right)^{6} - 168 \, a^{5} \tan\left(d x + c\right)^{5} - 210 i \, a^{5} \tan\left(d x + c\right)^{4} - 504 \, a^{5} \tan\left(d x + c\right)^{3} + 420 i \, a^{5} \tan\left(d x + c\right)^{2} + 168 \, a^{5} \tan\left(d x + c\right)}{168 \, d}"," ",0,"1/168*(21*I*a^5*tan(d*x + c)^8 + 120*a^5*tan(d*x + c)^7 - 252*I*a^5*tan(d*x + c)^6 - 168*a^5*tan(d*x + c)^5 - 210*I*a^5*tan(d*x + c)^4 - 504*a^5*tan(d*x + c)^3 + 420*I*a^5*tan(d*x + c)^2 + 168*a^5*tan(d*x + c))/d","B",0
62,1,21,0,0.414565," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","-\frac{i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{6}}{6 \, a d}"," ",0,"-1/6*I*(I*a*tan(d*x + c) + a)^6/(a*d)","A",0
63,1,165,0,0.670837," ","integrate((a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","a^{5} x + \frac{5 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{5}}{3 \, d} + \frac{10 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{5}}{d} + \frac{i \, a^{5} {\left(\frac{4 \, \sin\left(d x + c\right)^{2} - 3}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 2 \, \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{4 \, d} + \frac{5 i \, a^{5} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{d} + \frac{5 i \, a^{5} \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^5*x + 5/3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^5/d + 10*(d*x + c - tan(d*x + c))*a^5/d + 1/4*I*a^5*((4*sin(d*x + c)^2 - 3)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 2*log(sin(d*x + c)^2 - 1))/d + 5*I*a^5*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d + 5*I*a^5*log(sec(d*x + c))/d","A",0
64,1,86,0,0.675724," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","-\frac{-i \, a^{5} \tan\left(d x + c\right)^{2} + 24 \, {\left(d x + c\right)} a^{5} + 12 i \, a^{5} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 10 \, a^{5} \tan\left(d x + c\right) - \frac{16 \, {\left(a^{5} \tan\left(d x + c\right) - i \, a^{5}\right)}}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"-1/2*(-I*a^5*tan(d*x + c)^2 + 24*(d*x + c)*a^5 + 12*I*a^5*log(tan(d*x + c)^2 + 1) - 10*a^5*tan(d*x + c) - 16*(a^5*tan(d*x + c) - I*a^5)/(tan(d*x + c)^2 + 1))/d","A",0
65,1,88,0,0.573286," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{8 \, {\left(d x + c\right)} a^{5} + 4 i \, a^{5} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - \frac{32 \, a^{5} \tan\left(d x + c\right)^{3} - 48 i \, a^{5} \tan\left(d x + c\right)^{2} - 16 i \, a^{5}}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*(8*(d*x + c)*a^5 + 4*I*a^5*log(tan(d*x + c)^2 + 1) - (32*a^5*tan(d*x + c)^3 - 48*I*a^5*tan(d*x + c)^2 - 16*I*a^5)/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
66,1,93,0,0.931587," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{-24 i \, a^{5} \tan\left(d x + c\right)^{4} - 80 \, a^{5} \tan\left(d x + c\right)^{3} + 96 i \, a^{5} \tan\left(d x + c\right)^{2} + 48 \, a^{5} \tan\left(d x + c\right) - 8 i \, a^{5}}{48 \, {\left(\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1\right)} d}"," ",0,"1/48*(-24*I*a^5*tan(d*x + c)^4 - 80*a^5*tan(d*x + c)^3 + 96*I*a^5*tan(d*x + c)^2 + 48*a^5*tan(d*x + c) - 8*I*a^5)/((tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1)*d)","B",0
67,1,103,0,0.728601," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{-96 i \, a^{5} \tan\left(d x + c\right)^{4} - 384 \, a^{5} \tan\left(d x + c\right)^{3} + 576 i \, a^{5} \tan\left(d x + c\right)^{2} + 384 \, a^{5} \tan\left(d x + c\right) - 96 i \, a^{5}}{384 \, {\left(\tan\left(d x + c\right)^{8} + 4 \, \tan\left(d x + c\right)^{6} + 6 \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{2} + 1\right)} d}"," ",0,"1/384*(-96*I*a^5*tan(d*x + c)^4 - 384*a^5*tan(d*x + c)^3 + 576*I*a^5*tan(d*x + c)^2 + 384*a^5*tan(d*x + c) - 96*I*a^5)/((tan(d*x + c)^8 + 4*tan(d*x + c)^6 + 6*tan(d*x + c)^4 + 4*tan(d*x + c)^2 + 1)*d)","B",0
68,1,164,0,0.650695," ","integrate(cos(d*x+c)^10*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{120 \, {\left(d x + c\right)} a^{5} + \frac{120 \, a^{5} \tan\left(d x + c\right)^{9} + 560 \, a^{5} \tan\left(d x + c\right)^{7} + 1024 \, a^{5} \tan\left(d x + c\right)^{5} - 640 i \, a^{5} \tan\left(d x + c\right)^{4} - 1840 \, a^{5} \tan\left(d x + c\right)^{3} + 4480 i \, a^{5} \tan\left(d x + c\right)^{2} + 3720 \, a^{5} \tan\left(d x + c\right) - 1024 i \, a^{5}}{\tan\left(d x + c\right)^{10} + 5 \, \tan\left(d x + c\right)^{8} + 10 \, \tan\left(d x + c\right)^{6} + 10 \, \tan\left(d x + c\right)^{4} + 5 \, \tan\left(d x + c\right)^{2} + 1}}{3840 \, d}"," ",0,"1/3840*(120*(d*x + c)*a^5 + (120*a^5*tan(d*x + c)^9 + 560*a^5*tan(d*x + c)^7 + 1024*a^5*tan(d*x + c)^5 - 640*I*a^5*tan(d*x + c)^4 - 1840*a^5*tan(d*x + c)^3 + 4480*I*a^5*tan(d*x + c)^2 + 3720*a^5*tan(d*x + c) - 1024*I*a^5)/(tan(d*x + c)^10 + 5*tan(d*x + c)^8 + 10*tan(d*x + c)^6 + 10*tan(d*x + c)^4 + 5*tan(d*x + c)^2 + 1))/d","A",0
69,1,187,0,0.538597," ","integrate(cos(d*x+c)^12*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{840 \, {\left(d x + c\right)} a^{5} + \frac{840 \, a^{5} \tan\left(d x + c\right)^{11} + 4760 \, a^{5} \tan\left(d x + c\right)^{9} + 11088 \, a^{5} \tan\left(d x + c\right)^{7} + 13488 \, a^{5} \tan\left(d x + c\right)^{5} - 1920 i \, a^{5} \tan\left(d x + c\right)^{4} + 360 \, a^{5} \tan\left(d x + c\right)^{3} + 14592 i \, a^{5} \tan\left(d x + c\right)^{2} + 14520 \, a^{5} \tan\left(d x + c\right) - 3968 i \, a^{5}}{\tan\left(d x + c\right)^{12} + 6 \, \tan\left(d x + c\right)^{10} + 15 \, \tan\left(d x + c\right)^{8} + 20 \, \tan\left(d x + c\right)^{6} + 15 \, \tan\left(d x + c\right)^{4} + 6 \, \tan\left(d x + c\right)^{2} + 1}}{15360 \, d}"," ",0,"1/15360*(840*(d*x + c)*a^5 + (840*a^5*tan(d*x + c)^11 + 4760*a^5*tan(d*x + c)^9 + 11088*a^5*tan(d*x + c)^7 + 13488*a^5*tan(d*x + c)^5 - 1920*I*a^5*tan(d*x + c)^4 + 360*a^5*tan(d*x + c)^3 + 14592*I*a^5*tan(d*x + c)^2 + 14520*a^5*tan(d*x + c) - 3968*I*a^5)/(tan(d*x + c)^12 + 6*tan(d*x + c)^10 + 15*tan(d*x + c)^8 + 20*tan(d*x + c)^6 + 15*tan(d*x + c)^4 + 6*tan(d*x + c)^2 + 1))/d","A",0
70,1,215,0,0.757315," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\frac{75 \, a^{5} {\left(\frac{2 \, {\left(5 \, \sin\left(d x + c\right)^{3} - 3 \, \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)} + 600 \, a^{5} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} + 240 \, a^{5} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + \frac{1200 i \, a^{5}}{\cos\left(d x + c\right)} + \frac{800 i \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{5}}{\cos\left(d x + c\right)^{3}} + \frac{16 i \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} + 3\right)} a^{5}}{\cos\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"1/240*(75*a^5*(2*(5*sin(d*x + c)^3 - 3*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)) + 600*a^5*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) + 240*a^5*log(sec(d*x + c) + tan(d*x + c)) + 1200*I*a^5/cos(d*x + c) + 800*I*(3*cos(d*x + c)^2 - 1)*a^5/cos(d*x + c)^3 + 16*I*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 + 3)*a^5/cos(d*x + c)^5)/d","A",0
71,1,173,0,0.637631," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","-\frac{15 \, a^{5} {\left(\frac{2 \, \sin\left(d x + c\right)}{\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) - 4 \, \sin\left(d x + c\right)\right)} + 120 i \, a^{5} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + 4 i \, a^{5} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)} + 60 \, a^{5} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 60 i \, a^{5} \cos\left(d x + c\right) - 12 \, a^{5} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(15*a^5*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)) + 120*I*a^5*(1/cos(d*x + c) + cos(d*x + c)) + 4*I*a^5*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) + 60*a^5*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 60*I*a^5*cos(d*x + c) - 12*a^5*sin(d*x + c))/d","A",0
72,1,154,0,0.750746," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","-\frac{10 i \, a^{5} \cos\left(d x + c\right)^{3} + 20 \, a^{5} \sin\left(d x + c\right)^{3} + 2 i \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a^{5} + 20 i \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{5} + 5 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a^{5} + 2 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{5}}{6 \, d}"," ",0,"-1/6*(10*I*a^5*cos(d*x + c)^3 + 20*a^5*sin(d*x + c)^3 + 2*I*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^5 + 20*I*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^5 + 5*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a^5 + 2*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^5)/d","A",0
73,1,152,0,0.395373," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","-\frac{15 i \, a^{5} \cos\left(d x + c\right)^{5} - 15 \, a^{5} \sin\left(d x + c\right)^{5} + 10 i \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{5} + i \, {\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} a^{5} - 10 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{5} - {\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}}{15 \, d}"," ",0,"-1/15*(15*I*a^5*cos(d*x + c)^5 - 15*a^5*sin(d*x + c)^5 + 10*I*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^5 + I*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*a^5 - 10*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^5 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^5)/d","B",0
74,1,187,0,0.368781," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","-\frac{75 i \, a^{5} \cos\left(d x + c\right)^{7} + i \, {\left(15 \, \cos\left(d x + c\right)^{7} - 42 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3}\right)} a^{5} + 30 i \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{5} + 10 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a^{5} + 15 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 7 \, \sin\left(d x + c\right)^{5}\right)} a^{5} + 3 \, {\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^{5}}{105 \, d}"," ",0,"-1/105*(75*I*a^5*cos(d*x + c)^7 + I*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*a^5 + 30*I*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^5 + 10*(15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a^5 + 15*(5*sin(d*x + c)^7 - 7*sin(d*x + c)^5)*a^5 + 3*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^5)/d","B",0
75,1,217,0,0.552428," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","-\frac{175 i \, a^{5} \cos\left(d x + c\right)^{9} + i \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a^{5} + 50 i \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{5} - 5 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 90 \, \sin\left(d x + c\right)^{7} + 63 \, \sin\left(d x + c\right)^{5}\right)} a^{5} - 10 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 135 \, \sin\left(d x + c\right)^{7} + 189 \, \sin\left(d x + c\right)^{5} - 105 \, \sin\left(d x + c\right)^{3}\right)} a^{5} - {\left(35 \, \sin\left(d x + c\right)^{9} - 180 \, \sin\left(d x + c\right)^{7} + 378 \, \sin\left(d x + c\right)^{5} - 420 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)\right)} a^{5}}{315 \, d}"," ",0,"-1/315*(175*I*a^5*cos(d*x + c)^9 + I*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^5 + 50*I*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^5 - 5*(35*sin(d*x + c)^9 - 90*sin(d*x + c)^7 + 63*sin(d*x + c)^5)*a^5 - 10*(35*sin(d*x + c)^9 - 135*sin(d*x + c)^7 + 189*sin(d*x + c)^5 - 105*sin(d*x + c)^3)*a^5 - (35*sin(d*x + c)^9 - 180*sin(d*x + c)^7 + 378*sin(d*x + c)^5 - 420*sin(d*x + c)^3 + 315*sin(d*x + c))*a^5)/d","A",0
76,1,246,0,0.480471," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","-\frac{315 i \, a^{5} \cos\left(d x + c\right)^{11} + i \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a^{5} + 70 i \, {\left(9 \, \cos\left(d x + c\right)^{11} - 11 \, \cos\left(d x + c\right)^{9}\right)} a^{5} + 2 \, {\left(315 \, \sin\left(d x + c\right)^{11} - 1540 \, \sin\left(d x + c\right)^{9} + 2970 \, \sin\left(d x + c\right)^{7} - 2772 \, \sin\left(d x + c\right)^{5} + 1155 \, \sin\left(d x + c\right)^{3}\right)} a^{5} + 3 \, {\left(105 \, \sin\left(d x + c\right)^{11} - 385 \, \sin\left(d x + c\right)^{9} + 495 \, \sin\left(d x + c\right)^{7} - 231 \, \sin\left(d x + c\right)^{5}\right)} a^{5} + {\left(63 \, \sin\left(d x + c\right)^{11} - 385 \, \sin\left(d x + c\right)^{9} + 990 \, \sin\left(d x + c\right)^{7} - 1386 \, \sin\left(d x + c\right)^{5} + 1155 \, \sin\left(d x + c\right)^{3} - 693 \, \sin\left(d x + c\right)\right)} a^{5}}{693 \, d}"," ",0,"-1/693*(315*I*a^5*cos(d*x + c)^11 + I*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a^5 + 70*I*(9*cos(d*x + c)^11 - 11*cos(d*x + c)^9)*a^5 + 2*(315*sin(d*x + c)^11 - 1540*sin(d*x + c)^9 + 2970*sin(d*x + c)^7 - 2772*sin(d*x + c)^5 + 1155*sin(d*x + c)^3)*a^5 + 3*(105*sin(d*x + c)^11 - 385*sin(d*x + c)^9 + 495*sin(d*x + c)^7 - 231*sin(d*x + c)^5)*a^5 + (63*sin(d*x + c)^11 - 385*sin(d*x + c)^9 + 990*sin(d*x + c)^7 - 1386*sin(d*x + c)^5 + 1155*sin(d*x + c)^3 - 693*sin(d*x + c))*a^5)/d","A",0
77,1,186,0,0.321263," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{3003 \, a^{8} \tan\left(d x + c\right)^{15} - 25740 i \, a^{8} \tan\left(d x + c\right)^{14} - 86625 \, a^{8} \tan\left(d x + c\right)^{13} + 120120 i \, a^{8} \tan\left(d x + c\right)^{12} - 45045 \, a^{8} \tan\left(d x + c\right)^{11} + 396396 i \, a^{8} \tan\left(d x + c\right)^{10} + 495495 \, a^{8} \tan\left(d x + c\right)^{9} + 637065 \, a^{8} \tan\left(d x + c\right)^{7} - 660660 i \, a^{8} \tan\left(d x + c\right)^{6} - 99099 \, a^{8} \tan\left(d x + c\right)^{5} - 360360 i \, a^{8} \tan\left(d x + c\right)^{4} - 375375 \, a^{8} \tan\left(d x + c\right)^{3} + 180180 i \, a^{8} \tan\left(d x + c\right)^{2} + 45045 \, a^{8} \tan\left(d x + c\right)}{45045 \, d}"," ",0,"1/45045*(3003*a^8*tan(d*x + c)^15 - 25740*I*a^8*tan(d*x + c)^14 - 86625*a^8*tan(d*x + c)^13 + 120120*I*a^8*tan(d*x + c)^12 - 45045*a^8*tan(d*x + c)^11 + 396396*I*a^8*tan(d*x + c)^10 + 495495*a^8*tan(d*x + c)^9 + 637065*a^8*tan(d*x + c)^7 - 660660*I*a^8*tan(d*x + c)^6 - 99099*a^8*tan(d*x + c)^5 - 360360*I*a^8*tan(d*x + c)^4 - 375375*a^8*tan(d*x + c)^3 + 180180*I*a^8*tan(d*x + c)^2 + 45045*a^8*tan(d*x + c))/d","B",0
78,1,173,0,0.399594," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{495 \, a^{8} \tan\left(d x + c\right)^{13} - 4290 i \, a^{8} \tan\left(d x + c\right)^{12} - 15210 \, a^{8} \tan\left(d x + c\right)^{11} + 25740 i \, a^{8} \tan\left(d x + c\right)^{10} + 10725 \, a^{8} \tan\left(d x + c\right)^{9} + 38610 i \, a^{8} \tan\left(d x + c\right)^{8} + 77220 \, a^{8} \tan\left(d x + c\right)^{7} - 51480 i \, a^{8} \tan\left(d x + c\right)^{6} + 19305 \, a^{8} \tan\left(d x + c\right)^{5} - 64350 i \, a^{8} \tan\left(d x + c\right)^{4} - 55770 \, a^{8} \tan\left(d x + c\right)^{3} + 25740 i \, a^{8} \tan\left(d x + c\right)^{2} + 6435 \, a^{8} \tan\left(d x + c\right)}{6435 \, d}"," ",0,"1/6435*(495*a^8*tan(d*x + c)^13 - 4290*I*a^8*tan(d*x + c)^12 - 15210*a^8*tan(d*x + c)^11 + 25740*I*a^8*tan(d*x + c)^10 + 10725*a^8*tan(d*x + c)^9 + 38610*I*a^8*tan(d*x + c)^8 + 77220*a^8*tan(d*x + c)^7 - 51480*I*a^8*tan(d*x + c)^6 + 19305*a^8*tan(d*x + c)^5 - 64350*I*a^8*tan(d*x + c)^4 - 55770*a^8*tan(d*x + c)^3 + 25740*I*a^8*tan(d*x + c)^2 + 6435*a^8*tan(d*x + c))/d","B",0
79,1,134,0,0.333431," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{45 \, a^{8} \tan\left(d x + c\right)^{11} - 396 i \, a^{8} \tan\left(d x + c\right)^{10} - 1485 \, a^{8} \tan\left(d x + c\right)^{9} + 2970 i \, a^{8} \tan\left(d x + c\right)^{8} + 2970 \, a^{8} \tan\left(d x + c\right)^{7} + 4158 \, a^{8} \tan\left(d x + c\right)^{5} - 5940 i \, a^{8} \tan\left(d x + c\right)^{4} - 4455 \, a^{8} \tan\left(d x + c\right)^{3} + 1980 i \, a^{8} \tan\left(d x + c\right)^{2} + 495 \, a^{8} \tan\left(d x + c\right)}{495 \, d}"," ",0,"1/495*(45*a^8*tan(d*x + c)^11 - 396*I*a^8*tan(d*x + c)^10 - 1485*a^8*tan(d*x + c)^9 + 2970*I*a^8*tan(d*x + c)^8 + 2970*a^8*tan(d*x + c)^7 + 4158*a^8*tan(d*x + c)^5 - 5940*I*a^8*tan(d*x + c)^4 - 4455*a^8*tan(d*x + c)^3 + 1980*I*a^8*tan(d*x + c)^2 + 495*a^8*tan(d*x + c))/d","B",0
80,1,21,0,0.507242," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{9}}{9 \, a d}"," ",0,"-1/9*I*(I*a*tan(d*x + c) + a)^9/(a*d)","A",0
81,1,121,0,0.646219," ","integrate((a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{15 \, a^{8} \tan\left(d x + c\right)^{7} - 140 i \, a^{8} \tan\left(d x + c\right)^{6} - 609 \, a^{8} \tan\left(d x + c\right)^{5} + 1680 i \, a^{8} \tan\left(d x + c\right)^{4} + 3465 \, a^{8} \tan\left(d x + c\right)^{3} - 6300 i \, a^{8} \tan\left(d x + c\right)^{2} + 13440 \, {\left(d x + c\right)} a^{8} + 6720 i \, a^{8} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 13335 \, a^{8} \tan\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*a^8*tan(d*x + c)^7 - 140*I*a^8*tan(d*x + c)^6 - 609*a^8*tan(d*x + c)^5 + 1680*I*a^8*tan(d*x + c)^4 + 3465*a^8*tan(d*x + c)^3 - 6300*I*a^8*tan(d*x + c)^2 + 13440*(d*x + c)*a^8 + 6720*I*a^8*log(tan(d*x + c)^2 + 1) - 13335*a^8*tan(d*x + c))/d","A",0
82,1,124,0,0.711943," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{a^{8} \tan\left(d x + c\right)^{5} - 10 i \, a^{8} \tan\left(d x + c\right)^{4} - 50 \, a^{8} \tan\left(d x + c\right)^{3} + 180 i \, a^{8} \tan\left(d x + c\right)^{2} - 960 \, {\left(d x + c\right)} a^{8} - 480 i \, a^{8} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 645 \, a^{8} \tan\left(d x + c\right) + \frac{320 \, {\left(a^{8} \tan\left(d x + c\right) - i \, a^{8}\right)}}{\tan\left(d x + c\right)^{2} + 1}}{5 \, d}"," ",0,"1/5*(a^8*tan(d*x + c)^5 - 10*I*a^8*tan(d*x + c)^4 - 50*a^8*tan(d*x + c)^3 + 180*I*a^8*tan(d*x + c)^2 - 960*(d*x + c)*a^8 - 480*I*a^8*log(tan(d*x + c)^2 + 1) + 645*a^8*tan(d*x + c) + 320*(a^8*tan(d*x + c) - I*a^8)/(tan(d*x + c)^2 + 1))/d","A",0
83,1,136,0,0.640907," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{8 \, a^{8} \tan\left(d x + c\right)^{3} - 96 i \, a^{8} \tan\left(d x + c\right)^{2} + 1920 \, {\left(d x + c\right)} a^{8} + 960 i \, a^{8} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 744 \, a^{8} \tan\left(d x + c\right) - \frac{3 \, {\left(640 \, a^{8} \tan\left(d x + c\right)^{3} - 768 i \, a^{8} \tan\left(d x + c\right)^{2} + 384 \, a^{8} \tan\left(d x + c\right) - 512 i \, a^{8}\right)}}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{24 \, d}"," ",0,"1/24*(8*a^8*tan(d*x + c)^3 - 96*I*a^8*tan(d*x + c)^2 + 1920*(d*x + c)*a^8 + 960*I*a^8*log(tan(d*x + c)^2 + 1) - 744*a^8*tan(d*x + c) - 3*(640*a^8*tan(d*x + c)^3 - 768*I*a^8*tan(d*x + c)^2 + 384*a^8*tan(d*x + c) - 512*I*a^8)/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
84,1,146,0,0.698328," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{384 \, {\left(d x + c\right)} a^{8} + 192 i \, a^{8} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 48 \, a^{8} \tan\left(d x + c\right) - \frac{1152 \, a^{8} \tan\left(d x + c\right)^{5} - 1920 i \, a^{8} \tan\left(d x + c\right)^{4} + 512 \, a^{8} \tan\left(d x + c\right)^{3} - 1536 i \, a^{8} \tan\left(d x + c\right)^{2} + 384 \, a^{8} \tan\left(d x + c\right) - 640 i \, a^{8}}{\tan\left(d x + c\right)^{6} + 3 \, \tan\left(d x + c\right)^{4} + 3 \, \tan\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"-1/48*(384*(d*x + c)*a^8 + 192*I*a^8*log(tan(d*x + c)^2 + 1) - 48*a^8*tan(d*x + c) - (1152*a^8*tan(d*x + c)^5 - 1920*I*a^8*tan(d*x + c)^4 + 512*a^8*tan(d*x + c)^3 - 1536*I*a^8*tan(d*x + c)^2 + 384*a^8*tan(d*x + c) - 640*I*a^8)/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1))/d","A",0
85,1,137,0,0.765054," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{384 \, a^{8} \tan\left(d x + c\right)^{7} - 1536 i \, a^{8} \tan\left(d x + c\right)^{6} - 2688 \, a^{8} \tan\left(d x + c\right)^{5} + 3072 i \, a^{8} \tan\left(d x + c\right)^{4} + 2688 \, a^{8} \tan\left(d x + c\right)^{3} - 1536 i \, a^{8} \tan\left(d x + c\right)^{2} - 384 \, a^{8} \tan\left(d x + c\right)}{384 \, {\left(\tan\left(d x + c\right)^{8} + 4 \, \tan\left(d x + c\right)^{6} + 6 \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{2} + 1\right)} d}"," ",0,"-1/384*(384*a^8*tan(d*x + c)^7 - 1536*I*a^8*tan(d*x + c)^6 - 2688*a^8*tan(d*x + c)^5 + 3072*I*a^8*tan(d*x + c)^4 + 2688*a^8*tan(d*x + c)^3 - 1536*I*a^8*tan(d*x + c)^2 - 384*a^8*tan(d*x + c))/((tan(d*x + c)^8 + 4*tan(d*x + c)^6 + 6*tan(d*x + c)^4 + 4*tan(d*x + c)^2 + 1)*d)","B",0
86,1,152,0,0.837854," ","integrate(cos(d*x+c)^10*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{1280 \, a^{8} \tan\left(d x + c\right)^{7} - 7680 i \, a^{8} \tan\left(d x + c\right)^{6} - 19712 \, a^{8} \tan\left(d x + c\right)^{5} + 28160 i \, a^{8} \tan\left(d x + c\right)^{4} + 24320 \, a^{8} \tan\left(d x + c\right)^{3} - 12800 i \, a^{8} \tan\left(d x + c\right)^{2} - 3840 \, a^{8} \tan\left(d x + c\right) + 512 i \, a^{8}}{3840 \, {\left(\tan\left(d x + c\right)^{10} + 5 \, \tan\left(d x + c\right)^{8} + 10 \, \tan\left(d x + c\right)^{6} + 10 \, \tan\left(d x + c\right)^{4} + 5 \, \tan\left(d x + c\right)^{2} + 1\right)} d}"," ",0,"-1/3840*(1280*a^8*tan(d*x + c)^7 - 7680*I*a^8*tan(d*x + c)^6 - 19712*a^8*tan(d*x + c)^5 + 28160*I*a^8*tan(d*x + c)^4 + 24320*a^8*tan(d*x + c)^3 - 12800*I*a^8*tan(d*x + c)^2 - 3840*a^8*tan(d*x + c) + 512*I*a^8)/((tan(d*x + c)^10 + 5*tan(d*x + c)^8 + 10*tan(d*x + c)^6 + 10*tan(d*x + c)^4 + 5*tan(d*x + c)^2 + 1)*d)","B",0
87,1,162,0,0.900303," ","integrate(cos(d*x+c)^12*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{3072 \, a^{8} \tan\left(d x + c\right)^{7} - 20480 i \, a^{8} \tan\left(d x + c\right)^{6} - 58368 \, a^{8} \tan\left(d x + c\right)^{5} + 92160 i \, a^{8} \tan\left(d x + c\right)^{4} + 87040 \, a^{8} \tan\left(d x + c\right)^{3} - 49152 i \, a^{8} \tan\left(d x + c\right)^{2} - 15360 \, a^{8} \tan\left(d x + c\right) + 2048 i \, a^{8}}{15360 \, {\left(\tan\left(d x + c\right)^{12} + 6 \, \tan\left(d x + c\right)^{10} + 15 \, \tan\left(d x + c\right)^{8} + 20 \, \tan\left(d x + c\right)^{6} + 15 \, \tan\left(d x + c\right)^{4} + 6 \, \tan\left(d x + c\right)^{2} + 1\right)} d}"," ",0,"-1/15360*(3072*a^8*tan(d*x + c)^7 - 20480*I*a^8*tan(d*x + c)^6 - 58368*a^8*tan(d*x + c)^5 + 92160*I*a^8*tan(d*x + c)^4 + 87040*a^8*tan(d*x + c)^3 - 49152*I*a^8*tan(d*x + c)^2 - 15360*a^8*tan(d*x + c) + 2048*I*a^8)/((tan(d*x + c)^12 + 6*tan(d*x + c)^10 + 15*tan(d*x + c)^8 + 20*tan(d*x + c)^6 + 15*tan(d*x + c)^4 + 6*tan(d*x + c)^2 + 1)*d)","B",0
88,1,172,0,0.671090," ","integrate(cos(d*x+c)^14*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{30720 \, a^{8} \tan\left(d x + c\right)^{7} - 215040 i \, a^{8} \tan\left(d x + c\right)^{6} - 645120 \, a^{8} \tan\left(d x + c\right)^{5} + 1075200 i \, a^{8} \tan\left(d x + c\right)^{4} + 1075200 \, a^{8} \tan\left(d x + c\right)^{3} - 645120 i \, a^{8} \tan\left(d x + c\right)^{2} - 215040 \, a^{8} \tan\left(d x + c\right) + 30720 i \, a^{8}}{215040 \, {\left(\tan\left(d x + c\right)^{14} + 7 \, \tan\left(d x + c\right)^{12} + 21 \, \tan\left(d x + c\right)^{10} + 35 \, \tan\left(d x + c\right)^{8} + 35 \, \tan\left(d x + c\right)^{6} + 21 \, \tan\left(d x + c\right)^{4} + 7 \, \tan\left(d x + c\right)^{2} + 1\right)} d}"," ",0,"-1/215040*(30720*a^8*tan(d*x + c)^7 - 215040*I*a^8*tan(d*x + c)^6 - 645120*a^8*tan(d*x + c)^5 + 1075200*I*a^8*tan(d*x + c)^4 + 1075200*a^8*tan(d*x + c)^3 - 645120*I*a^8*tan(d*x + c)^2 - 215040*a^8*tan(d*x + c) + 30720*I*a^8)/((tan(d*x + c)^14 + 7*tan(d*x + c)^12 + 21*tan(d*x + c)^10 + 35*tan(d*x + c)^8 + 35*tan(d*x + c)^6 + 21*tan(d*x + c)^4 + 7*tan(d*x + c)^2 + 1)*d)","B",0
89,1,246,0,0.456544," ","integrate(cos(d*x+c)^16*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{13440 \, {\left(d x + c\right)} a^{8} + \frac{13440 \, a^{8} \tan\left(d x + c\right)^{15} + 103040 \, a^{8} \tan\left(d x + c\right)^{13} + 343168 \, a^{8} \tan\left(d x + c\right)^{11} + 646784 \, a^{8} \tan\left(d x + c\right)^{9} + 369024 \, a^{8} \tan\left(d x + c\right)^{7} + 2752512 i \, a^{8} \tan\left(d x + c\right)^{6} + 9061248 \, a^{8} \tan\left(d x + c\right)^{5} - 14680064 i \, a^{8} \tan\left(d x + c\right)^{4} - 15012480 \, a^{8} \tan\left(d x + c\right)^{3} + 9568256 i \, a^{8} \tan\left(d x + c\right)^{2} + 3427200 \, a^{8} \tan\left(d x + c\right) - 524288 i \, a^{8}}{\tan\left(d x + c\right)^{16} + 8 \, \tan\left(d x + c\right)^{14} + 28 \, \tan\left(d x + c\right)^{12} + 56 \, \tan\left(d x + c\right)^{10} + 70 \, \tan\left(d x + c\right)^{8} + 56 \, \tan\left(d x + c\right)^{6} + 28 \, \tan\left(d x + c\right)^{4} + 8 \, \tan\left(d x + c\right)^{2} + 1}}{3440640 \, d}"," ",0,"1/3440640*(13440*(d*x + c)*a^8 + (13440*a^8*tan(d*x + c)^15 + 103040*a^8*tan(d*x + c)^13 + 343168*a^8*tan(d*x + c)^11 + 646784*a^8*tan(d*x + c)^9 + 369024*a^8*tan(d*x + c)^7 + 2752512*I*a^8*tan(d*x + c)^6 + 9061248*a^8*tan(d*x + c)^5 - 14680064*I*a^8*tan(d*x + c)^4 - 15012480*a^8*tan(d*x + c)^3 + 9568256*I*a^8*tan(d*x + c)^2 + 3427200*a^8*tan(d*x + c) - 524288*I*a^8)/(tan(d*x + c)^16 + 8*tan(d*x + c)^14 + 28*tan(d*x + c)^12 + 56*tan(d*x + c)^10 + 70*tan(d*x + c)^8 + 56*tan(d*x + c)^6 + 28*tan(d*x + c)^4 + 8*tan(d*x + c)^2 + 1))/d","A",0
90,1,269,0,0.508665," ","integrate(cos(d*x+c)^18*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{40320 \, {\left(d x + c\right)} a^{8} + \frac{40320 \, a^{8} \tan\left(d x + c\right)^{17} + 349440 \, a^{8} \tan\left(d x + c\right)^{15} + 1338624 \, a^{8} \tan\left(d x + c\right)^{13} + 2969856 \, a^{8} \tan\left(d x + c\right)^{11} + 4194304 \, a^{8} \tan\left(d x + c\right)^{9} + 3518208 \, a^{8} \tan\left(d x + c\right)^{7} + 2752512 i \, a^{8} \tan\left(d x + c\right)^{6} + 11047680 \, a^{8} \tan\left(d x + c\right)^{5} - 15335424 i \, a^{8} \tan\left(d x + c\right)^{4} - 15488256 \, a^{8} \tan\left(d x + c\right)^{3} + 10616832 i \, a^{8} \tan\left(d x + c\right)^{2} + 4088448 \, a^{8} \tan\left(d x + c\right) - 655360 i \, a^{8}}{\tan\left(d x + c\right)^{18} + 9 \, \tan\left(d x + c\right)^{16} + 36 \, \tan\left(d x + c\right)^{14} + 84 \, \tan\left(d x + c\right)^{12} + 126 \, \tan\left(d x + c\right)^{10} + 126 \, \tan\left(d x + c\right)^{8} + 84 \, \tan\left(d x + c\right)^{6} + 36 \, \tan\left(d x + c\right)^{4} + 9 \, \tan\left(d x + c\right)^{2} + 1}}{4128768 \, d}"," ",0,"1/4128768*(40320*(d*x + c)*a^8 + (40320*a^8*tan(d*x + c)^17 + 349440*a^8*tan(d*x + c)^15 + 1338624*a^8*tan(d*x + c)^13 + 2969856*a^8*tan(d*x + c)^11 + 4194304*a^8*tan(d*x + c)^9 + 3518208*a^8*tan(d*x + c)^7 + 2752512*I*a^8*tan(d*x + c)^6 + 11047680*a^8*tan(d*x + c)^5 - 15335424*I*a^8*tan(d*x + c)^4 - 15488256*a^8*tan(d*x + c)^3 + 10616832*I*a^8*tan(d*x + c)^2 + 4088448*a^8*tan(d*x + c) - 655360*I*a^8)/(tan(d*x + c)^18 + 9*tan(d*x + c)^16 + 36*tan(d*x + c)^14 + 84*tan(d*x + c)^12 + 126*tan(d*x + c)^10 + 126*tan(d*x + c)^8 + 84*tan(d*x + c)^6 + 36*tan(d*x + c)^4 + 9*tan(d*x + c)^2 + 1))/d","A",0
91,1,396,0,0.494286," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{5 \, a^{8} {\left(\frac{2 \, {\left(87 \, \sin\left(d x + c\right)^{5} - 136 \, \sin\left(d x + c\right)^{3} + 57 \, \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} + 105 \, \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, \log\left(\sin\left(d x + c\right) - 1\right) - 96 \, \sin\left(d x + c\right)\right)} + 840 \, a^{8} {\left(\frac{2 \, {\left(9 \, \sin\left(d x + c\right)^{3} - 7 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \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) - 16 \, \sin\left(d x + c\right)\right)} + 8400 \, a^{8} {\left(\frac{2 \, \sin\left(d x + c\right)}{\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) - 4 \, \sin\left(d x + c\right)\right)} + 26880 i \, a^{8} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + 8960 i \, a^{8} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)} + 768 i \, a^{8} {\left(\frac{15 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} + 1}{\cos\left(d x + c\right)^{5}} + 5 \, \cos\left(d x + c\right)\right)} + 6720 \, a^{8} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} + 3840 i \, a^{8} \cos\left(d x + c\right) - 480 \, a^{8} \sin\left(d x + c\right)}{480 \, d}"," ",0,"-1/480*(5*a^8*(2*(87*sin(d*x + c)^5 - 136*sin(d*x + c)^3 + 57*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) + 105*log(sin(d*x + c) + 1) - 105*log(sin(d*x + c) - 1) - 96*sin(d*x + c)) + 840*a^8*(2*(9*sin(d*x + c)^3 - 7*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) + 15*log(sin(d*x + c) + 1) - 15*log(sin(d*x + c) - 1) - 16*sin(d*x + c)) + 8400*a^8*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + 3*log(sin(d*x + c) + 1) - 3*log(sin(d*x + c) - 1) - 4*sin(d*x + c)) + 26880*I*a^8*(1/cos(d*x + c) + cos(d*x + c)) + 8960*I*a^8*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) + 768*I*a^8*((15*cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 1)/cos(d*x + c)^5 + 5*cos(d*x + c)) + 6720*a^8*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) + 3840*I*a^8*cos(d*x + c) - 480*a^8*sin(d*x + c))/d","B",0
92,1,352,0,0.460420," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{128 i \, a^{8} \cos\left(d x + c\right)^{3} + 448 \, a^{8} \sin\left(d x + c\right)^{3} + 896 i \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a^{8} + 128 i \, {\left(\cos\left(d x + c\right)^{3} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} - 9 \, \cos\left(d x + c\right)\right)} a^{8} + 896 i \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{8} + {\left(16 \, \sin\left(d x + c\right)^{3} - \frac{6 \, {\left(13 \, \sin\left(d x + c\right)^{3} - 11 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right) + 144 \, \sin\left(d x + c\right)\right)} a^{8} + 112 \, {\left(4 \, \sin\left(d x + c\right)^{3} - \frac{6 \, \sin\left(d x + c\right)}{\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) + 24 \, \sin\left(d x + c\right)\right)} a^{8} + 560 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, \sin\left(d x + c\right)\right)} a^{8} + 16 \, {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{8}}{48 \, d}"," ",0,"-1/48*(128*I*a^8*cos(d*x + c)^3 + 448*a^8*sin(d*x + c)^3 + 896*I*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^8 + 128*I*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*a^8 + 896*I*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^8 + (16*sin(d*x + c)^3 - 6*(13*sin(d*x + c)^3 - 11*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1) + 144*sin(d*x + c))*a^8 + 112*(4*sin(d*x + c)^3 - 6*sin(d*x + c)/(sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 24*sin(d*x + c))*a^8 + 560*(2*sin(d*x + c)^3 - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1) + 6*sin(d*x + c))*a^8 + 16*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^8)/d","B",0
93,1,326,0,0.493242," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{96 i \, a^{8} \cos\left(d x + c\right)^{5} - 840 \, a^{8} \sin\left(d x + c\right)^{5} + 224 i \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{8} + 224 i \, {\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} a^{8} + 96 i \, {\left(\cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3} + \frac{5}{\cos\left(d x + c\right)} + 15 \, \cos\left(d x + c\right)\right)} a^{8} - {\left(12 \, \sin\left(d x + c\right)^{5} + 40 \, \sin\left(d x + c\right)^{3} - \frac{30 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right) + 180 \, \sin\left(d x + c\right)\right)} a^{8} - 56 \, {\left(6 \, \sin\left(d x + c\right)^{5} + 10 \, \sin\left(d x + c\right)^{3} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right) + 30 \, \sin\left(d x + c\right)\right)} a^{8} - 112 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{8} - 4 \, {\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^{8}}{60 \, d}"," ",0,"-1/60*(96*I*a^8*cos(d*x + c)^5 - 840*a^8*sin(d*x + c)^5 + 224*I*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^8 + 224*I*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*a^8 + 96*I*(cos(d*x + c)^5 - 5*cos(d*x + c)^3 + 5/cos(d*x + c) + 15*cos(d*x + c))*a^8 - (12*sin(d*x + c)^5 + 40*sin(d*x + c)^3 - 30*sin(d*x + c)/(sin(d*x + c)^2 - 1) - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1) + 180*sin(d*x + c))*a^8 - 56*(6*sin(d*x + c)^5 + 10*sin(d*x + c)^3 - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1) + 30*sin(d*x + c))*a^8 - 112*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^8 - 4*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^8)/d","B",0
94,1,309,0,0.362285," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{240 i \, a^{8} \cos\left(d x + c\right)^{7} + 840 \, a^{8} \sin\left(d x + c\right)^{7} + 112 i \, {\left(15 \, \cos\left(d x + c\right)^{7} - 42 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3}\right)} a^{8} + 336 i \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{8} + 48 i \, {\left(5 \, \cos\left(d x + c\right)^{7} - 21 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3} - 35 \, \cos\left(d x + c\right)\right)} a^{8} + {\left(30 \, \sin\left(d x + c\right)^{7} + 42 \, \sin\left(d x + c\right)^{5} + 70 \, \sin\left(d x + c\right)^{3} - 105 \, \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, \log\left(\sin\left(d x + c\right) - 1\right) + 210 \, \sin\left(d x + c\right)\right)} a^{8} + 56 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a^{8} + 420 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 7 \, \sin\left(d x + c\right)^{5}\right)} a^{8} + 6 \, {\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^{8}}{210 \, d}"," ",0,"-1/210*(240*I*a^8*cos(d*x + c)^7 + 840*a^8*sin(d*x + c)^7 + 112*I*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*a^8 + 336*I*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^8 + 48*I*(5*cos(d*x + c)^7 - 21*cos(d*x + c)^5 + 35*cos(d*x + c)^3 - 35*cos(d*x + c))*a^8 + (30*sin(d*x + c)^7 + 42*sin(d*x + c)^5 + 70*sin(d*x + c)^3 - 105*log(sin(d*x + c) + 1) + 105*log(sin(d*x + c) - 1) + 210*sin(d*x + c))*a^8 + 56*(15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a^8 + 420*(5*sin(d*x + c)^7 - 7*sin(d*x + c)^5)*a^8 + 6*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^8)/d","B",0
95,1,302,0,0.481553," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{280 i \, a^{8} \cos\left(d x + c\right)^{9} - 35 \, a^{8} \sin\left(d x + c\right)^{9} + 56 i \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a^{8} + 8 i \, {\left(35 \, \cos\left(d x + c\right)^{9} - 135 \, \cos\left(d x + c\right)^{7} + 189 \, \cos\left(d x + c\right)^{5} - 105 \, \cos\left(d x + c\right)^{3}\right)} a^{8} + 280 i \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{8} - 70 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 90 \, \sin\left(d x + c\right)^{7} + 63 \, \sin\left(d x + c\right)^{5}\right)} a^{8} - 28 \, {\left(35 \, \sin\left(d x + c\right)^{9} - 135 \, \sin\left(d x + c\right)^{7} + 189 \, \sin\left(d x + c\right)^{5} - 105 \, \sin\left(d x + c\right)^{3}\right)} a^{8} - {\left(35 \, \sin\left(d x + c\right)^{9} - 180 \, \sin\left(d x + c\right)^{7} + 378 \, \sin\left(d x + c\right)^{5} - 420 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)\right)} a^{8} - 140 \, {\left(7 \, \sin\left(d x + c\right)^{9} - 9 \, \sin\left(d x + c\right)^{7}\right)} a^{8}}{315 \, d}"," ",0,"-1/315*(280*I*a^8*cos(d*x + c)^9 - 35*a^8*sin(d*x + c)^9 + 56*I*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^8 + 8*I*(35*cos(d*x + c)^9 - 135*cos(d*x + c)^7 + 189*cos(d*x + c)^5 - 105*cos(d*x + c)^3)*a^8 + 280*I*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^8 - 70*(35*sin(d*x + c)^9 - 90*sin(d*x + c)^7 + 63*sin(d*x + c)^5)*a^8 - 28*(35*sin(d*x + c)^9 - 135*sin(d*x + c)^7 + 189*sin(d*x + c)^5 - 105*sin(d*x + c)^3)*a^8 - (35*sin(d*x + c)^9 - 180*sin(d*x + c)^7 + 378*sin(d*x + c)^5 - 420*sin(d*x + c)^3 + 315*sin(d*x + c))*a^8 - 140*(7*sin(d*x + c)^9 - 9*sin(d*x + c)^7)*a^8)/d","B",0
96,1,355,0,0.379078," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{2520 i \, a^{8} \cos\left(d x + c\right)^{11} + 24 i \, {\left(105 \, \cos\left(d x + c\right)^{11} - 385 \, \cos\left(d x + c\right)^{9} + 495 \, \cos\left(d x + c\right)^{7} - 231 \, \cos\left(d x + c\right)^{5}\right)} a^{8} + 280 i \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a^{8} + 1960 i \, {\left(9 \, \cos\left(d x + c\right)^{11} - 11 \, \cos\left(d x + c\right)^{9}\right)} a^{8} + 28 \, {\left(315 \, \sin\left(d x + c\right)^{11} - 1540 \, \sin\left(d x + c\right)^{9} + 2970 \, \sin\left(d x + c\right)^{7} - 2772 \, \sin\left(d x + c\right)^{5} + 1155 \, \sin\left(d x + c\right)^{3}\right)} a^{8} + 210 \, {\left(105 \, \sin\left(d x + c\right)^{11} - 385 \, \sin\left(d x + c\right)^{9} + 495 \, \sin\left(d x + c\right)^{7} - 231 \, \sin\left(d x + c\right)^{5}\right)} a^{8} + 140 \, {\left(63 \, \sin\left(d x + c\right)^{11} - 154 \, \sin\left(d x + c\right)^{9} + 99 \, \sin\left(d x + c\right)^{7}\right)} a^{8} + 5 \, {\left(63 \, \sin\left(d x + c\right)^{11} - 385 \, \sin\left(d x + c\right)^{9} + 990 \, \sin\left(d x + c\right)^{7} - 1386 \, \sin\left(d x + c\right)^{5} + 1155 \, \sin\left(d x + c\right)^{3} - 693 \, \sin\left(d x + c\right)\right)} a^{8} + 35 \, {\left(9 \, \sin\left(d x + c\right)^{11} - 11 \, \sin\left(d x + c\right)^{9}\right)} a^{8}}{3465 \, d}"," ",0,"-1/3465*(2520*I*a^8*cos(d*x + c)^11 + 24*I*(105*cos(d*x + c)^11 - 385*cos(d*x + c)^9 + 495*cos(d*x + c)^7 - 231*cos(d*x + c)^5)*a^8 + 280*I*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a^8 + 1960*I*(9*cos(d*x + c)^11 - 11*cos(d*x + c)^9)*a^8 + 28*(315*sin(d*x + c)^11 - 1540*sin(d*x + c)^9 + 2970*sin(d*x + c)^7 - 2772*sin(d*x + c)^5 + 1155*sin(d*x + c)^3)*a^8 + 210*(105*sin(d*x + c)^11 - 385*sin(d*x + c)^9 + 495*sin(d*x + c)^7 - 231*sin(d*x + c)^5)*a^8 + 140*(63*sin(d*x + c)^11 - 154*sin(d*x + c)^9 + 99*sin(d*x + c)^7)*a^8 + 5*(63*sin(d*x + c)^11 - 385*sin(d*x + c)^9 + 990*sin(d*x + c)^7 - 1386*sin(d*x + c)^5 + 1155*sin(d*x + c)^3 - 693*sin(d*x + c))*a^8 + 35*(9*sin(d*x + c)^11 - 11*sin(d*x + c)^9)*a^8)/d","B",0
97,1,405,0,0.417799," ","integrate(cos(d*x+c)^13*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{5544 i \, a^{8} \cos\left(d x + c\right)^{13} + 24 i \, {\left(231 \, \cos\left(d x + c\right)^{13} - 819 \, \cos\left(d x + c\right)^{11} + 1001 \, \cos\left(d x + c\right)^{9} - 429 \, \cos\left(d x + c\right)^{7}\right)} a^{8} + 392 i \, {\left(99 \, \cos\left(d x + c\right)^{13} - 234 \, \cos\left(d x + c\right)^{11} + 143 \, \cos\left(d x + c\right)^{9}\right)} a^{8} + 3528 i \, {\left(11 \, \cos\left(d x + c\right)^{13} - 13 \, \cos\left(d x + c\right)^{11}\right)} a^{8} - 42 \, {\left(1155 \, \sin\left(d x + c\right)^{13} - 5460 \, \sin\left(d x + c\right)^{11} + 10010 \, \sin\left(d x + c\right)^{9} - 8580 \, \sin\left(d x + c\right)^{7} + 3003 \, \sin\left(d x + c\right)^{5}\right)} a^{8} - 28 \, {\left(693 \, \sin\left(d x + c\right)^{13} - 4095 \, \sin\left(d x + c\right)^{11} + 10010 \, \sin\left(d x + c\right)^{9} - 12870 \, \sin\left(d x + c\right)^{7} + 9009 \, \sin\left(d x + c\right)^{5} - 3003 \, \sin\left(d x + c\right)^{3}\right)} a^{8} - 84 \, {\left(231 \, \sin\left(d x + c\right)^{13} - 819 \, \sin\left(d x + c\right)^{11} + 1001 \, \sin\left(d x + c\right)^{9} - 429 \, \sin\left(d x + c\right)^{7}\right)} a^{8} - 3 \, {\left(231 \, \sin\left(d x + c\right)^{13} - 1638 \, \sin\left(d x + c\right)^{11} + 5005 \, \sin\left(d x + c\right)^{9} - 8580 \, \sin\left(d x + c\right)^{7} + 9009 \, \sin\left(d x + c\right)^{5} - 6006 \, \sin\left(d x + c\right)^{3} + 3003 \, \sin\left(d x + c\right)\right)} a^{8} - 7 \, {\left(99 \, \sin\left(d x + c\right)^{13} - 234 \, \sin\left(d x + c\right)^{11} + 143 \, \sin\left(d x + c\right)^{9}\right)} a^{8}}{9009 \, d}"," ",0,"-1/9009*(5544*I*a^8*cos(d*x + c)^13 + 24*I*(231*cos(d*x + c)^13 - 819*cos(d*x + c)^11 + 1001*cos(d*x + c)^9 - 429*cos(d*x + c)^7)*a^8 + 392*I*(99*cos(d*x + c)^13 - 234*cos(d*x + c)^11 + 143*cos(d*x + c)^9)*a^8 + 3528*I*(11*cos(d*x + c)^13 - 13*cos(d*x + c)^11)*a^8 - 42*(1155*sin(d*x + c)^13 - 5460*sin(d*x + c)^11 + 10010*sin(d*x + c)^9 - 8580*sin(d*x + c)^7 + 3003*sin(d*x + c)^5)*a^8 - 28*(693*sin(d*x + c)^13 - 4095*sin(d*x + c)^11 + 10010*sin(d*x + c)^9 - 12870*sin(d*x + c)^7 + 9009*sin(d*x + c)^5 - 3003*sin(d*x + c)^3)*a^8 - 84*(231*sin(d*x + c)^13 - 819*sin(d*x + c)^11 + 1001*sin(d*x + c)^9 - 429*sin(d*x + c)^7)*a^8 - 3*(231*sin(d*x + c)^13 - 1638*sin(d*x + c)^11 + 5005*sin(d*x + c)^9 - 8580*sin(d*x + c)^7 + 9009*sin(d*x + c)^5 - 6006*sin(d*x + c)^3 + 3003*sin(d*x + c))*a^8 - 7*(99*sin(d*x + c)^13 - 234*sin(d*x + c)^11 + 143*sin(d*x + c)^9)*a^8)/d","B",0
98,1,453,0,0.511297," ","integrate(cos(d*x+c)^15*(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{3432 i \, a^{8} \cos\left(d x + c\right)^{15} + 8 i \, {\left(429 \, \cos\left(d x + c\right)^{15} - 1485 \, \cos\left(d x + c\right)^{13} + 1755 \, \cos\left(d x + c\right)^{11} - 715 \, \cos\left(d x + c\right)^{9}\right)} a^{8} + 168 i \, {\left(143 \, \cos\left(d x + c\right)^{15} - 330 \, \cos\left(d x + c\right)^{13} + 195 \, \cos\left(d x + c\right)^{11}\right)} a^{8} + 1848 i \, {\left(13 \, \cos\left(d x + c\right)^{15} - 15 \, \cos\left(d x + c\right)^{13}\right)} a^{8} + 4 \, {\left(3003 \, \sin\left(d x + c\right)^{15} - 13860 \, \sin\left(d x + c\right)^{13} + 24570 \, \sin\left(d x + c\right)^{11} - 20020 \, \sin\left(d x + c\right)^{9} + 6435 \, \sin\left(d x + c\right)^{7}\right)} a^{8} + 10 \, {\left(3003 \, \sin\left(d x + c\right)^{15} - 17325 \, \sin\left(d x + c\right)^{13} + 40950 \, \sin\left(d x + c\right)^{11} - 50050 \, \sin\left(d x + c\right)^{9} + 32175 \, \sin\left(d x + c\right)^{7} - 9009 \, \sin\left(d x + c\right)^{5}\right)} a^{8} + 4 \, {\left(3003 \, \sin\left(d x + c\right)^{15} - 20790 \, \sin\left(d x + c\right)^{13} + 61425 \, \sin\left(d x + c\right)^{11} - 100100 \, \sin\left(d x + c\right)^{9} + 96525 \, \sin\left(d x + c\right)^{7} - 54054 \, \sin\left(d x + c\right)^{5} + 15015 \, \sin\left(d x + c\right)^{3}\right)} a^{8} + {\left(429 \, \sin\left(d x + c\right)^{15} - 1485 \, \sin\left(d x + c\right)^{13} + 1755 \, \sin\left(d x + c\right)^{11} - 715 \, \sin\left(d x + c\right)^{9}\right)} a^{8} + {\left(429 \, \sin\left(d x + c\right)^{15} - 3465 \, \sin\left(d x + c\right)^{13} + 12285 \, \sin\left(d x + c\right)^{11} - 25025 \, \sin\left(d x + c\right)^{9} + 32175 \, \sin\left(d x + c\right)^{7} - 27027 \, \sin\left(d x + c\right)^{5} + 15015 \, \sin\left(d x + c\right)^{3} - 6435 \, \sin\left(d x + c\right)\right)} a^{8}}{6435 \, d}"," ",0,"-1/6435*(3432*I*a^8*cos(d*x + c)^15 + 8*I*(429*cos(d*x + c)^15 - 1485*cos(d*x + c)^13 + 1755*cos(d*x + c)^11 - 715*cos(d*x + c)^9)*a^8 + 168*I*(143*cos(d*x + c)^15 - 330*cos(d*x + c)^13 + 195*cos(d*x + c)^11)*a^8 + 1848*I*(13*cos(d*x + c)^15 - 15*cos(d*x + c)^13)*a^8 + 4*(3003*sin(d*x + c)^15 - 13860*sin(d*x + c)^13 + 24570*sin(d*x + c)^11 - 20020*sin(d*x + c)^9 + 6435*sin(d*x + c)^7)*a^8 + 10*(3003*sin(d*x + c)^15 - 17325*sin(d*x + c)^13 + 40950*sin(d*x + c)^11 - 50050*sin(d*x + c)^9 + 32175*sin(d*x + c)^7 - 9009*sin(d*x + c)^5)*a^8 + 4*(3003*sin(d*x + c)^15 - 20790*sin(d*x + c)^13 + 61425*sin(d*x + c)^11 - 100100*sin(d*x + c)^9 + 96525*sin(d*x + c)^7 - 54054*sin(d*x + c)^5 + 15015*sin(d*x + c)^3)*a^8 + (429*sin(d*x + c)^15 - 1485*sin(d*x + c)^13 + 1755*sin(d*x + c)^11 - 715*sin(d*x + c)^9)*a^8 + (429*sin(d*x + c)^15 - 3465*sin(d*x + c)^13 + 12285*sin(d*x + c)^11 - 25025*sin(d*x + c)^9 + 32175*sin(d*x + c)^7 - 27027*sin(d*x + c)^5 + 15015*sin(d*x + c)^3 - 6435*sin(d*x + c))*a^8)/d","B",0
99,1,87,0,0.423971," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{-105 i \, \tan\left(d x + c\right)^{8} + 120 \, \tan\left(d x + c\right)^{7} - 420 i \, \tan\left(d x + c\right)^{6} + 504 \, \tan\left(d x + c\right)^{5} - 630 i \, \tan\left(d x + c\right)^{4} + 840 \, \tan\left(d x + c\right)^{3} - 420 i \, \tan\left(d x + c\right)^{2} + 840 \, \tan\left(d x + c\right)}{840 \, a d}"," ",0,"1/840*(-105*I*tan(d*x + c)^8 + 120*tan(d*x + c)^7 - 420*I*tan(d*x + c)^6 + 504*tan(d*x + c)^5 - 630*I*tan(d*x + c)^4 + 840*tan(d*x + c)^3 - 420*I*tan(d*x + c)^2 + 840*tan(d*x + c))/(a*d)","A",0
100,1,67,0,0.388336," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{10 i \, \tan\left(d x + c\right)^{6} - 12 \, \tan\left(d x + c\right)^{5} + 30 i \, \tan\left(d x + c\right)^{4} - 40 \, \tan\left(d x + c\right)^{3} + 30 i \, \tan\left(d x + c\right)^{2} - 60 \, \tan\left(d x + c\right)}{60 \, a d}"," ",0,"-1/60*(10*I*tan(d*x + c)^6 - 12*tan(d*x + c)^5 + 30*I*tan(d*x + c)^4 - 40*tan(d*x + c)^3 + 30*I*tan(d*x + c)^2 - 60*tan(d*x + c))/(a*d)","A",0
101,1,47,0,0.546999," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{-3 i \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{3} - 6 i \, \tan\left(d x + c\right)^{2} + 12 \, \tan\left(d x + c\right)}{12 \, a d}"," ",0,"1/12*(-3*I*tan(d*x + c)^4 + 4*tan(d*x + c)^3 - 6*I*tan(d*x + c)^2 + 12*tan(d*x + c))/(a*d)","A",0
102,1,27,0,0.313304," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, \tan\left(d x + c\right)^{2} - 2 \, \tan\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(I*tan(d*x + c)^2 - 2*tan(d*x + c))/(a*d)","A",0
103,1,20,0,0.325920," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, \log\left(i \, a \tan\left(d x + c\right) + a\right)}{a d}"," ",0,"-I*log(I*a*tan(d*x + c) + a)/(a*d)","A",0
104,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
105,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
106,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
107,1,289,0,0.508880," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, {\left(-\frac{75 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{30 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{240 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{30 i \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{120 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{75 i \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 24\right)}}{-120 i \, a + \frac{600 i \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1200 i \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1200 i \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{600 i \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{120 i \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \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}}{8 \, d}"," ",0,"1/8*(16*(-75*I*sin(d*x + c)/(cos(d*x + c) + 1) + 30*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 240*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 30*I*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 120*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 75*I*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 24)/(-120*I*a + 600*I*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1200*I*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1200*I*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 600*I*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 120*I*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 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)/d","B",0
108,1,186,0,0.369793," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(\frac{3 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3 i \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 2\right)}}{6 i \, a - \frac{18 i \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 i \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6 i \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \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}}{2 \, d}"," ",0,"1/2*(4*(3*I*sin(d*x + c)/(cos(d*x + c) + 1) + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3*I*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2)/(6*I*a - 18*I*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 18*I*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6*I*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a - log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a)/d","B",0
109,1,83,0,0.473619," ","integrate(sec(d*x+c)^3/(a+I*a*tan(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}{-i \, a + \frac{i \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{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/(-I*a + I*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","B",0
110,1,29,0,0.709701," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2}{{\left(-i \, a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)} d}"," ",0,"2/((-I*a + a*sin(d*x + c)/(cos(d*x + c) + 1))*d)","A",0
111,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
112,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
113,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
114,1,77,0,0.372746," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{15 \, \tan\left(d x + c\right)^{7} + 35 i \, \tan\left(d x + c\right)^{6} + 21 \, \tan\left(d x + c\right)^{5} + 105 i \, \tan\left(d x + c\right)^{4} - 35 \, \tan\left(d x + c\right)^{3} + 105 i \, \tan\left(d x + c\right)^{2} - 105 \, \tan\left(d x + c\right)}{105 \, a^{2} d}"," ",0,"-1/105*(15*tan(d*x + c)^7 + 35*I*tan(d*x + c)^6 + 21*tan(d*x + c)^5 + 105*I*tan(d*x + c)^4 - 35*tan(d*x + c)^3 + 105*I*tan(d*x + c)^2 - 105*tan(d*x + c))/(a^2*d)","A",0
115,1,47,0,0.316556," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, \tan\left(d x + c\right)^{5} + 5 i \, \tan\left(d x + c\right)^{4} + 10 i \, \tan\left(d x + c\right)^{2} - 10 \, \tan\left(d x + c\right)}{10 \, a^{2} d}"," ",0,"-1/10*(2*tan(d*x + c)^5 + 5*I*tan(d*x + c)^4 + 10*I*tan(d*x + c)^2 - 10*tan(d*x + c))/(a^2*d)","A",0
116,1,35,0,0.382340," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\tan\left(d x + c\right)^{3} + 3 i \, \tan\left(d x + c\right)^{2} - 3 \, \tan\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"-1/3*(tan(d*x + c)^3 + 3*I*tan(d*x + c)^2 - 3*tan(d*x + c))/(a^2*d)","A",0
117,1,32,0,0.321706," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{-\frac{2 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{2}} - \frac{\tan\left(d x + c\right)}{a^{2}}}{d}"," ",0,"(-2*I*log(I*tan(d*x + c) + 1)/a^2 - tan(d*x + c)/a^2)/d","A",0
118,1,21,0,0.324197," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{i}{{\left(i \, a \tan\left(d x + c\right) + a\right)} a d}"," ",0,"I/((I*a*tan(d*x + c) + a)*a*d)","A",0
119,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
120,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
121,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
122,1,421,0,0.362193," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{135 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{96 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{445 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{960 i \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{330 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{960 i \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{330 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{480 i \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{445 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{480 i \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{135 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 96 i\right)}}{a^{2} - \frac{6 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{20 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{6 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} + \frac{105 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} - \frac{105 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{240 \, d}"," ",0,"1/240*(2*(135*sin(d*x + c)/(cos(d*x + c) + 1) + 96*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 445*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 960*I*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 330*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 960*I*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 330*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 480*I*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 445*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 480*I*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 135*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 96*I)/(a^2 - 6*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 20*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 6*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) + 105*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 - 105*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","B",0
123,1,295,0,0.386185," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{33 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{48 i \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{33 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{48 i \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{9 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 16 i\right)}}{a^{2} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{15 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} - \frac{15 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{24 \, d}"," ",0,"1/24*(2*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 33*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 48*I*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 33*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 48*I*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 9*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 16*I)/(a^2 - 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 15*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 - 15*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","B",0
124,1,167,0,0.607491," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 4 i\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{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{2}} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{2}}}{2 \, d}"," ",0,"-1/2*(2*(sin(d*x + c)/(cos(d*x + c) + 1) - 4*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4*I)/(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) - 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^2 + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^2)/d","B",0
125,1,117,0,0.638398," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{-2 i \, \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - 2 i \, \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - 4 i \, \cos\left(d x + c\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) - \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) - 4 \, \sin\left(d x + c\right)}{2 \, a^{2} d}"," ",0,"-1/2*(-2*I*arctan2(cos(d*x + c), sin(d*x + c) + 1) - 2*I*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - 4*I*cos(d*x + c) + 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*sin(d*x + c))/(a^2*d)","B",0
126,1,45,0,0.478043," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{i \, \cos\left(3 \, d x + 3 \, c\right) + 3 i \, \cos\left(d x + c\right) + \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(d x + c\right)}{6 \, a^{2} d}"," ",0,"1/6*(I*cos(3*d*x + 3*c) + 3*I*cos(d*x + c) + sin(3*d*x + 3*c) + 3*sin(d*x + c))/(a^2*d)","A",0
127,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
128,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
129,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
130,1,87,0,0.451575," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{42 i \, \tan\left(d x + c\right)^{10} - 140 \, \tan\left(d x + c\right)^{9} - 480 \, \tan\left(d x + c\right)^{7} - 420 i \, \tan\left(d x + c\right)^{6} - 504 \, \tan\left(d x + c\right)^{5} - 840 i \, \tan\left(d x + c\right)^{4} - 630 i \, \tan\left(d x + c\right)^{2} + 420 \, \tan\left(d x + c\right)}{420 \, a^{3} d}"," ",0,"1/420*(42*I*tan(d*x + c)^10 - 140*tan(d*x + c)^9 - 480*tan(d*x + c)^7 - 420*I*tan(d*x + c)^6 - 504*tan(d*x + c)^5 - 840*I*tan(d*x + c)^4 - 630*I*tan(d*x + c)^2 + 420*tan(d*x + c))/(a^3*d)","A",0
131,1,87,0,0.437141," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{-21 i \, \tan\left(d x + c\right)^{8} + 72 \, \tan\left(d x + c\right)^{7} + 28 i \, \tan\left(d x + c\right)^{6} + 168 \, \tan\left(d x + c\right)^{5} + 210 i \, \tan\left(d x + c\right)^{4} + 56 \, \tan\left(d x + c\right)^{3} + 252 i \, \tan\left(d x + c\right)^{2} - 168 \, \tan\left(d x + c\right)}{168 \, a^{3} d}"," ",0,"-1/168*(-21*I*tan(d*x + c)^8 + 72*tan(d*x + c)^7 + 28*I*tan(d*x + c)^6 + 168*tan(d*x + c)^5 + 210*I*tan(d*x + c)^4 + 56*tan(d*x + c)^3 + 252*I*tan(d*x + c)^2 - 168*tan(d*x + c))/(a^3*d)","A",0
132,1,67,0,0.316124," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{5 i \, \tan\left(d x + c\right)^{6} - 18 \, \tan\left(d x + c\right)^{5} - 15 i \, \tan\left(d x + c\right)^{4} - 20 \, \tan\left(d x + c\right)^{3} - 45 i \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right)}{30 \, a^{3} d}"," ",0,"1/30*(5*I*tan(d*x + c)^6 - 18*tan(d*x + c)^5 - 15*I*tan(d*x + c)^4 - 20*tan(d*x + c)^3 - 45*I*tan(d*x + c)^2 + 30*tan(d*x + c))/(a^3*d)","A",0
133,1,47,0,0.358193," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{-i \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{3} + 6 i \, \tan\left(d x + c\right)^{2} - 4 \, \tan\left(d x + c\right)}{4 \, a^{3} d}"," ",0,"-1/4*(-I*tan(d*x + c)^4 + 4*tan(d*x + c)^3 + 6*I*tan(d*x + c)^2 - 4*tan(d*x + c))/(a^3*d)","B",0
134,1,45,0,0.409883," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{i \, \tan\left(d x + c\right)^{2} - 6 \, \tan\left(d x + c\right)}{a^{3}} - \frac{8 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((I*tan(d*x + c)^2 - 6*tan(d*x + c))/a^3 - 8*I*log(I*tan(d*x + c) + 1)/a^3)/d","A",0
135,1,66,0,0.595847," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(-i \, \tan\left(d x + c\right) - 1\right)}}{2 i \, a^{3} \tan\left(d x + c\right)^{2} + 4 \, a^{3} \tan\left(d x + c\right) - 2 i \, a^{3}} - \frac{i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{3}}}{d}"," ",0,"-(4*(-I*tan(d*x + c) - 1)/(2*I*a^3*tan(d*x + c)^2 + 4*a^3*tan(d*x + c) - 2*I*a^3) - I*log(I*tan(d*x + c) + 1)/a^3)/d","A",0
136,1,21,0,0.349250," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{i}{2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a d}"," ",0,"1/2*I/((I*a*tan(d*x + c) + a)^2*a*d)","A",0
137,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
138,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
139,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
140,1,341,0,0.453424," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{16 \, {\left(-\frac{15 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{320 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{390 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{400 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{960 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{390 i \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{360 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{15 i \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 136\right)}}{-120 i \, a^{3} + \frac{600 i \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1200 i \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1200 i \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{600 i \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{120 i \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{7 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} - \frac{7 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{8 \, d}"," ",0,"1/8*(16*(-15*I*sin(d*x + c)/(cos(d*x + c) + 1) + 320*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 390*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 400*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 960*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 390*I*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 360*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 15*I*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 136)/(-120*I*a^3 + 600*I*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1200*I*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1200*I*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 600*I*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 120*I*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 7*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 - 7*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","B",0
141,1,215,0,0.437647," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(-\frac{9 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{9 i \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 22\right)}}{6 i \, a^{3} - \frac{18 i \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 i \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6 i \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{5 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{3}} - \frac{5 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*(4*(-9*I*sin(d*x + c)/(cos(d*x + c) + 1) - 48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 18*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 9*I*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 22)/(6*I*a^3 - 18*I*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 18*I*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6*I*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 5*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^3 - 5*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^3)/d","B",0
142,1,329,0,0.543523," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(6 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(d x + c\right) + 6 i \, \sin\left(3 \, d x + 3 \, c\right) + 6 i \, \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(6 \, \cos\left(3 \, d x + 3 \, c\right) + 6 \, \cos\left(d x + c\right) + 6 i \, \sin\left(3 \, d x + 3 \, c\right) + 6 i \, \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - {\left(-3 i \, \cos\left(3 \, d x + 3 \, c\right) - 3 i \, \cos\left(d x + c\right) + 3 \, \sin\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(d x + c\right)\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) - {\left(3 i \, \cos\left(3 \, d x + 3 \, c\right) + 3 i \, \cos\left(d x + c\right) - 3 \, \sin\left(3 \, d x + 3 \, c\right) - 3 \, \sin\left(d x + c\right)\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) + 12 \, \cos\left(2 \, d x + 2 \, c\right) + 12 i \, \sin\left(2 \, d x + 2 \, c\right) + 8}{{\left(-2 i \, a^{3} \cos\left(3 \, d x + 3 \, c\right) - 2 i \, a^{3} \cos\left(d x + c\right) + 2 \, a^{3} \sin\left(3 \, d x + 3 \, c\right) + 2 \, a^{3} \sin\left(d x + c\right)\right)} d}"," ",0,"((6*cos(3*d*x + 3*c) + 6*cos(d*x + c) + 6*I*sin(3*d*x + 3*c) + 6*I*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (6*cos(3*d*x + 3*c) + 6*cos(d*x + c) + 6*I*sin(3*d*x + 3*c) + 6*I*sin(d*x + c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - (-3*I*cos(3*d*x + 3*c) - 3*I*cos(d*x + c) + 3*sin(3*d*x + 3*c) + 3*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (3*I*cos(3*d*x + 3*c) + 3*I*cos(d*x + c) - 3*sin(3*d*x + 3*c) - 3*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 12*cos(2*d*x + 2*c) + 12*I*sin(2*d*x + 2*c) + 8)/((-2*I*a^3*cos(3*d*x + 3*c) - 2*I*a^3*cos(d*x + c) + 2*a^3*sin(3*d*x + 3*c) + 2*a^3*sin(d*x + c))*d)","B",0
143,1,29,0,0.370147," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{i \, \cos\left(3 \, d x + 3 \, c\right) + \sin\left(3 \, d x + 3 \, c\right)}{3 \, a^{3} d}"," ",0,"1/3*(I*cos(3*d*x + 3*c) + sin(3*d*x + 3*c))/(a^3*d)","A",0
144,1,69,0,0.418213," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 i \, \cos\left(5 \, d x + 5 \, c\right) + 10 i \, \cos\left(3 \, d x + 3 \, c\right) + 15 i \, \cos\left(d x + c\right) + 3 \, \sin\left(5 \, d x + 5 \, c\right) + 10 \, \sin\left(3 \, d x + 3 \, c\right) + 15 \, \sin\left(d x + c\right)}{60 \, a^{3} d}"," ",0,"1/60*(3*I*cos(5*d*x + 5*c) + 10*I*cos(3*d*x + 3*c) + 15*I*cos(d*x + c) + 3*sin(5*d*x + 5*c) + 10*sin(3*d*x + 3*c) + 15*sin(d*x + c))/(a^3*d)","A",0
145,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
146,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
147,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
148,1,97,0,0.389150," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{14 \, \tan\left(d x + c\right)^{9} + 63 i \, \tan\left(d x + c\right)^{8} - 72 \, \tan\left(d x + c\right)^{7} + 84 i \, \tan\left(d x + c\right)^{6} - 252 \, \tan\left(d x + c\right)^{5} - 126 i \, \tan\left(d x + c\right)^{4} - 168 \, \tan\left(d x + c\right)^{3} - 252 i \, \tan\left(d x + c\right)^{2} + 126 \, \tan\left(d x + c\right)}{126 \, a^{4} d}"," ",0,"1/126*(14*tan(d*x + c)^9 + 63*I*tan(d*x + c)^8 - 72*tan(d*x + c)^7 + 84*I*tan(d*x + c)^6 - 252*tan(d*x + c)^5 - 126*I*tan(d*x + c)^4 - 168*tan(d*x + c)^3 - 252*I*tan(d*x + c)^2 + 126*tan(d*x + c))/(a^4*d)","A",0
149,1,67,0,0.522387," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, \tan\left(d x + c\right)^{7} + 14 i \, \tan\left(d x + c\right)^{6} - 21 \, \tan\left(d x + c\right)^{5} - 35 \, \tan\left(d x + c\right)^{3} - 42 i \, \tan\left(d x + c\right)^{2} + 21 \, \tan\left(d x + c\right)}{21 \, a^{4} d}"," ",0,"1/21*(3*tan(d*x + c)^7 + 14*I*tan(d*x + c)^6 - 21*tan(d*x + c)^5 - 35*tan(d*x + c)^3 - 42*I*tan(d*x + c)^2 + 21*tan(d*x + c))/(a^4*d)","A",0
150,1,57,0,0.365052," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, \tan\left(d x + c\right)^{5} + 15 i \, \tan\left(d x + c\right)^{4} - 30 \, \tan\left(d x + c\right)^{3} - 30 i \, \tan\left(d x + c\right)^{2} + 15 \, \tan\left(d x + c\right)}{15 \, a^{4} d}"," ",0,"1/15*(3*tan(d*x + c)^5 + 15*I*tan(d*x + c)^4 - 30*tan(d*x + c)^3 - 30*I*tan(d*x + c)^2 + 15*tan(d*x + c))/(a^4*d)","B",0
151,1,53,0,0.768665," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{\tan\left(d x + c\right)^{3} + 6 i \, \tan\left(d x + c\right)^{2} - 21 \, \tan\left(d x + c\right)}{a^{4}} - \frac{24 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{4}}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 6*I*tan(d*x + c)^2 - 21*tan(d*x + c))/a^4 - 24*I*log(I*tan(d*x + c) + 1)/a^4)/d","A",0
152,1,96,0,0.806661," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{12 \, {\left(\tan\left(d x + c\right)^{2} - 2 i \, \tan\left(d x + c\right) - 1\right)}}{3 \, a^{4} \tan\left(d x + c\right)^{3} - 9 i \, a^{4} \tan\left(d x + c\right)^{2} - 9 \, a^{4} \tan\left(d x + c\right) + 3 i \, a^{4}} + \frac{4 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{4}} + \frac{\tan\left(d x + c\right)}{a^{4}}}{d}"," ",0,"(12*(tan(d*x + c)^2 - 2*I*tan(d*x + c) - 1)/(3*a^4*tan(d*x + c)^3 - 9*I*a^4*tan(d*x + c)^2 - 9*a^4*tan(d*x + c) + 3*I*a^4) + 4*I*log(I*tan(d*x + c) + 1)/a^4 + tan(d*x + c)/a^4)/d","A",0
153,1,67,0,0.680255," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, {\left(\tan\left(d x + c\right)^{2} - i \, \tan\left(d x + c\right)\right)}}{{\left(3 \, a^{4} \tan\left(d x + c\right)^{3} - 9 i \, a^{4} \tan\left(d x + c\right)^{2} - 9 \, a^{4} \tan\left(d x + c\right) + 3 i \, a^{4}\right)} d}"," ",0,"-3*(tan(d*x + c)^2 - I*tan(d*x + c))/((3*a^4*tan(d*x + c)^3 - 9*I*a^4*tan(d*x + c)^2 - 9*a^4*tan(d*x + c) + 3*I*a^4)*d)","B",0
154,1,21,0,0.384474," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{i}{3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a d}"," ",0,"1/3*I/((I*a*tan(d*x + c) + a)^3*a*d)","A",0
155,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
156,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
157,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
158,1,295,0,0.545371," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{81 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{544 i \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{105 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{480 i \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{105 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{96 i \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{81 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 160 i\right)}}{a^{4} - \frac{4 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{105 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{a^{4}} + \frac{105 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{a^{4}}}{24 \, d}"," ",0,"-1/24*(2*(81*sin(d*x + c)/(cos(d*x + c) + 1) - 544*I*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 105*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 480*I*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 105*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 96*I*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 81*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 160*I)/(a^4 - 4*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 105*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/a^4 + 105*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/a^4)/d","B",0
159,1,467,0,0.964518," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{{\left(30 \, \cos\left(5 \, d x + 5 \, c\right) + 60 \, \cos\left(3 \, d x + 3 \, c\right) + 30 \, \cos\left(d x + c\right) + 30 i \, \sin\left(5 \, d x + 5 \, c\right) + 60 i \, \sin\left(3 \, d x + 3 \, c\right) + 30 i \, \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(30 \, \cos\left(5 \, d x + 5 \, c\right) + 60 \, \cos\left(3 \, d x + 3 \, c\right) + 30 \, \cos\left(d x + c\right) + 30 i \, \sin\left(5 \, d x + 5 \, c\right) + 60 i \, \sin\left(3 \, d x + 3 \, c\right) + 30 i \, \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - {\left(-15 i \, \cos\left(5 \, d x + 5 \, c\right) - 30 i \, \cos\left(3 \, d x + 3 \, c\right) - 15 i \, \cos\left(d x + c\right) + 15 \, \sin\left(5 \, d x + 5 \, c\right) + 30 \, \sin\left(3 \, d x + 3 \, c\right) + 15 \, \sin\left(d x + c\right)\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) - {\left(15 i \, \cos\left(5 \, d x + 5 \, c\right) + 30 i \, \cos\left(3 \, d x + 3 \, c\right) + 15 i \, \cos\left(d x + c\right) - 15 \, \sin\left(5 \, d x + 5 \, c\right) - 30 \, \sin\left(3 \, d x + 3 \, c\right) - 15 \, \sin\left(d x + c\right)\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) + 60 \, \cos\left(4 \, d x + 4 \, c\right) + 100 \, \cos\left(2 \, d x + 2 \, c\right) + 60 i \, \sin\left(4 \, d x + 4 \, c\right) + 100 i \, \sin\left(2 \, d x + 2 \, c\right) + 32}{{\left(-4 i \, a^{4} \cos\left(5 \, d x + 5 \, c\right) - 8 i \, a^{4} \cos\left(3 \, d x + 3 \, c\right) - 4 i \, a^{4} \cos\left(d x + c\right) + 4 \, a^{4} \sin\left(5 \, d x + 5 \, c\right) + 8 \, a^{4} \sin\left(3 \, d x + 3 \, c\right) + 4 \, a^{4} \sin\left(d x + c\right)\right)} d}"," ",0,"((30*cos(5*d*x + 5*c) + 60*cos(3*d*x + 3*c) + 30*cos(d*x + c) + 30*I*sin(5*d*x + 5*c) + 60*I*sin(3*d*x + 3*c) + 30*I*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (30*cos(5*d*x + 5*c) + 60*cos(3*d*x + 3*c) + 30*cos(d*x + c) + 30*I*sin(5*d*x + 5*c) + 60*I*sin(3*d*x + 3*c) + 30*I*sin(d*x + c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - (-15*I*cos(5*d*x + 5*c) - 30*I*cos(3*d*x + 3*c) - 15*I*cos(d*x + c) + 15*sin(5*d*x + 5*c) + 30*sin(3*d*x + 3*c) + 15*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (15*I*cos(5*d*x + 5*c) + 30*I*cos(3*d*x + 3*c) + 15*I*cos(d*x + c) - 15*sin(5*d*x + 5*c) - 30*sin(3*d*x + 3*c) - 15*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 60*cos(4*d*x + 4*c) + 100*cos(2*d*x + 2*c) + 60*I*sin(4*d*x + 4*c) + 100*I*sin(2*d*x + 2*c) + 32)/((-4*I*a^4*cos(5*d*x + 5*c) - 8*I*a^4*cos(3*d*x + 3*c) - 4*I*a^4*cos(d*x + c) + 4*a^4*sin(5*d*x + 5*c) + 8*a^4*sin(3*d*x + 3*c) + 4*a^4*sin(d*x + c))*d)","B",0
160,1,141,0,0.552547," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{-6 i \, \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - 6 i \, \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) + 4 i \, \cos\left(3 \, d x + 3 \, c\right) - 12 i \, \cos\left(d x + c\right) + 3 \, \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) - 3 \, \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) + 4 \, \sin\left(3 \, d x + 3 \, c\right) - 12 \, \sin\left(d x + c\right)}{6 \, a^{4} d}"," ",0,"1/6*(-6*I*arctan2(cos(d*x + c), sin(d*x + c) + 1) - 6*I*arctan2(cos(d*x + c), -sin(d*x + c) + 1) + 4*I*cos(3*d*x + 3*c) - 12*I*cos(d*x + c) + 3*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - 3*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 4*sin(3*d*x + 3*c) - 12*sin(d*x + c))/(a^4*d)","A",0
161,1,53,0,0.370674," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 i \, \cos\left(5 \, d x + 5 \, c\right) + 5 i \, \cos\left(3 \, d x + 3 \, c\right) + 3 \, \sin\left(5 \, d x + 5 \, c\right) + 5 \, \sin\left(3 \, d x + 3 \, c\right)}{30 \, a^{4} d}"," ",0,"1/30*(3*I*cos(5*d*x + 5*c) + 5*I*cos(3*d*x + 3*c) + 3*sin(5*d*x + 5*c) + 5*sin(3*d*x + 3*c))/(a^4*d)","A",0
162,1,91,0,0.442670," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{5 i \, \cos\left(7 \, d x + 7 \, c\right) + 21 i \, \cos\left(5 \, d x + 5 \, c\right) + 35 i \, \cos\left(3 \, d x + 3 \, c\right) + 35 i \, \cos\left(d x + c\right) + 5 \, \sin\left(7 \, d x + 7 \, c\right) + 21 \, \sin\left(5 \, d x + 5 \, c\right) + 35 \, \sin\left(3 \, d x + 3 \, c\right) + 35 \, \sin\left(d x + c\right)}{280 \, a^{4} d}"," ",0,"1/280*(5*I*cos(7*d*x + 7*c) + 21*I*cos(5*d*x + 5*c) + 35*I*cos(3*d*x + 3*c) + 35*I*cos(d*x + c) + 5*sin(7*d*x + 7*c) + 21*sin(5*d*x + 5*c) + 35*sin(3*d*x + 3*c) + 35*sin(d*x + c))/(a^4*d)","A",0
163,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
164,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
165,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
166,1,232,0,0.437202," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{\frac{5 \, {\left(2240 \, \tan\left(d x + c\right)^{6} - 13440 i \, \tan\left(d x + c\right)^{5} - 33600 \, \tan\left(d x + c\right)^{4} + 44800 i \, \tan\left(d x + c\right)^{3} + 33600 \, \tan\left(d x + c\right)^{2} - 13440 i \, \tan\left(d x + c\right) - 2240\right)}}{35 \, a^{8} \tan\left(d x + c\right)^{7} - 245 i \, a^{8} \tan\left(d x + c\right)^{6} - 735 \, a^{8} \tan\left(d x + c\right)^{5} + 1225 i \, a^{8} \tan\left(d x + c\right)^{4} + 1225 \, a^{8} \tan\left(d x + c\right)^{3} - 735 i \, a^{8} \tan\left(d x + c\right)^{2} - 245 \, a^{8} \tan\left(d x + c\right) + 35 i \, a^{8}} + \frac{\tan\left(d x + c\right)^{5} + 10 i \, \tan\left(d x + c\right)^{4} - 50 \, \tan\left(d x + c\right)^{3} - 180 i \, \tan\left(d x + c\right)^{2} + 645 \, \tan\left(d x + c\right)}{a^{8}} + \frac{960 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{8}}}{5 \, d}"," ",0,"1/5*(5*(2240*tan(d*x + c)^6 - 13440*I*tan(d*x + c)^5 - 33600*tan(d*x + c)^4 + 44800*I*tan(d*x + c)^3 + 33600*tan(d*x + c)^2 - 13440*I*tan(d*x + c) - 2240)/(35*a^8*tan(d*x + c)^7 - 245*I*a^8*tan(d*x + c)^6 - 735*a^8*tan(d*x + c)^5 + 1225*I*a^8*tan(d*x + c)^4 + 1225*a^8*tan(d*x + c)^3 - 735*I*a^8*tan(d*x + c)^2 - 245*a^8*tan(d*x + c) + 35*I*a^8) + (tan(d*x + c)^5 + 10*I*tan(d*x + c)^4 - 50*tan(d*x + c)^3 - 180*I*tan(d*x + c)^2 + 645*tan(d*x + c))/a^8 + 960*I*log(I*tan(d*x + c) + 1)/a^8)/d","A",0
167,1,213,0,0.356139," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(1680 \, \tan\left(d x + c\right)^{6} - 9744 i \, \tan\left(d x + c\right)^{5} - 23520 \, \tan\left(d x + c\right)^{4} + 30240 i \, \tan\left(d x + c\right)^{3} + 21840 \, \tan\left(d x + c\right)^{2} - 8400 i \, \tan\left(d x + c\right) - 1344\right)}}{21 \, a^{8} \tan\left(d x + c\right)^{7} - 147 i \, a^{8} \tan\left(d x + c\right)^{6} - 441 \, a^{8} \tan\left(d x + c\right)^{5} + 735 i \, a^{8} \tan\left(d x + c\right)^{4} + 735 \, a^{8} \tan\left(d x + c\right)^{3} - 441 i \, a^{8} \tan\left(d x + c\right)^{2} - 147 \, a^{8} \tan\left(d x + c\right) + 21 i \, a^{8}} - \frac{\tan\left(d x + c\right)^{3} + 12 i \, \tan\left(d x + c\right)^{2} - 93 \, \tan\left(d x + c\right)}{a^{8}} + \frac{240 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{8}}}{3 \, d}"," ",0,"-1/3*(3*(1680*tan(d*x + c)^6 - 9744*I*tan(d*x + c)^5 - 23520*tan(d*x + c)^4 + 30240*I*tan(d*x + c)^3 + 21840*tan(d*x + c)^2 - 8400*I*tan(d*x + c) - 1344)/(21*a^8*tan(d*x + c)^7 - 147*I*a^8*tan(d*x + c)^6 - 441*a^8*tan(d*x + c)^5 + 735*I*a^8*tan(d*x + c)^4 + 735*a^8*tan(d*x + c)^3 - 441*I*a^8*tan(d*x + c)^2 - 147*a^8*tan(d*x + c) + 21*I*a^8) - (tan(d*x + c)^3 + 12*I*tan(d*x + c)^2 - 93*tan(d*x + c))/a^8 + 240*I*log(I*tan(d*x + c) + 1)/a^8)/d","A",0
168,1,189,0,0.672164," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{\frac{2520 \, \tan\left(d x + c\right)^{6} - 13440 i \, \tan\left(d x + c\right)^{5} - 29960 \, \tan\left(d x + c\right)^{4} + 35840 i \, \tan\left(d x + c\right)^{3} + 24360 \, \tan\left(d x + c\right)^{2} - 8960 i \, \tan\left(d x + c\right) - 1400}{105 \, a^{8} \tan\left(d x + c\right)^{7} - 735 i \, a^{8} \tan\left(d x + c\right)^{6} - 2205 \, a^{8} \tan\left(d x + c\right)^{5} + 3675 i \, a^{8} \tan\left(d x + c\right)^{4} + 3675 \, a^{8} \tan\left(d x + c\right)^{3} - 2205 i \, a^{8} \tan\left(d x + c\right)^{2} - 735 \, a^{8} \tan\left(d x + c\right) + 105 i \, a^{8}} + \frac{8 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{8}} + \frac{\tan\left(d x + c\right)}{a^{8}}}{d}"," ",0,"((2520*tan(d*x + c)^6 - 13440*I*tan(d*x + c)^5 - 29960*tan(d*x + c)^4 + 35840*I*tan(d*x + c)^3 + 24360*tan(d*x + c)^2 - 8960*I*tan(d*x + c) - 1400)/(105*a^8*tan(d*x + c)^7 - 735*I*a^8*tan(d*x + c)^6 - 2205*a^8*tan(d*x + c)^5 + 3675*I*a^8*tan(d*x + c)^4 + 3675*a^8*tan(d*x + c)^3 - 2205*I*a^8*tan(d*x + c)^2 - 735*a^8*tan(d*x + c) + 105*I*a^8) + 8*I*log(I*tan(d*x + c) + 1)/a^8 + tan(d*x + c)/a^8)/d","A",0
169,1,161,0,0.369724," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{35 \, \tan\left(d x + c\right)^{6} - 105 i \, \tan\left(d x + c\right)^{5} - 140 \, \tan\left(d x + c\right)^{4} + 140 i \, \tan\left(d x + c\right)^{3} + 105 \, \tan\left(d x + c\right)^{2} - 35 i \, \tan\left(d x + c\right)}{{\left(35 \, a^{8} \tan\left(d x + c\right)^{7} - 245 i \, a^{8} \tan\left(d x + c\right)^{6} - 735 \, a^{8} \tan\left(d x + c\right)^{5} + 1225 i \, a^{8} \tan\left(d x + c\right)^{4} + 1225 \, a^{8} \tan\left(d x + c\right)^{3} - 735 i \, a^{8} \tan\left(d x + c\right)^{2} - 245 \, a^{8} \tan\left(d x + c\right) + 35 i \, a^{8}\right)} d}"," ",0,"-(35*tan(d*x + c)^6 - 105*I*tan(d*x + c)^5 - 140*tan(d*x + c)^4 + 140*I*tan(d*x + c)^3 + 105*tan(d*x + c)^2 - 35*I*tan(d*x + c))/((35*a^8*tan(d*x + c)^7 - 245*I*a^8*tan(d*x + c)^6 - 735*a^8*tan(d*x + c)^5 + 1225*I*a^8*tan(d*x + c)^4 + 1225*a^8*tan(d*x + c)^3 - 735*I*a^8*tan(d*x + c)^2 - 245*a^8*tan(d*x + c) + 35*I*a^8)*d)","B",0
170,1,142,0,0.341605," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{35 \, \tan\left(d x + c\right)^{4} - 35 i \, \tan\left(d x + c\right)^{3} + 21 \, \tan\left(d x + c\right)^{2} - 7 i \, \tan\left(d x + c\right) + 14}{{\left(105 \, a^{8} \tan\left(d x + c\right)^{7} - 735 i \, a^{8} \tan\left(d x + c\right)^{6} - 2205 \, a^{8} \tan\left(d x + c\right)^{5} + 3675 i \, a^{8} \tan\left(d x + c\right)^{4} + 3675 \, a^{8} \tan\left(d x + c\right)^{3} - 2205 i \, a^{8} \tan\left(d x + c\right)^{2} - 735 \, a^{8} \tan\left(d x + c\right) + 105 i \, a^{8}\right)} d}"," ",0,"-(35*tan(d*x + c)^4 - 35*I*tan(d*x + c)^3 + 21*tan(d*x + c)^2 - 7*I*tan(d*x + c) + 14)/((105*a^8*tan(d*x + c)^7 - 735*I*a^8*tan(d*x + c)^6 - 2205*a^8*tan(d*x + c)^5 + 3675*I*a^8*tan(d*x + c)^4 + 3675*a^8*tan(d*x + c)^3 - 2205*I*a^8*tan(d*x + c)^2 - 735*a^8*tan(d*x + c) + 105*I*a^8)*d)","B",0
171,1,122,0,0.475795," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{7 \, {\left(3 \, \tan\left(d x + c\right)^{2} - i \, \tan\left(d x + c\right) + 2\right)}}{{\left(105 \, a^{8} \tan\left(d x + c\right)^{7} - 735 i \, a^{8} \tan\left(d x + c\right)^{6} - 2205 \, a^{8} \tan\left(d x + c\right)^{5} + 3675 i \, a^{8} \tan\left(d x + c\right)^{4} + 3675 \, a^{8} \tan\left(d x + c\right)^{3} - 2205 i \, a^{8} \tan\left(d x + c\right)^{2} - 735 \, a^{8} \tan\left(d x + c\right) + 105 i \, a^{8}\right)} d}"," ",0,"-7*(3*tan(d*x + c)^2 - I*tan(d*x + c) + 2)/((105*a^8*tan(d*x + c)^7 - 735*I*a^8*tan(d*x + c)^6 - 2205*a^8*tan(d*x + c)^5 + 3675*I*a^8*tan(d*x + c)^4 + 3675*a^8*tan(d*x + c)^3 - 2205*I*a^8*tan(d*x + c)^2 - 735*a^8*tan(d*x + c) + 105*I*a^8)*d)","B",0
172,1,21,0,0.540980," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{i}{7 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{7} a d}"," ",0,"1/7*I/((I*a*tan(d*x + c) + a)^7*a*d)","A",0
173,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
174,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
175,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
176,1,796,0,1.236100," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","-\frac{{\left(6930 \, \cos\left(11 \, d x + 11 \, c\right) + 27720 \, \cos\left(9 \, d x + 9 \, c\right) + 41580 \, \cos\left(7 \, d x + 7 \, c\right) + 27720 \, \cos\left(5 \, d x + 5 \, c\right) + 6930 \, \cos\left(3 \, d x + 3 \, c\right) + 6930 i \, \sin\left(11 \, d x + 11 \, c\right) + 27720 i \, \sin\left(9 \, d x + 9 \, c\right) + 41580 i \, \sin\left(7 \, d x + 7 \, c\right) + 27720 i \, \sin\left(5 \, d x + 5 \, c\right) + 6930 i \, \sin\left(3 \, d x + 3 \, c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(6930 \, \cos\left(11 \, d x + 11 \, c\right) + 27720 \, \cos\left(9 \, d x + 9 \, c\right) + 41580 \, \cos\left(7 \, d x + 7 \, c\right) + 27720 \, \cos\left(5 \, d x + 5 \, c\right) + 6930 \, \cos\left(3 \, d x + 3 \, c\right) + 6930 i \, \sin\left(11 \, d x + 11 \, c\right) + 27720 i \, \sin\left(9 \, d x + 9 \, c\right) + 41580 i \, \sin\left(7 \, d x + 7 \, c\right) + 27720 i \, \sin\left(5 \, d x + 5 \, c\right) + 6930 i \, \sin\left(3 \, d x + 3 \, c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - {\left(-3465 i \, \cos\left(11 \, d x + 11 \, c\right) - 13860 i \, \cos\left(9 \, d x + 9 \, c\right) - 20790 i \, \cos\left(7 \, d x + 7 \, c\right) - 13860 i \, \cos\left(5 \, d x + 5 \, c\right) - 3465 i \, \cos\left(3 \, d x + 3 \, c\right) + 3465 \, \sin\left(11 \, d x + 11 \, c\right) + 13860 \, \sin\left(9 \, d x + 9 \, c\right) + 20790 \, \sin\left(7 \, d x + 7 \, c\right) + 13860 \, \sin\left(5 \, d x + 5 \, c\right) + 3465 \, \sin\left(3 \, d x + 3 \, c\right)\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) - {\left(3465 i \, \cos\left(11 \, d x + 11 \, c\right) + 13860 i \, \cos\left(9 \, d x + 9 \, c\right) + 20790 i \, \cos\left(7 \, d x + 7 \, c\right) + 13860 i \, \cos\left(5 \, d x + 5 \, c\right) + 3465 i \, \cos\left(3 \, d x + 3 \, c\right) - 3465 \, \sin\left(11 \, d x + 11 \, c\right) - 13860 \, \sin\left(9 \, d x + 9 \, c\right) - 20790 \, \sin\left(7 \, d x + 7 \, c\right) - 13860 \, \sin\left(5 \, d x + 5 \, c\right) - 3465 \, \sin\left(3 \, d x + 3 \, c\right)\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) + 13860 \, \cos\left(10 \, d x + 10 \, c\right) + 50820 \, \cos\left(8 \, d x + 8 \, c\right) + 67452 \, \cos\left(6 \, d x + 6 \, c\right) + 36828 \, \cos\left(4 \, d x + 4 \, c\right) + 5632 \, \cos\left(2 \, d x + 2 \, c\right) + 13860 i \, \sin\left(10 \, d x + 10 \, c\right) + 50820 i \, \sin\left(8 \, d x + 8 \, c\right) + 67452 i \, \sin\left(6 \, d x + 6 \, c\right) + 36828 i \, \sin\left(4 \, d x + 4 \, c\right) + 5632 i \, \sin\left(2 \, d x + 2 \, c\right) - 512}{{\left(-48 i \, a^{8} \cos\left(11 \, d x + 11 \, c\right) - 192 i \, a^{8} \cos\left(9 \, d x + 9 \, c\right) - 288 i \, a^{8} \cos\left(7 \, d x + 7 \, c\right) - 192 i \, a^{8} \cos\left(5 \, d x + 5 \, c\right) - 48 i \, a^{8} \cos\left(3 \, d x + 3 \, c\right) + 48 \, a^{8} \sin\left(11 \, d x + 11 \, c\right) + 192 \, a^{8} \sin\left(9 \, d x + 9 \, c\right) + 288 \, a^{8} \sin\left(7 \, d x + 7 \, c\right) + 192 \, a^{8} \sin\left(5 \, d x + 5 \, c\right) + 48 \, a^{8} \sin\left(3 \, d x + 3 \, c\right)\right)} d}"," ",0,"-((6930*cos(11*d*x + 11*c) + 27720*cos(9*d*x + 9*c) + 41580*cos(7*d*x + 7*c) + 27720*cos(5*d*x + 5*c) + 6930*cos(3*d*x + 3*c) + 6930*I*sin(11*d*x + 11*c) + 27720*I*sin(9*d*x + 9*c) + 41580*I*sin(7*d*x + 7*c) + 27720*I*sin(5*d*x + 5*c) + 6930*I*sin(3*d*x + 3*c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (6930*cos(11*d*x + 11*c) + 27720*cos(9*d*x + 9*c) + 41580*cos(7*d*x + 7*c) + 27720*cos(5*d*x + 5*c) + 6930*cos(3*d*x + 3*c) + 6930*I*sin(11*d*x + 11*c) + 27720*I*sin(9*d*x + 9*c) + 41580*I*sin(7*d*x + 7*c) + 27720*I*sin(5*d*x + 5*c) + 6930*I*sin(3*d*x + 3*c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - (-3465*I*cos(11*d*x + 11*c) - 13860*I*cos(9*d*x + 9*c) - 20790*I*cos(7*d*x + 7*c) - 13860*I*cos(5*d*x + 5*c) - 3465*I*cos(3*d*x + 3*c) + 3465*sin(11*d*x + 11*c) + 13860*sin(9*d*x + 9*c) + 20790*sin(7*d*x + 7*c) + 13860*sin(5*d*x + 5*c) + 3465*sin(3*d*x + 3*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (3465*I*cos(11*d*x + 11*c) + 13860*I*cos(9*d*x + 9*c) + 20790*I*cos(7*d*x + 7*c) + 13860*I*cos(5*d*x + 5*c) + 3465*I*cos(3*d*x + 3*c) - 3465*sin(11*d*x + 11*c) - 13860*sin(9*d*x + 9*c) - 20790*sin(7*d*x + 7*c) - 13860*sin(5*d*x + 5*c) - 3465*sin(3*d*x + 3*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 13860*cos(10*d*x + 10*c) + 50820*cos(8*d*x + 8*c) + 67452*cos(6*d*x + 6*c) + 36828*cos(4*d*x + 4*c) + 5632*cos(2*d*x + 2*c) + 13860*I*sin(10*d*x + 10*c) + 50820*I*sin(8*d*x + 8*c) + 67452*I*sin(6*d*x + 6*c) + 36828*I*sin(4*d*x + 4*c) + 5632*I*sin(2*d*x + 2*c) - 512)/((-48*I*a^8*cos(11*d*x + 11*c) - 192*I*a^8*cos(9*d*x + 9*c) - 288*I*a^8*cos(7*d*x + 7*c) - 192*I*a^8*cos(5*d*x + 5*c) - 48*I*a^8*cos(3*d*x + 3*c) + 48*a^8*sin(11*d*x + 11*c) + 192*a^8*sin(9*d*x + 9*c) + 288*a^8*sin(7*d*x + 7*c) + 192*a^8*sin(5*d*x + 5*c) + 48*a^8*sin(3*d*x + 3*c))*d)","B",0
177,1,541,0,0.630146," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{{\left(630 \, \cos\left(9 \, d x + 9 \, c\right) + 1260 \, \cos\left(7 \, d x + 7 \, c\right) + 630 \, \cos\left(5 \, d x + 5 \, c\right) + 630 i \, \sin\left(9 \, d x + 9 \, c\right) + 1260 i \, \sin\left(7 \, d x + 7 \, c\right) + 630 i \, \sin\left(5 \, d x + 5 \, c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(630 \, \cos\left(9 \, d x + 9 \, c\right) + 1260 \, \cos\left(7 \, d x + 7 \, c\right) + 630 \, \cos\left(5 \, d x + 5 \, c\right) + 630 i \, \sin\left(9 \, d x + 9 \, c\right) + 1260 i \, \sin\left(7 \, d x + 7 \, c\right) + 630 i \, \sin\left(5 \, d x + 5 \, c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - {\left(-315 i \, \cos\left(9 \, d x + 9 \, c\right) - 630 i \, \cos\left(7 \, d x + 7 \, c\right) - 315 i \, \cos\left(5 \, d x + 5 \, c\right) + 315 \, \sin\left(9 \, d x + 9 \, c\right) + 630 \, \sin\left(7 \, d x + 7 \, c\right) + 315 \, \sin\left(5 \, d x + 5 \, c\right)\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) - {\left(315 i \, \cos\left(9 \, d x + 9 \, c\right) + 630 i \, \cos\left(7 \, d x + 7 \, c\right) + 315 i \, \cos\left(5 \, d x + 5 \, c\right) - 315 \, \sin\left(9 \, d x + 9 \, c\right) - 630 \, \sin\left(7 \, d x + 7 \, c\right) - 315 \, \sin\left(5 \, d x + 5 \, c\right)\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) + 1260 \, \cos\left(8 \, d x + 8 \, c\right) + 2100 \, \cos\left(6 \, d x + 6 \, c\right) + 672 \, \cos\left(4 \, d x + 4 \, c\right) - 96 \, \cos\left(2 \, d x + 2 \, c\right) + 1260 i \, \sin\left(8 \, d x + 8 \, c\right) + 2100 i \, \sin\left(6 \, d x + 6 \, c\right) + 672 i \, \sin\left(4 \, d x + 4 \, c\right) - 96 i \, \sin\left(2 \, d x + 2 \, c\right) + 32}{{\left(-20 i \, a^{8} \cos\left(9 \, d x + 9 \, c\right) - 40 i \, a^{8} \cos\left(7 \, d x + 7 \, c\right) - 20 i \, a^{8} \cos\left(5 \, d x + 5 \, c\right) + 20 \, a^{8} \sin\left(9 \, d x + 9 \, c\right) + 40 \, a^{8} \sin\left(7 \, d x + 7 \, c\right) + 20 \, a^{8} \sin\left(5 \, d x + 5 \, c\right)\right)} d}"," ",0,"((630*cos(9*d*x + 9*c) + 1260*cos(7*d*x + 7*c) + 630*cos(5*d*x + 5*c) + 630*I*sin(9*d*x + 9*c) + 1260*I*sin(7*d*x + 7*c) + 630*I*sin(5*d*x + 5*c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (630*cos(9*d*x + 9*c) + 1260*cos(7*d*x + 7*c) + 630*cos(5*d*x + 5*c) + 630*I*sin(9*d*x + 9*c) + 1260*I*sin(7*d*x + 7*c) + 630*I*sin(5*d*x + 5*c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - (-315*I*cos(9*d*x + 9*c) - 630*I*cos(7*d*x + 7*c) - 315*I*cos(5*d*x + 5*c) + 315*sin(9*d*x + 9*c) + 630*sin(7*d*x + 7*c) + 315*sin(5*d*x + 5*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (315*I*cos(9*d*x + 9*c) + 630*I*cos(7*d*x + 7*c) + 315*I*cos(5*d*x + 5*c) - 315*sin(9*d*x + 9*c) - 630*sin(7*d*x + 7*c) - 315*sin(5*d*x + 5*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 1260*cos(8*d*x + 8*c) + 2100*cos(6*d*x + 6*c) + 672*cos(4*d*x + 4*c) - 96*cos(2*d*x + 2*c) + 1260*I*sin(8*d*x + 8*c) + 2100*I*sin(6*d*x + 6*c) + 672*I*sin(4*d*x + 4*c) - 96*I*sin(2*d*x + 2*c) + 32)/((-20*I*a^8*cos(9*d*x + 9*c) - 40*I*a^8*cos(7*d*x + 7*c) - 20*I*a^8*cos(5*d*x + 5*c) + 20*a^8*sin(9*d*x + 9*c) + 40*a^8*sin(7*d*x + 7*c) + 20*a^8*sin(5*d*x + 5*c))*d)","B",0
178,1,185,0,0.749550," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{-210 i \, \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - 210 i \, \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) + 60 i \, \cos\left(7 \, d x + 7 \, c\right) - 84 i \, \cos\left(5 \, d x + 5 \, c\right) + 140 i \, \cos\left(3 \, d x + 3 \, c\right) - 420 i \, \cos\left(d x + c\right) + 105 \, \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) - 105 \, \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) + 60 \, \sin\left(7 \, d x + 7 \, c\right) - 84 \, \sin\left(5 \, d x + 5 \, c\right) + 140 \, \sin\left(3 \, d x + 3 \, c\right) - 420 \, \sin\left(d x + c\right)}{210 \, a^{8} d}"," ",0,"1/210*(-210*I*arctan2(cos(d*x + c), sin(d*x + c) + 1) - 210*I*arctan2(cos(d*x + c), -sin(d*x + c) + 1) + 60*I*cos(7*d*x + 7*c) - 84*I*cos(5*d*x + 5*c) + 140*I*cos(3*d*x + 3*c) - 420*I*cos(d*x + c) + 105*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - 105*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 60*sin(7*d*x + 7*c) - 84*sin(5*d*x + 5*c) + 140*sin(3*d*x + 3*c) - 420*sin(d*x + c))/(a^8*d)","A",0
179,1,53,0,0.679878," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{7 i \, \cos\left(9 \, d x + 9 \, c\right) + 9 i \, \cos\left(7 \, d x + 7 \, c\right) + 7 \, \sin\left(9 \, d x + 9 \, c\right) + 9 \, \sin\left(7 \, d x + 7 \, c\right)}{126 \, a^{8} d}"," ",0,"1/126*(7*I*cos(9*d*x + 9*c) + 9*I*cos(7*d*x + 7*c) + 7*sin(9*d*x + 9*c) + 9*sin(7*d*x + 7*c))/(a^8*d)","A",0
180,1,97,0,0.405463," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{105 i \, \cos\left(11 \, d x + 11 \, c\right) + 385 i \, \cos\left(9 \, d x + 9 \, c\right) + 495 i \, \cos\left(7 \, d x + 7 \, c\right) + 231 i \, \cos\left(5 \, d x + 5 \, c\right) + 105 \, \sin\left(11 \, d x + 11 \, c\right) + 385 \, \sin\left(9 \, d x + 9 \, c\right) + 495 \, \sin\left(7 \, d x + 7 \, c\right) + 231 \, \sin\left(5 \, d x + 5 \, c\right)}{9240 \, a^{8} d}"," ",0,"1/9240*(105*I*cos(11*d*x + 11*c) + 385*I*cos(9*d*x + 9*c) + 495*I*cos(7*d*x + 7*c) + 231*I*cos(5*d*x + 5*c) + 105*sin(11*d*x + 11*c) + 385*sin(9*d*x + 9*c) + 495*sin(7*d*x + 7*c) + 231*sin(5*d*x + 5*c))/(a^8*d)","A",0
181,1,141,0,0.416637," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{693 i \, \cos\left(13 \, d x + 13 \, c\right) + 4095 i \, \cos\left(11 \, d x + 11 \, c\right) + 10010 i \, \cos\left(9 \, d x + 9 \, c\right) + 12870 i \, \cos\left(7 \, d x + 7 \, c\right) + 9009 i \, \cos\left(5 \, d x + 5 \, c\right) + 3003 i \, \cos\left(3 \, d x + 3 \, c\right) + 693 \, \sin\left(13 \, d x + 13 \, c\right) + 4095 \, \sin\left(11 \, d x + 11 \, c\right) + 10010 \, \sin\left(9 \, d x + 9 \, c\right) + 12870 \, \sin\left(7 \, d x + 7 \, c\right) + 9009 \, \sin\left(5 \, d x + 5 \, c\right) + 3003 \, \sin\left(3 \, d x + 3 \, c\right)}{288288 \, a^{8} d}"," ",0,"1/288288*(693*I*cos(13*d*x + 13*c) + 4095*I*cos(11*d*x + 11*c) + 10010*I*cos(9*d*x + 9*c) + 12870*I*cos(7*d*x + 7*c) + 9009*I*cos(5*d*x + 5*c) + 3003*I*cos(3*d*x + 3*c) + 693*sin(13*d*x + 13*c) + 4095*sin(11*d*x + 11*c) + 10010*sin(9*d*x + 9*c) + 12870*sin(7*d*x + 7*c) + 9009*sin(5*d*x + 5*c) + 3003*sin(3*d*x + 3*c))/(a^8*d)","A",0
182,1,179,0,0.649624," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\frac{429 i \, \cos\left(15 \, d x + 15 \, c\right) + 3465 i \, \cos\left(13 \, d x + 13 \, c\right) + 12285 i \, \cos\left(11 \, d x + 11 \, c\right) + 25025 i \, \cos\left(9 \, d x + 9 \, c\right) + 32175 i \, \cos\left(7 \, d x + 7 \, c\right) + 27027 i \, \cos\left(5 \, d x + 5 \, c\right) + 15015 i \, \cos\left(3 \, d x + 3 \, c\right) + 6435 i \, \cos\left(d x + c\right) + 429 \, \sin\left(15 \, d x + 15 \, c\right) + 3465 \, \sin\left(13 \, d x + 13 \, c\right) + 12285 \, \sin\left(11 \, d x + 11 \, c\right) + 25025 \, \sin\left(9 \, d x + 9 \, c\right) + 32175 \, \sin\left(7 \, d x + 7 \, c\right) + 27027 \, \sin\left(5 \, d x + 5 \, c\right) + 15015 \, \sin\left(3 \, d x + 3 \, c\right) + 6435 \, \sin\left(d x + c\right)}{823680 \, a^{8} d}"," ",0,"1/823680*(429*I*cos(15*d*x + 15*c) + 3465*I*cos(13*d*x + 13*c) + 12285*I*cos(11*d*x + 11*c) + 25025*I*cos(9*d*x + 9*c) + 32175*I*cos(7*d*x + 7*c) + 27027*I*cos(5*d*x + 5*c) + 15015*I*cos(3*d*x + 3*c) + 6435*I*cos(d*x + c) + 429*sin(15*d*x + 15*c) + 3465*sin(13*d*x + 13*c) + 12285*sin(11*d*x + 11*c) + 25025*sin(9*d*x + 9*c) + 32175*sin(7*d*x + 7*c) + 27027*sin(5*d*x + 5*c) + 15015*sin(3*d*x + 3*c) + 6435*sin(d*x + c))/(a^8*d)","A",0
183,-2,0,0,0.000000," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
184,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
185,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(7/2)*(I*a*tan(d*x + c) + a), x)","F",0
186,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/2)*(I*a*tan(d*x + c) + a), x)","F",0
187,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a), x)","F",0
188,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int \sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a), x)","F",0
189,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\sqrt{e \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/sqrt(e*sec(d*x + c)), x)","F",0
190,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*sec(d*x + c))^(3/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*sec(d*x + c))^(5/2), x)","F",0
192,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*sec(d*x + c))^(7/2), x)","F",0
193,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a)^2, x)","F",0
194,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\int \sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a)^2, x)","F",0
195,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/sqrt(e*sec(d*x + c)), x)","F",0
196,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(3/2), x)","F",0
197,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(5/2), x)","F",0
198,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(7/2), x)","F",0
199,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(9/2), x)","F",0
200,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(11/2), x)","F",0
201,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(7/2)*(I*a*tan(d*x + c) + a)^3, x)","F",0
202,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/2)*(I*a*tan(d*x + c) + a)^3, x)","F",0
203,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a)^3, x)","F",0
204,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\int \sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a)^3, x)","F",0
205,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\sqrt{e \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/sqrt(e*sec(d*x + c)), x)","F",0
206,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/(e*sec(d*x + c))^(3/2), x)","F",0
207,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/(e*sec(d*x + c))^(5/2), x)","F",0
208,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/(e*sec(d*x + c))^(7/2), x)","F",0
209,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\left(e \sec\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/(e*sec(d*x + c))^(9/2), x)","F",0
210,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\left(e \sec\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/(e*sec(d*x + c))^(11/2), x)","F",0
211,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\left(e \sec\left(d x + c\right)\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/(e*sec(d*x + c))^(13/2), x)","F",0
212,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(15/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\left(e \sec\left(d x + c\right)\right)^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/(e*sec(d*x + c))^(15/2), x)","F",0
213,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a)^4, x)","F",0
214,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\int \sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a)^4, x)","F",0
215,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{\sqrt{e \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^4/sqrt(e*sec(d*x + c)), x)","F",0
216,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^4/(e*sec(d*x + c))^(3/2), x)","F",0
217,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^4/(e*sec(d*x + c))^(5/2), x)","F",0
218,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^4/(e*sec(d*x + c))^(7/2), x)","F",0
219,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{\left(e \sec\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^4/(e*sec(d*x + c))^(9/2), x)","F",0
220,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{\left(e \sec\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^4/(e*sec(d*x + c))^(11/2), x)","F",0
221,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{\left(e \sec\left(d x + c\right)\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^4/(e*sec(d*x + c))^(13/2), x)","F",0
222,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(15/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}{\left(e \sec\left(d x + c\right)\right)^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^4/(e*sec(d*x + c))^(15/2), x)","F",0
223,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
224,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
225,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
226,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
227,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
228,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
229,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
230,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
231,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
232,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
233,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
234,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
235,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
236,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
237,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
238,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
239,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
240,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
241,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
242,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
243,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
244,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
245,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(15/2)/(a+I*a*tan(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
246,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(13/2)/(a+I*a*tan(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
247,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(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
248,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
249,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(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
250,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(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
251,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(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
252,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(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
253,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(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
254,-2,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(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
255,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
256,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
257,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
258,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
259,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
260,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
261,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
262,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
263,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)*(I*a*tan(f*x + e) + a), x)","F",0
264,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)*(I*a*tan(f*x + e) + a), x)","F",0
265,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)/(d*sec(f*x + e))^(1/3), x)","F",0
266,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)/(d*sec(f*x + e))^(5/3), x)","F",0
267,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)*(I*a*tan(f*x + e) + a)^2, x)","F",0
268,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)*(I*a*tan(f*x + e) + a)^2, x)","F",0
269,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(1/3), x)","F",0
270,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(5/3), x)","F",0
271,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
272,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
273,-2,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
274,-2,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
275,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
276,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
277,-2,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
278,-2,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
279,1,76,0,0.529310," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(429 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{15}{2}} - 2970 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} a + 7020 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{2} - 5720 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{3}\right)}}{6435 \, a^{7} d}"," ",0,"2/6435*I*(429*(I*a*tan(d*x + c) + a)^(15/2) - 2970*(I*a*tan(d*x + c) + a)^(13/2)*a + 7020*(I*a*tan(d*x + c) + a)^(11/2)*a^2 - 5720*(I*a*tan(d*x + c) + a)^(9/2)*a^3)/(a^7*d)","A",0
280,1,58,0,0.414217," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(63 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 308 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 396 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2}\right)}}{693 \, a^{5} d}"," ",0,"-2/693*I*(63*(I*a*tan(d*x + c) + a)^(11/2) - 308*(I*a*tan(d*x + c) + a)^(9/2)*a + 396*(I*a*tan(d*x + c) + a)^(7/2)*a^2)/(a^5*d)","A",0
281,1,40,0,0.540112," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 14 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a\right)}}{35 \, a^{3} d}"," ",0,"2/35*I*(5*(I*a*tan(d*x + c) + a)^(7/2) - 14*(I*a*tan(d*x + c) + a)^(5/2)*a)/(a^3*d)","A",0
282,1,21,0,0.424959," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{3 \, a d}"," ",0,"-2/3*I*(I*a*tan(d*x + c) + a)^(3/2)/(a*d)","A",0
283,1,122,0,0.520839," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(3 \, \sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} - 4 \, a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 2 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a}\right)}}{16 \, a d}"," ",0,"1/16*I*(3*sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(3*(I*a*tan(d*x + c) + a)*a^2 - 4*a^3)/((I*a*tan(d*x + c) + a)^(3/2) - 2*sqrt(I*a*tan(d*x + c) + a)*a))/(a*d)","A",0
284,1,176,0,0.851345," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(105 \, \sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{2} - 350 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{3} + 224 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} + 64 \, a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2}}\right)}}{768 \, a d}"," ",0,"1/768*I*(105*sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(105*(I*a*tan(d*x + c) + a)^3*a^2 - 350*(I*a*tan(d*x + c) + a)^2*a^3 + 224*(I*a*tan(d*x + c) + a)*a^4 + 64*a^5)/((I*a*tan(d*x + c) + a)^(7/2) - 4*(I*a*tan(d*x + c) + a)^(5/2)*a + 4*(I*a*tan(d*x + c) + a)^(3/2)*a^2))/(a*d)","A",0
285,1,230,0,0.585238," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(3465 \, \sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(3465 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} a^{2} - 18480 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a^{3} + 30492 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{4} - 12672 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{5} - 2816 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{6} - 1536 \, a^{7}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2} - 8 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{3}}\right)}}{30720 \, a d}"," ",0,"1/30720*I*(3465*sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(3465*(I*a*tan(d*x + c) + a)^5*a^2 - 18480*(I*a*tan(d*x + c) + a)^4*a^3 + 30492*(I*a*tan(d*x + c) + a)^3*a^4 - 12672*(I*a*tan(d*x + c) + a)^2*a^5 - 2816*(I*a*tan(d*x + c) + a)*a^6 - 1536*a^7)/((I*a*tan(d*x + c) + a)^(11/2) - 6*(I*a*tan(d*x + c) + a)^(9/2)*a + 12*(I*a*tan(d*x + c) + a)^(7/2)*a^2 - 8*(I*a*tan(d*x + c) + a)^(5/2)*a^3))/(a*d)","A",0
286,-1,0,0,0.000000," ","integrate(sec(d*x+c)^7*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,1,225,0,33.002483," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(-600 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 600 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 240 i \, \sqrt{2}\right)} \sqrt{a}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(225 \, \cos\left(4 \, d x + 4 \, c\right) + 450 \, \cos\left(2 \, d x + 2 \, c\right) + 225 i \, \sin\left(4 \, d x + 4 \, c\right) + 450 i \, \sin\left(2 \, d x + 2 \, c\right) + 225\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left(-225 i \, \cos\left(4 \, d x + 4 \, c\right) - 450 i \, \cos\left(2 \, d x + 2 \, c\right) + 225 \, \sin\left(4 \, d x + 4 \, c\right) + 450 \, \sin\left(2 \, d x + 2 \, c\right) - 225 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)\right)} d}"," ",0,"-(-600*I*sqrt(2)*cos(2*d*x + 2*c) + 600*sqrt(2)*sin(2*d*x + 2*c) - 240*I*sqrt(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)^(1/4)*((225*cos(4*d*x + 4*c) + 450*cos(2*d*x + 2*c) + 225*I*sin(4*d*x + 4*c) + 450*I*sin(2*d*x + 2*c) + 225)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (-225*I*cos(4*d*x + 4*c) - 450*I*cos(2*d*x + 2*c) + 225*sin(4*d*x + 4*c) + 450*sin(2*d*x + 2*c) - 225*I)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*d)","B",0
289,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sec(d*x + c), x)","F",0
290,1,774,0,1.071017," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(-4 i \, \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) + 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} - {\left(2 \, \sqrt{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) - 2 \, \sqrt{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) - i \, \sqrt{2} \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) + i \, \sqrt{2} \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)\right)} \sqrt{a}}{8 \, d}"," ",0,"1/8*((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*I*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 4*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) - (2*sqrt(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) - 2*sqrt(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) - I*sqrt(2)*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) + I*sqrt(2)*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))*sqrt(a))/d","B",0
291,1,934,0,0.821650," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, d x + 2 \, 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(-8 i \, \sqrt{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 8 \, \sqrt{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(12 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 12 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 48 i \, \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) - 12 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, \sqrt{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} - {\left(30 \, \sqrt{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) - 30 \, \sqrt{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) - 15 i \, \sqrt{2} \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) + 15 i \, \sqrt{2} \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)\right)} \sqrt{a}}{192 \, d}"," ",0,"1/192*((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*(-8*I*sqrt(2)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 8*sqrt(2)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((12*I*sqrt(2)*cos(2*d*x + 2*c) + 12*sqrt(2)*sin(2*d*x + 2*c) - 48*I*sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 12*(sqrt(2)*cos(2*d*x + 2*c) - I*sqrt(2)*sin(2*d*x + 2*c) - 4*sqrt(2))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) - (30*sqrt(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) - 30*sqrt(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) - 15*I*sqrt(2)*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) + 15*I*sqrt(2)*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))*sqrt(a))/d","B",0
292,1,2215,0,2.004186," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(60 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 60 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 160 i \, \sqrt{2}\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) - 20 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 3 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sqrt{2}\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} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(32 i \, \sqrt{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} + 32 i \, \sqrt{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} + 64 i \, \sqrt{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) + 32 i \, \sqrt{2}\right)} \cos\left(\frac{5}{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(-100 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 400 i \, \sqrt{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) - 100 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 400 \, \sqrt{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) + 960 i \, \sqrt{2}\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) - 32 \, {\left(\sqrt{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} + \sqrt{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 \, \sqrt{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) + \sqrt{2}\right)} \sin\left(\frac{5}{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(100 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 400 \, \sqrt{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) - 100 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 400 i \, \sqrt{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) - 960 \, \sqrt{2}\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} + {\left(630 \, \sqrt{2} \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) - 630 \, \sqrt{2} \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) - 315 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\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} \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)^{2} + \sqrt{\cos\left(\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} \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)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \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) + 315 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\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} \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)^{2} + \sqrt{\cos\left(\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} \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)^{2} - 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \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}}{5120 \, d}"," ",0,"-1/5120*((cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(3/4)*((60*I*sqrt(2)*cos(4*d*x + 4*c) + 60*sqrt(2)*sin(4*d*x + 4*c) + 160*I*sqrt(2))*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)) - 20*(3*sqrt(2)*cos(4*d*x + 4*c) - 3*I*sqrt(2)*sin(4*d*x + 4*c) + 8*sqrt(2))*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) + (cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*((32*I*sqrt(2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 32*I*sqrt(2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 64*I*sqrt(2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 32*I*sqrt(2))*cos(5/2*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)) + (-100*I*sqrt(2)*cos(4*d*x + 4*c) - 400*I*sqrt(2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 100*sqrt(2)*sin(4*d*x + 4*c) - 400*sqrt(2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 960*I*sqrt(2))*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) - 32*(sqrt(2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sqrt(2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*sqrt(2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + sqrt(2))*sin(5/2*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)) + (100*sqrt(2)*cos(4*d*x + 4*c) + 400*sqrt(2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 100*I*sqrt(2)*sin(4*d*x + 4*c) - 400*I*sqrt(2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 960*sqrt(2))*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) + (630*sqrt(2)*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) - 630*sqrt(2)*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) - 315*I*sqrt(2)*log(sqrt(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)*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))^2 + sqrt(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)*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))^2 + 2*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*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) + 315*I*sqrt(2)*log(sqrt(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)*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))^2 + sqrt(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)*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))^2 - 2*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*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))/d","B",0
293,1,76,0,0.430345," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(715 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{17}{2}} - 4862 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{15}{2}} a + 11220 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} a^{2} - 8840 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{3}\right)}}{12155 \, a^{7} d}"," ",0,"2/12155*I*(715*(I*a*tan(d*x + c) + a)^(17/2) - 4862*(I*a*tan(d*x + c) + a)^(15/2)*a + 11220*(I*a*tan(d*x + c) + a)^(13/2)*a^2 - 8840*(I*a*tan(d*x + c) + a)^(11/2)*a^3)/(a^7*d)","A",0
294,1,58,0,0.327897," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(99 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 468 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a + 572 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{2}\right)}}{1287 \, a^{5} d}"," ",0,"-2/1287*I*(99*(I*a*tan(d*x + c) + a)^(13/2) - 468*(I*a*tan(d*x + c) + a)^(11/2)*a + 572*(I*a*tan(d*x + c) + a)^(9/2)*a^2)/(a^5*d)","A",0
295,1,40,0,0.338875," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(7 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 18 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a\right)}}{63 \, a^{3} d}"," ",0,"2/63*I*(7*(I*a*tan(d*x + c) + a)^(9/2) - 18*(I*a*tan(d*x + c) + a)^(7/2)*a)/(a^3*d)","A",0
296,1,21,0,0.369366," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{5 \, a d}"," ",0,"-2/5*I*(I*a*tan(d*x + c) + a)^(5/2)/(a*d)","A",0
297,1,98,0,0.801008," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(\sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{16 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{3}}{4 i \, a \tan\left(d x + c\right) - 4 \, a}\right)}}{8 \, a d}"," ",0,"1/8*I*(sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 16*sqrt(I*a*tan(d*x + c) + a)*a^3/(4*I*a*tan(d*x + c) - 4*a))/(a*d)","A",0
298,1,158,0,0.891300," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(15 \, \sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{3} - 50 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} + 32 \, a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 4 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}}\right)}}{128 \, a d}"," ",0,"1/128*I*(15*sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(15*(I*a*tan(d*x + c) + a)^2*a^3 - 50*(I*a*tan(d*x + c) + a)*a^4 + 32*a^5)/((I*a*tan(d*x + c) + a)^(5/2) - 4*(I*a*tan(d*x + c) + a)^(3/2)*a + 4*sqrt(I*a*tan(d*x + c) + a)*a^2))/(a*d)","A",0
299,1,212,0,0.808874," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(315 \, \sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(315 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a^{3} - 1680 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{4} + 2772 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{5} - 1152 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{6} - 256 \, a^{7}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 8 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3}}\right)}}{3072 \, a d}"," ",0,"1/3072*I*(315*sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(315*(I*a*tan(d*x + c) + a)^4*a^3 - 1680*(I*a*tan(d*x + c) + a)^3*a^4 + 2772*(I*a*tan(d*x + c) + a)^2*a^5 - 1152*(I*a*tan(d*x + c) + a)*a^6 - 256*a^7)/((I*a*tan(d*x + c) + a)^(9/2) - 6*(I*a*tan(d*x + c) + a)^(7/2)*a + 12*(I*a*tan(d*x + c) + a)^(5/2)*a^2 - 8*(I*a*tan(d*x + c) + a)^(3/2)*a^3))/(a*d)","A",0
300,1,996,0,21.081925," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(-17075520 i \, \sqrt{2} a \cos\left(6 \, d x + 6 \, c\right) - 14636160 i \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) - 6504960 i \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 17075520 \, \sqrt{2} a \sin\left(6 \, d x + 6 \, c\right) + 14636160 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 6504960 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) - 1182720 i \, \sqrt{2} a\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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}}{{\left({\left(5336100 \, \cos\left(2 \, d x + 2 \, c\right)^{3} + 1334025 \, {\left(4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 5336100 i \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 1334025 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(8 \, d x + 8 \, c\right) + 5336100 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(6 \, d x + 6 \, c\right) + 8004150 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 12006225 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(-1334025 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 1334025 i \, \sin\left(2 \, d x + 2 \, c\right)^{2} - 2668050 i \, \cos\left(2 \, d x + 2 \, c\right) - 1334025 i\right)} \sin\left(8 \, d x + 8 \, c\right) - {\left(-5336100 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 5336100 i \, \sin\left(2 \, d x + 2 \, c\right)^{2} - 10672200 i \, \cos\left(2 \, d x + 2 \, c\right) - 5336100 i\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(-8004150 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 8004150 i \, \sin\left(2 \, d x + 2 \, c\right)^{2} - 16008300 i \, \cos\left(2 \, d x + 2 \, c\right) - 8004150 i\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(-5336100 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 10672200 i \, \cos\left(2 \, d x + 2 \, c\right) - 5336100 i\right)} \sin\left(2 \, d x + 2 \, c\right) + 8004150 \, \cos\left(2 \, d x + 2 \, c\right) + 1334025\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(-5336100 i \, \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-5336100 i \, \cos\left(2 \, d x + 2 \, c\right) - 1334025 i\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 5336100 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + {\left(-1334025 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 1334025 i \, \sin\left(2 \, d x + 2 \, c\right)^{2} - 2668050 i \, \cos\left(2 \, d x + 2 \, c\right) - 1334025 i\right)} \cos\left(8 \, d x + 8 \, c\right) + {\left(-5336100 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 5336100 i \, \sin\left(2 \, d x + 2 \, c\right)^{2} - 10672200 i \, \cos\left(2 \, d x + 2 \, c\right) - 5336100 i\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(-8004150 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 8004150 i \, \sin\left(2 \, d x + 2 \, c\right)^{2} - 16008300 i \, \cos\left(2 \, d x + 2 \, c\right) - 8004150 i\right)} \cos\left(4 \, d x + 4 \, c\right) - 12006225 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 1334025 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(8 \, d x + 8 \, c\right) + 5336100 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(6 \, d x + 6 \, c\right) + 8004150 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) + 5336100 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) - 8004150 i \, \cos\left(2 \, d x + 2 \, c\right) - 1334025 i\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)} d}"," ",0,"-(-17075520*I*sqrt(2)*a*cos(6*d*x + 6*c) - 14636160*I*sqrt(2)*a*cos(4*d*x + 4*c) - 6504960*I*sqrt(2)*a*cos(2*d*x + 2*c) + 17075520*sqrt(2)*a*sin(6*d*x + 6*c) + 14636160*sqrt(2)*a*sin(4*d*x + 4*c) + 6504960*sqrt(2)*a*sin(2*d*x + 2*c) - 1182720*I*sqrt(2)*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)*sqrt(a)/(((5336100*cos(2*d*x + 2*c)^3 + 1334025*(4*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c)^2 + 5336100*I*sin(2*d*x + 2*c)^3 + 1334025*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(8*d*x + 8*c) + 5336100*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(6*d*x + 6*c) + 8004150*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 12006225*cos(2*d*x + 2*c)^2 - (-1334025*I*cos(2*d*x + 2*c)^2 - 1334025*I*sin(2*d*x + 2*c)^2 - 2668050*I*cos(2*d*x + 2*c) - 1334025*I)*sin(8*d*x + 8*c) - (-5336100*I*cos(2*d*x + 2*c)^2 - 5336100*I*sin(2*d*x + 2*c)^2 - 10672200*I*cos(2*d*x + 2*c) - 5336100*I)*sin(6*d*x + 6*c) - (-8004150*I*cos(2*d*x + 2*c)^2 - 8004150*I*sin(2*d*x + 2*c)^2 - 16008300*I*cos(2*d*x + 2*c) - 8004150*I)*sin(4*d*x + 4*c) - (-5336100*I*cos(2*d*x + 2*c)^2 - 10672200*I*cos(2*d*x + 2*c) - 5336100*I)*sin(2*d*x + 2*c) + 8004150*cos(2*d*x + 2*c) + 1334025)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (-5336100*I*cos(2*d*x + 2*c)^3 + (-5336100*I*cos(2*d*x + 2*c) - 1334025*I)*sin(2*d*x + 2*c)^2 + 5336100*sin(2*d*x + 2*c)^3 + (-1334025*I*cos(2*d*x + 2*c)^2 - 1334025*I*sin(2*d*x + 2*c)^2 - 2668050*I*cos(2*d*x + 2*c) - 1334025*I)*cos(8*d*x + 8*c) + (-5336100*I*cos(2*d*x + 2*c)^2 - 5336100*I*sin(2*d*x + 2*c)^2 - 10672200*I*cos(2*d*x + 2*c) - 5336100*I)*cos(6*d*x + 6*c) + (-8004150*I*cos(2*d*x + 2*c)^2 - 8004150*I*sin(2*d*x + 2*c)^2 - 16008300*I*cos(2*d*x + 2*c) - 8004150*I)*cos(4*d*x + 4*c) - 12006225*I*cos(2*d*x + 2*c)^2 + 1334025*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(8*d*x + 8*c) + 5336100*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(6*d*x + 6*c) + 8004150*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) + 5336100*(cos(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) - 8004150*I*cos(2*d*x + 2*c) - 1334025*I)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*d)","B",0
301,1,584,0,1.535766," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(-560 i \, \sqrt{2} a \cos\left(4 \, d x + 4 \, c\right) - 448 i \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 560 \, \sqrt{2} a \sin\left(4 \, d x + 4 \, c\right) + 448 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) - 128 i \, \sqrt{2} a\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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}}{{\left({\left(210 \, \cos\left(2 \, d x + 2 \, c\right)^{3} + 105 \, {\left(2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 210 i \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 105 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) + 525 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(-105 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 105 i \, \sin\left(2 \, d x + 2 \, c\right)^{2} - 210 i \, \cos\left(2 \, d x + 2 \, c\right) - 105 i\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(-210 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 420 i \, \cos\left(2 \, d x + 2 \, c\right) - 210 i\right)} \sin\left(2 \, d x + 2 \, c\right) + 420 \, \cos\left(2 \, d x + 2 \, c\right) + 105\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(-210 i \, \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-210 i \, \cos\left(2 \, d x + 2 \, c\right) - 105 i\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 210 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + {\left(-105 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 105 i \, \sin\left(2 \, d x + 2 \, c\right)^{2} - 210 i \, \cos\left(2 \, d x + 2 \, c\right) - 105 i\right)} \cos\left(4 \, d x + 4 \, c\right) - 525 i \, \cos\left(2 \, d x + 2 \, c\right)^{2} + 105 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(4 \, d x + 4 \, c\right) + 210 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right) - 420 i \, \cos\left(2 \, d x + 2 \, c\right) - 105 i\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)} d}"," ",0,"-(-560*I*sqrt(2)*a*cos(4*d*x + 4*c) - 448*I*sqrt(2)*a*cos(2*d*x + 2*c) + 560*sqrt(2)*a*sin(4*d*x + 4*c) + 448*sqrt(2)*a*sin(2*d*x + 2*c) - 128*I*sqrt(2)*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)*sqrt(a)/(((210*cos(2*d*x + 2*c)^3 + 105*(2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c)^2 + 210*I*sin(2*d*x + 2*c)^3 + 105*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*cos(4*d*x + 4*c) + 525*cos(2*d*x + 2*c)^2 - (-105*I*cos(2*d*x + 2*c)^2 - 105*I*sin(2*d*x + 2*c)^2 - 210*I*cos(2*d*x + 2*c) - 105*I)*sin(4*d*x + 4*c) - (-210*I*cos(2*d*x + 2*c)^2 - 420*I*cos(2*d*x + 2*c) - 210*I)*sin(2*d*x + 2*c) + 420*cos(2*d*x + 2*c) + 105)*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (-210*I*cos(2*d*x + 2*c)^3 + (-210*I*cos(2*d*x + 2*c) - 105*I)*sin(2*d*x + 2*c)^2 + 210*sin(2*d*x + 2*c)^3 + (-105*I*cos(2*d*x + 2*c)^2 - 105*I*sin(2*d*x + 2*c)^2 - 210*I*cos(2*d*x + 2*c) - 105*I)*cos(4*d*x + 4*c) - 525*I*cos(2*d*x + 2*c)^2 + 105*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(4*d*x + 4*c) + 210*(cos(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c) - 420*I*cos(2*d*x + 2*c) - 105*I)*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*d)","B",0
302,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
303,1,201,0,0.862849," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(i \, a^{\frac{3}{2}} - \frac{2 i \, a^{\frac{3}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{i \, a^{\frac{3}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}{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}} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{\sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 1\right)}}"," ",0,"2*(I*a^(3/2) - 2*I*a^(3/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + I*a^(3/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2)/(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)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) - 2*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1))","B",0
304,1,883,0,0.670982," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(i \, \sqrt{2} a \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sqrt{2} a \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} \sqrt{a} + 12 \, {\left(i \, \sqrt{2} a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sqrt{2} a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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} + {\left(6 \, \sqrt{2} 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) - 6 \, \sqrt{2} 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) - 3 i \, \sqrt{2} a \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 i \, \sqrt{2} a \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)\right)} \sqrt{a}}{48 \, d}"," ",0,"-1/48*(4*(I*sqrt(2)*a*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - sqrt(2)*a*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*sqrt(a) + 12*(I*sqrt(2)*a*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - sqrt(2)*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) + (6*sqrt(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)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*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) - 6*sqrt(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)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*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*I*sqrt(2)*a*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*I*sqrt(2)*a*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))*sqrt(a))/d","B",0
305,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,1,76,0,0.439958," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(1105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{19}{2}} - 7410 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{17}{2}} a + 16796 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{15}{2}} a^{2} - 12920 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} a^{3}\right)}}{20995 \, a^{7} d}"," ",0,"2/20995*I*(1105*(I*a*tan(d*x + c) + a)^(19/2) - 7410*(I*a*tan(d*x + c) + a)^(17/2)*a + 16796*(I*a*tan(d*x + c) + a)^(15/2)*a^2 - 12920*(I*a*tan(d*x + c) + a)^(13/2)*a^3)/(a^7*d)","A",0
307,1,58,0,0.446466," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(143 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{15}{2}} - 660 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} a + 780 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{2}\right)}}{2145 \, a^{5} d}"," ",0,"-2/2145*I*(143*(I*a*tan(d*x + c) + a)^(15/2) - 660*(I*a*tan(d*x + c) + a)^(13/2)*a + 780*(I*a*tan(d*x + c) + a)^(11/2)*a^2)/(a^5*d)","A",0
308,1,40,0,0.531378," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(9 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 22 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a\right)}}{99 \, a^{3} d}"," ",0,"2/99*I*(9*(I*a*tan(d*x + c) + a)^(11/2) - 22*(I*a*tan(d*x + c) + a)^(9/2)*a)/(a^3*d)","A",0
309,1,21,0,0.323485," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}{7 \, a d}"," ",0,"-2/7*I*(I*a*tan(d*x + c) + a)^(7/2)/(a*d)","A",0
310,1,98,0,0.546011," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - \frac{8 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4}}{2 i \, a \tan\left(d x + c\right) - 2 \, a}\right)}}{4 \, a d}"," ",0,"-1/4*I*(sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - 8*sqrt(I*a*tan(d*x + c) + a)*a^4/(2*I*a*tan(d*x + c) - 2*a))/(a*d)","A",0
311,1,140,0,0.620994," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, {\left(3 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{4} - 10 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a + 4 \, a^{2}}\right)}}{64 \, a d}"," ",0,"1/64*I*(3*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(3*(I*a*tan(d*x + c) + a)^(3/2)*a^4 - 10*sqrt(I*a*tan(d*x + c) + a)*a^5)/((I*a*tan(d*x + c) + a)^2 - 4*(I*a*tan(d*x + c) + a)*a + 4*a^2))/(a*d)","A",0
312,1,194,0,0.666896," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, {\left(105 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{4} - 560 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{5} + 924 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{6} - 384 \, a^{7}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} - 8 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{3}}\right)}}{1536 \, a d}"," ",0,"1/1536*I*(105*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(105*(I*a*tan(d*x + c) + a)^3*a^4 - 560*(I*a*tan(d*x + c) + a)^2*a^5 + 924*(I*a*tan(d*x + c) + a)*a^6 - 384*a^7)/((I*a*tan(d*x + c) + a)^(7/2) - 6*(I*a*tan(d*x + c) + a)^(5/2)*a + 12*(I*a*tan(d*x + c) + a)^(3/2)*a^2 - 8*sqrt(I*a*tan(d*x + c) + a)*a^3))/(a*d)","A",0
313,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
315,1,331,0,0.990304," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(-3 i \, a^{\frac{5}{2}} - \frac{2 \, a^{\frac{5}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 i \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{9 i \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 i \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}{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{4 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 i \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{\sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 1\right)}}"," ",0,"2*(-3*I*a^(5/2) - 2*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) + 9*I*a^(5/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a^(5/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 9*I*a^(5/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*a^(5/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*I*a^(5/2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2)/(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)*(4*I*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*I*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1))","B",0
316,1,328,0,1.208272," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(i \, a^{\frac{5}{2}} - \frac{4 i \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 i \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 i \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{i \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}{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{6 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{18 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{18 i \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{6 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 i \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - 3\right)}}"," ",0,"2*(I*a^(5/2) - 4*I*a^(5/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*I*a^(5/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*I*a^(5/2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + I*a^(5/2)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2)/(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)*(-6*I*sin(d*x + c)/(cos(d*x + c) + 1) - 6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 18*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 18*I*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 6*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*I*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 3))","B",0
317,1,1075,0,1.103729," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{20 \, {\left(i \, \sqrt{2} a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} \sqrt{a} - {\left(-60 i \, \sqrt{2} a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 60 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-12 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - 12 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 24 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 12 i \, \sqrt{2} a^{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 12 \, {\left(\sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{2}\right)} \sin\left(\frac{5}{2} \, \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} + {\left(30 \, \sqrt{2} 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) - 30 \, \sqrt{2} 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) - 15 i \, \sqrt{2} a^{2} \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) + 15 i \, \sqrt{2} a^{2} \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)\right)} \sqrt{a}}{480 \, d}"," ",0,"-1/480*(20*(I*sqrt(2)*a^2*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - sqrt(2)*a^2*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*sqrt(a) - (-60*I*sqrt(2)*a^2*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 60*sqrt(2)*a^2*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (-12*I*sqrt(2)*a^2*cos(2*d*x + 2*c)^2 - 12*I*sqrt(2)*a^2*sin(2*d*x + 2*c)^2 - 24*I*sqrt(2)*a^2*cos(2*d*x + 2*c) - 12*I*sqrt(2)*a^2)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 12*(sqrt(2)*a^2*cos(2*d*x + 2*c)^2 + sqrt(2)*a^2*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^2*cos(2*d*x + 2*c) + sqrt(2)*a^2)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(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) + (30*sqrt(2)*a^2*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 1) - 30*sqrt(2)*a^2*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 1) - 15*I*sqrt(2)*a^2*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) + 15*I*sqrt(2)*a^2*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))*sqrt(a))/d","B",0
318,-1,0,0,0.000000," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,1,76,0,0.328318," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(1615 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{21}{2}} - 10710 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{19}{2}} a + 23940 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{17}{2}} a^{2} - 18088 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{15}{2}} a^{3}\right)}}{33915 \, a^{7} d}"," ",0,"2/33915*I*(1615*(I*a*tan(d*x + c) + a)^(21/2) - 10710*(I*a*tan(d*x + c) + a)^(19/2)*a + 23940*(I*a*tan(d*x + c) + a)^(17/2)*a^2 - 18088*(I*a*tan(d*x + c) + a)^(15/2)*a^3)/(a^7*d)","A",0
320,1,58,0,0.674762," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(195 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{17}{2}} - 884 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{15}{2}} a + 1020 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} a^{2}\right)}}{3315 \, a^{5} d}"," ",0,"-2/3315*I*(195*(I*a*tan(d*x + c) + a)^(17/2) - 884*(I*a*tan(d*x + c) + a)^(15/2)*a + 1020*(I*a*tan(d*x + c) + a)^(13/2)*a^2)/(a^5*d)","A",0
321,1,40,0,0.667994," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(11 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 26 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a\right)}}{143 \, a^{3} d}"," ",0,"2/143*I*(11*(I*a*tan(d*x + c) + a)^(13/2) - 26*(I*a*tan(d*x + c) + a)^(11/2)*a)/(a^3*d)","A",0
322,1,21,0,0.416547," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}}}{9 \, a d}"," ",0,"-2/9*I*(I*a*tan(d*x + c) + a)^(9/2)/(a*d)","A",0
323,1,117,0,0.647795," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{i \, {\left(3 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 4 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4} - \frac{4 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{5}}{i \, a \tan\left(d x + c\right) - a}\right)}}{2 \, a d}"," ",0,"-1/2*I*(3*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*sqrt(I*a*tan(d*x + c) + a)*a^4 - 4*sqrt(I*a*tan(d*x + c) + a)*a^5/(I*a*tan(d*x + c) - a))/(a*d)","A",0
324,1,138,0,0.589141," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{5} + 2 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{6}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a + 4 \, a^{2}}\right)}}{32 \, a d}"," ",0,"-1/32*I*(sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*((I*a*tan(d*x + c) + a)^(3/2)*a^5 + 2*sqrt(I*a*tan(d*x + c) + a)*a^6)/((I*a*tan(d*x + c) + a)^2 - 4*(I*a*tan(d*x + c) + a)*a + 4*a^2))/(a*d)","A",0
325,1,176,0,0.597389," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{i \, {\left(15 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{5} - 80 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{6} + 132 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{7}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} - 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a + 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} - 8 \, a^{3}}\right)}}{768 \, a d}"," ",0,"1/768*I*(15*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(15*(I*a*tan(d*x + c) + a)^(5/2)*a^5 - 80*(I*a*tan(d*x + c) + a)^(3/2)*a^6 + 132*sqrt(I*a*tan(d*x + c) + a)*a^7)/((I*a*tan(d*x + c) + a)^3 - 6*(I*a*tan(d*x + c) + a)^2*a + 12*(I*a*tan(d*x + c) + a)*a^2 - 8*a^3))/(a*d)","A",0
326,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*sec(d*x + c), x)","F",0
327,1,418,0,1.026278," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(23 i \, a^{\frac{7}{2}} + \frac{20 \, a^{\frac{7}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{88 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{60 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{130 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{60 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{88 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{20 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{23 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{7}{2}}}{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{18 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{42 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{42 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{42 i \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{42 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{18 i \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - 3\right)}}"," ",0,"2*(23*I*a^(7/2) + 20*a^(7/2)*sin(d*x + c)/(cos(d*x + c) + 1) - 88*I*a^(7/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 60*a^(7/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 130*I*a^(7/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 60*a^(7/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 88*I*a^(7/2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 20*a^(7/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 23*I*a^(7/2)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(7/2)/(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)*(-18*I*sin(d*x + c)/(cos(d*x + c) + 1) + 42*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 42*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 42*I*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 42*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 18*I*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 3))","B",0
328,1,504,0,0.719978," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-i \, a^{\frac{7}{2}} - \frac{6 \, a^{\frac{7}{2}} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{24 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{10 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{10 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{24 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{5 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{6 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{7}{2}}}{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{12 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{24 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{42 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{42 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{24 i \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{9 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{12 i \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{3 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 3\right)}}"," ",0,"-2*(-I*a^(7/2) - 6*a^(7/2)*sin(d*x + c)/(cos(d*x + c) + 1) + 5*I*a^(7/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 24*a^(7/2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 10*I*a^(7/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^(7/2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 10*I*a^(7/2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 24*a^(7/2)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 5*I*a^(7/2)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 6*a^(7/2)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + I*a^(7/2)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(7/2)/(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)*(12*I*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 24*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 42*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 42*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 24*I*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 9*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 12*I*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 3))","B",0
329,1,454,0,0.664896," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(i \, a^{\frac{7}{2}} - \frac{6 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{20 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{6 i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{i \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{7}{2}}}{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{10 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{20 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{50 i \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{25 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{100 i \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{100 i \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{25 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{50 i \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{20 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{10 i \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{5 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - 5\right)}}"," ",0,"2*(I*a^(7/2) - 6*I*a^(7/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*I*a^(7/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 20*I*a^(7/2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*I*a^(7/2)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 6*I*a^(7/2)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + I*a^(7/2)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(7/2)/(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)*(-10*I*sin(d*x + c)/(cos(d*x + c) + 1) - 20*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 50*I*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 25*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 100*I*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 100*I*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 25*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 50*I*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 20*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 10*I*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 5*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 5))","B",0
330,1,1250,0,1.056126," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{{\left(-140 i \, \sqrt{2} a^{3} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 140 \, \sqrt{2} a^{3} \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(-60 i \, \sqrt{2} a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} - 60 i \, \sqrt{2} a^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - 120 i \, \sqrt{2} a^{3} \cos\left(2 \, d x + 2 \, c\right) - 60 i \, \sqrt{2} a^{3}\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 60 \, {\left(\sqrt{2} a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{3} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{3}\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{3}{4}} \sqrt{a} + {\left(-420 i \, \sqrt{2} a^{3} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 420 \, \sqrt{2} a^{3} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-84 i \, \sqrt{2} a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} - 84 i \, \sqrt{2} a^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} - 168 i \, \sqrt{2} a^{3} \cos\left(2 \, d x + 2 \, c\right) - 84 i \, \sqrt{2} a^{3}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 84 \, {\left(\sqrt{2} a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{2} a^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \sqrt{2} a^{3} \cos\left(2 \, d x + 2 \, c\right) + \sqrt{2} a^{3}\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)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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} - {\left(210 \, \sqrt{2} a^{3} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{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) - 210 \, \sqrt{2} a^{3} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{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) - 105 i \, \sqrt{2} a^{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) + 105 i \, \sqrt{2} a^{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)\right)} \sqrt{a}}{6720 \, d}"," ",0,"1/6720*((-140*I*sqrt(2)*a^3*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 140*sqrt(2)*a^3*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (-60*I*sqrt(2)*a^3*cos(2*d*x + 2*c)^2 - 60*I*sqrt(2)*a^3*sin(2*d*x + 2*c)^2 - 120*I*sqrt(2)*a^3*cos(2*d*x + 2*c) - 60*I*sqrt(2)*a^3)*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 60*(sqrt(2)*a^3*cos(2*d*x + 2*c)^2 + sqrt(2)*a^3*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^3*cos(2*d*x + 2*c) + sqrt(2)*a^3)*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(3/4)*sqrt(a) + (-420*I*sqrt(2)*a^3*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 420*sqrt(2)*a^3*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + (-84*I*sqrt(2)*a^3*cos(2*d*x + 2*c)^2 - 84*I*sqrt(2)*a^3*sin(2*d*x + 2*c)^2 - 168*I*sqrt(2)*a^3*cos(2*d*x + 2*c) - 84*I*sqrt(2)*a^3)*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 84*(sqrt(2)*a^3*cos(2*d*x + 2*c)^2 + sqrt(2)*a^3*sin(2*d*x + 2*c)^2 + 2*sqrt(2)*a^3*cos(2*d*x + 2*c) + sqrt(2)*a^3)*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*(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) - (210*sqrt(2)*a^3*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*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) - 210*sqrt(2)*a^3*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*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) - 105*I*sqrt(2)*a^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) + 105*I*sqrt(2)*a^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))*sqrt(a))/d","B",0
331,-1,0,0,0.000000," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,1,297,0,0.766333," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(15015 \, \sqrt{i \, a \tan\left(d x + c\right) + a} - \frac{3003 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}\right)}}{a^{2}} + \frac{143 \, {\left(35 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 180 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 378 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4}\right)}}{a^{4}} - \frac{5 \, {\left(231 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 1638 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{6}\right)}}{a^{6}}\right)}}{15015 \, a d}"," ",0,"-2/15015*I*(15015*sqrt(I*a*tan(d*x + c) + a) - 3003*(3*(I*a*tan(d*x + c) + a)^(5/2) - 10*(I*a*tan(d*x + c) + a)^(3/2)*a + 15*sqrt(I*a*tan(d*x + c) + a)*a^2)/a^2 + 143*(35*(I*a*tan(d*x + c) + a)^(9/2) - 180*(I*a*tan(d*x + c) + a)^(7/2)*a + 378*(I*a*tan(d*x + c) + a)^(5/2)*a^2 - 420*(I*a*tan(d*x + c) + a)^(3/2)*a^3 + 315*sqrt(I*a*tan(d*x + c) + a)*a^4)/a^4 - 5*(231*(I*a*tan(d*x + c) + a)^(13/2) - 1638*(I*a*tan(d*x + c) + a)^(11/2)*a + 5005*(I*a*tan(d*x + c) + a)^(9/2)*a^2 - 8580*(I*a*tan(d*x + c) + a)^(7/2)*a^3 + 9009*(I*a*tan(d*x + c) + a)^(5/2)*a^4 - 6006*(I*a*tan(d*x + c) + a)^(3/2)*a^5 + 3003*sqrt(I*a*tan(d*x + c) + a)*a^6)/a^6)/(a*d)","B",0
334,1,169,0,0.449699," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(315 \, \sqrt{i \, a \tan\left(d x + c\right) + a} - \frac{42 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}\right)}}{a^{2}} + \frac{35 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 180 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 378 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4}}{a^{4}}\right)}}{315 \, a d}"," ",0,"-2/315*I*(315*sqrt(I*a*tan(d*x + c) + a) - 42*(3*(I*a*tan(d*x + c) + a)^(5/2) - 10*(I*a*tan(d*x + c) + a)^(3/2)*a + 15*sqrt(I*a*tan(d*x + c) + a)*a^2)/a^2 + (35*(I*a*tan(d*x + c) + a)^(9/2) - 180*(I*a*tan(d*x + c) + a)^(7/2)*a + 378*(I*a*tan(d*x + c) + a)^(5/2)*a^2 - 420*(I*a*tan(d*x + c) + a)^(3/2)*a^3 + 315*sqrt(I*a*tan(d*x + c) + a)*a^4)/a^4)/(a*d)","B",0
335,1,79,0,0.324364," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(15 \, \sqrt{i \, a \tan\left(d x + c\right) + a} - \frac{3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}}{a^{2}}\right)}}{15 \, a d}"," ",0,"-2/15*I*(15*sqrt(I*a*tan(d*x + c) + a) - (3*(I*a*tan(d*x + c) + a)^(5/2) - 10*(I*a*tan(d*x + c) + a)^(3/2)*a + 15*sqrt(I*a*tan(d*x + c) + a)*a^2)/a^2)/(a*d)","A",0
336,1,21,0,0.539194," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, \sqrt{i \, a \tan\left(d x + c\right) + a}}{a d}"," ",0,"-2*I*sqrt(I*a*tan(d*x + c) + a)/(a*d)","A",0
337,1,138,0,0.620466," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(15 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a - 20 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} - 8 \, a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a}\right)}}{96 \, a d}"," ",0,"1/96*I*(15*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(15*(I*a*tan(d*x + c) + a)^2*a - 20*(I*a*tan(d*x + c) + a)*a^2 - 8*a^3)/((I*a*tan(d*x + c) + a)^(5/2) - 2*(I*a*tan(d*x + c) + a)^(3/2)*a))/(a*d)","A",0
338,1,192,0,0.842659," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(315 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(315 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a - 1050 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{2} + 672 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{3} + 192 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} + 128 \, a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2}}\right)}}{2560 \, a d}"," ",0,"1/2560*I*(315*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(315*(I*a*tan(d*x + c) + a)^4*a - 1050*(I*a*tan(d*x + c) + a)^3*a^2 + 672*(I*a*tan(d*x + c) + a)^2*a^3 + 192*(I*a*tan(d*x + c) + a)*a^4 + 128*a^5)/((I*a*tan(d*x + c) + a)^(9/2) - 4*(I*a*tan(d*x + c) + a)^(7/2)*a + 4*(I*a*tan(d*x + c) + a)^(5/2)*a^2))/(a*d)","A",0
339,1,246,0,0.559830," ","integrate(cos(d*x+c)^6/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(45045 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(45045 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{6} a - 240240 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} a^{2} + 396396 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a^{3} - 164736 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{4} - 36608 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{5} - 19968 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{6} - 15360 \, a^{7}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a + 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{2} - 8 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{3}}\right)}}{430080 \, a d}"," ",0,"1/430080*I*(45045*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(45045*(I*a*tan(d*x + c) + a)^6*a - 240240*(I*a*tan(d*x + c) + a)^5*a^2 + 396396*(I*a*tan(d*x + c) + a)^4*a^3 - 164736*(I*a*tan(d*x + c) + a)^3*a^4 - 36608*(I*a*tan(d*x + c) + a)^2*a^5 - 19968*(I*a*tan(d*x + c) + a)*a^6 - 15360*a^7)/((I*a*tan(d*x + c) + a)^(13/2) - 6*(I*a*tan(d*x + c) + a)^(11/2)*a + 12*(I*a*tan(d*x + c) + a)^(9/2)*a^2 - 8*(I*a*tan(d*x + c) + a)^(7/2)*a^3))/(a*d)","A",0
340,1,608,0,0.897275," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-1241 i \, \sqrt{a} - \frac{5194 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6090 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2490 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14430 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{33618 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{13442 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{18590 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{18590 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{13442 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{33618 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{14430 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{2490 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{6090 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{5194 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{1241 i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1}}{6435 \, {\left(a - \frac{8 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{56 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{56 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{8 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}\right)} d \sqrt{-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}"," ",0,"-2/6435*(-1241*I*sqrt(a) - 5194*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) + 6090*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2490*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14430*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 33618*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 13442*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 18590*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 18590*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 13442*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 33618*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 14430*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 2490*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 6090*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 5194*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 1241*I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/((a - 8*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 56*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 56*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 8*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16)*d*sqrt(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
341,1,474,0,0.791328," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-151 i \, \sqrt{a} - \frac{542 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{484 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{22 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{627 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{1452 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1452 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{627 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{22 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{484 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{542 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{151 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1}}{693 \, {\left(a - \frac{6 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{20 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{6 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d \sqrt{-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}"," ",0,"-2/693*(-151*I*sqrt(a) - 542*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) + 484*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 22*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 627*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1452*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1452*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 627*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 22*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 484*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 542*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 151*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/((a - 6*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 20*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 6*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d*sqrt(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
342,1,340,0,0.562872," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-9 i \, \sqrt{a} - \frac{26 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{14 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{26 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1}}{35 \, {\left(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}}\right)} d \sqrt{-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}"," ",0,"-2/35*(-9*I*sqrt(a) - 26*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) + 14*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 14*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 26*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/((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)*d*sqrt(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
343,1,206,0,0.686994," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-i \, \sqrt{a} - \frac{2 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1}}{3 \, {\left(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}}\right)} d \sqrt{-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}"," ",0,"-2/3*(-I*sqrt(a) - 2*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/((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)*d*sqrt(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
344,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
345,1,837,0,1.270460," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(4 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 8 i \, \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) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 2 \, \sqrt{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} - {\left(6 \, \sqrt{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) - 6 \, \sqrt{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) - 3 i \, \sqrt{2} \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 i \, \sqrt{2} \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)\right)} \sqrt{a}}{32 \, a d}"," ",0,"1/32*((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*I*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c) - 8*I*sqrt(2))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 4*(sqrt(2)*cos(2*d*x + 2*c) - I*sqrt(2)*sin(2*d*x + 2*c) - 2*sqrt(2))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) - (6*sqrt(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) - 6*sqrt(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) - 3*I*sqrt(2)*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*I*sqrt(2)*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))*sqrt(a))/(a*d)","B",0
346,1,1939,0,1.451380," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\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(12 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 32 i \, \sqrt{2}\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) - 4 \, {\left(3 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 3 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sqrt{2}\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} + {\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(12 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 144 i \, \sqrt{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) + 12 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 144 \, \sqrt{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) - 288 i \, \sqrt{2}\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(12 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 144 \, \sqrt{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) - 12 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 144 i \, \sqrt{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) - 288 \, \sqrt{2}\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} - {\left(210 \, \sqrt{2} \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) - 210 \, \sqrt{2} \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) - 105 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\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} \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)^{2} + \sqrt{\cos\left(\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} \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)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \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) + 105 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\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} \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)^{2} + \sqrt{\cos\left(\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} \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)^{2} - 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \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}}{1536 \, a d}"," ",0,"1/1536*((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)*((12*I*sqrt(2)*cos(4*d*x + 4*c) + 12*sqrt(2)*sin(4*d*x + 4*c) - 32*I*sqrt(2))*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)) - 4*(3*sqrt(2)*cos(4*d*x + 4*c) - 3*I*sqrt(2)*sin(4*d*x + 4*c) - 8*sqrt(2))*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) + (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)*((12*I*sqrt(2)*cos(4*d*x + 4*c) + 144*I*sqrt(2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 12*sqrt(2)*sin(4*d*x + 4*c) + 144*sqrt(2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 288*I*sqrt(2))*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)) - (12*sqrt(2)*cos(4*d*x + 4*c) + 144*sqrt(2)*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 12*I*sqrt(2)*sin(4*d*x + 4*c) - 144*I*sqrt(2)*sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) - 288*sqrt(2))*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) - (210*sqrt(2)*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) - 210*sqrt(2)*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) - 105*I*sqrt(2)*log(sqrt(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)*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))^2 + sqrt(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)*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))^2 + 2*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*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) + 105*I*sqrt(2)*log(sqrt(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)*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))^2 + sqrt(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)*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))^2 - 2*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) + 1))*sqrt(a))/(a*d)","B",0
347,1,76,0,0.366916," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 770 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 1980 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2} - 1848 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{3}\right)}}{1155 \, a^{7} d}"," ",0,"2/1155*I*(105*(I*a*tan(d*x + c) + a)^(11/2) - 770*(I*a*tan(d*x + c) + a)^(9/2)*a + 1980*(I*a*tan(d*x + c) + a)^(7/2)*a^2 - 1848*(I*a*tan(d*x + c) + a)^(5/2)*a^3)/(a^7*d)","A",0
348,1,58,0,0.414647," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 84 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 140 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2}\right)}}{105 \, a^{5} d}"," ",0,"-2/105*I*(15*(I*a*tan(d*x + c) + a)^(7/2) - 84*(I*a*tan(d*x + c) + a)^(5/2)*a + 140*(I*a*tan(d*x + c) + a)^(3/2)*a^2)/(a^5*d)","A",0
349,1,38,0,0.410546," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 6 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a\right)}}{3 \, a^{3} d}"," ",0,"2/3*I*((I*a*tan(d*x + c) + a)^(3/2) - 6*sqrt(I*a*tan(d*x + c) + a)*a)/(a^3*d)","A",0
350,1,21,0,0.452374," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 i}{\sqrt{i \, a \tan\left(d x + c\right) + a} a d}"," ",0,"2*I/(sqrt(I*a*tan(d*x + c) + a)*a*d)","A",0
351,1,153,0,0.504749," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{105 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} - 140 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a - 56 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} - 48 \, a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a}\right)}}{960 \, a d}"," ",0,"1/960*I*(105*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) + 4*(105*(I*a*tan(d*x + c) + a)^3 - 140*(I*a*tan(d*x + c) + a)^2*a - 56*(I*a*tan(d*x + c) + a)*a^2 - 48*a^3)/((I*a*tan(d*x + c) + a)^(7/2) - 2*(I*a*tan(d*x + c) + a)^(5/2)*a))/(a*d)","A",0
352,1,207,0,0.551000," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{3465 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(3465 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} - 11550 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a + 7392 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{2} + 2112 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{3} + 1408 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} + 1280 \, a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2}}\right)}}{35840 \, a d}"," ",0,"1/35840*I*(3465*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) + 4*(3465*(I*a*tan(d*x + c) + a)^5 - 11550*(I*a*tan(d*x + c) + a)^4*a + 7392*(I*a*tan(d*x + c) + a)^3*a^2 + 2112*(I*a*tan(d*x + c) + a)^2*a^3 + 1408*(I*a*tan(d*x + c) + a)*a^4 + 1280*a^5)/((I*a*tan(d*x + c) + a)^(11/2) - 4*(I*a*tan(d*x + c) + a)^(9/2)*a + 4*(I*a*tan(d*x + c) + a)^(7/2)*a^2))/(a*d)","A",0
353,1,261,0,0.813881," ","integrate(cos(d*x+c)^6/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{45045 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(45045 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{7} - 240240 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{6} a + 396396 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} a^{2} - 164736 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a^{3} - 36608 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{4} - 19968 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{5} - 15360 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{6} - 14336 \, a^{7}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{15}{2}} - 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} a + 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{2} - 8 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{3}}\right)}}{516096 \, a d}"," ",0,"1/516096*I*(45045*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) + 4*(45045*(I*a*tan(d*x + c) + a)^7 - 240240*(I*a*tan(d*x + c) + a)^6*a + 396396*(I*a*tan(d*x + c) + a)^5*a^2 - 164736*(I*a*tan(d*x + c) + a)^4*a^3 - 36608*(I*a*tan(d*x + c) + a)^3*a^4 - 19968*(I*a*tan(d*x + c) + a)^2*a^5 - 15360*(I*a*tan(d*x + c) + a)*a^6 - 14336*a^7)/((I*a*tan(d*x + c) + a)^(15/2) - 6*(I*a*tan(d*x + c) + a)^(13/2)*a + 12*(I*a*tan(d*x + c) + a)^(11/2)*a^2 - 8*(I*a*tan(d*x + c) + a)^(9/2)*a^3))/(a*d)","A",0
354,1,764,0,1.117404," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-1767 i \, \sqrt{a} - \frac{6854 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2088 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{16438 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5661 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{56984 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{13328 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{129336 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{7514 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{156468 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{156468 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{7514 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{129336 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{13328 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{56984 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{5661 i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{16438 \, \sqrt{a} \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{2088 i \, \sqrt{a} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} - \frac{6854 \, \sqrt{a} \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} + \frac{1767 i \, \sqrt{a} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}}\right)} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}^{\frac{3}{2}}}{12155 \, {\left(a^{2} - \frac{10 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{45 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{120 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{210 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{252 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{210 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{120 \, a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{45 \, a^{2} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{10 \, a^{2} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{a^{2} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}"," ",0,"-2/12155*(-1767*I*sqrt(a) - 6854*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) + 2088*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 16438*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5661*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 56984*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 13328*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 129336*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 7514*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 156468*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 156468*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 7514*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 129336*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 13328*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 56984*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 5661*I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 16438*sqrt(a)*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 2088*I*sqrt(a)*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 - 6854*sqrt(a)*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 + 1767*I*sqrt(a)*sin(d*x + c)^20/(cos(d*x + c) + 1)^20)*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(sin(d*x + c)/(cos(d*x + c) + 1) - 1)^(3/2)/((a^2 - 10*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 45*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 120*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 210*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 252*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 210*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 120*a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 45*a^2*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 10*a^2*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + a^2*sin(d*x + c)^20/(cos(d*x + c) + 1)^20)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2))","B",0
355,1,626,0,1.131310," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-203 i \, \sqrt{a} - \frac{678 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1802 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{26 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3614 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{858 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6578 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{6578 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{858 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{3614 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{26 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{1802 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{2 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{678 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{203 i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}\right)} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}^{\frac{3}{2}}}{1287 \, {\left(a^{2} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{56 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{56 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a^{2} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}"," ",0,"-2/1287*(-203*I*sqrt(a) - 678*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1802*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 26*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3614*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 858*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6578*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 6578*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 858*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 3614*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 26*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 1802*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 2*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 678*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 203*I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16)*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(sin(d*x + c)/(cos(d*x + c) + 1) - 1)^(3/2)/((a^2 - 8*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 56*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 56*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 8*a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a^2*sin(d*x + c)^16/(cos(d*x + c) + 1)^16)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2))","B",0
356,1,488,0,0.866856," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-11 i \, \sqrt{a} - \frac{30 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{12 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{86 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{9 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{108 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{108 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{9 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{86 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{12 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{30 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{11 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}^{\frac{3}{2}}}{63 \, {\left(a^{2} - \frac{6 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{20 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{6 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}"," ",0,"-2/63*(-11*I*sqrt(a) - 30*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 12*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 86*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 9*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 108*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 108*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 9*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 86*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 12*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 30*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 11*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(sin(d*x + c)/(cos(d*x + c) + 1) - 1)^(3/2)/((a^2 - 6*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 20*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 6*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2))","B",0
357,1,350,0,0.745446," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-i \, \sqrt{a} - \frac{2 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{6 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}^{\frac{3}{2}}}{5 \, {\left(a^{2} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}"," ",0,"-2/5*(-I*sqrt(a) - 2*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 6*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(sin(d*x + c)/(cos(d*x + c) + 1) - 1)^(3/2)/((a^2 - 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2))","B",0
358,1,814,0,1.103773," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(2 \, \sqrt{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) - 2 \, \sqrt{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) - i \, \sqrt{2} \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) + i \, \sqrt{2} \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)\right)} \sqrt{a} - {\left(-4 i \, \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) - 4 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 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}} a^{2} d}"," ",0,"-1/2*((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*(2*sqrt(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) - 2*sqrt(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) - I*sqrt(2)*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) + I*sqrt(2)*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))*sqrt(a) - (-4*I*sqrt(2)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 4*sqrt(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)*a^2*d)","B",0
359,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
360,1,1820,0,1.046017," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(36 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 36 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\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) - 36 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\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} + {\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(-28 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 28 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 32 i \, \sqrt{2}\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) + 4 \, {\left(7 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 7 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sqrt{2}\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} - {\left(30 \, \sqrt{2} \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) - 30 \, \sqrt{2} \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) - 15 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\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} \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)^{2} + \sqrt{\cos\left(\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} \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)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \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) + 15 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\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} \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)^{2} + \sqrt{\cos\left(\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} \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)^{2} - 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, d x + 4 \, c\right), \cos\left(4 \, d x + 4 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \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}}{256 \, a^{2} d}"," ",0,"1/256*((cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(3/4)*((36*I*sqrt(2)*cos(4*d*x + 4*c) + 36*sqrt(2)*sin(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)) - 36*(sqrt(2)*cos(4*d*x + 4*c) - I*sqrt(2)*sin(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) + (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)*((-28*I*sqrt(2)*cos(4*d*x + 4*c) - 28*sqrt(2)*sin(4*d*x + 4*c) - 32*I*sqrt(2))*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)) + 4*(7*sqrt(2)*cos(4*d*x + 4*c) - 7*I*sqrt(2)*sin(4*d*x + 4*c) + 8*sqrt(2))*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) - (30*sqrt(2)*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) - 30*sqrt(2)*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) - 15*I*sqrt(2)*log(sqrt(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)*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))^2 + sqrt(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)*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))^2 + 2*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*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) + 15*I*sqrt(2)*log(sqrt(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)*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))^2 + sqrt(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)*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))^2 - 2*(cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c)))^2 + 2*cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))), cos(1/2*arctan2(sin(4*d*x + 4*c), cos(4*d*x + 4*c))) + 1)) + 1))*sqrt(a))/(a^2*d)","B",0
361,1,2632,0,1.098830," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(32 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 360 i \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 32 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 360 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) - 64 i \, \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) - {\left(32 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 360 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) - 32 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) - 360 i \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) - 64 \, \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(12 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 12 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + {\left(12 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 12 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + {\left(24 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 24 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 12 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 12 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + {\left(-12 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 216 i \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 288 i \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) - 12 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) - 216 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 288 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) - 768 i \, \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) - 12 \, {\left({\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + {\left(12 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 216 \, \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) - 288 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) - 12 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) - 216 i \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 288 i \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 768 \, \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} - {\left(630 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + 1\right) - 630 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) - 1\right) - 315 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + 1\right) + 315 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)^{2} - 2 \, {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + 1\right)\right)} \sqrt{a}}{6144 \, a^{2} d}"," ",0,"1/6144*((cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(3/4)*((32*I*sqrt(2)*cos(6*d*x + 6*c) + 360*I*sqrt(2)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 32*sqrt(2)*sin(6*d*x + 6*c) + 360*sqrt(2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 64*I*sqrt(2))*cos(3/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - (32*sqrt(2)*cos(6*d*x + 6*c) + 360*sqrt(2)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 32*I*sqrt(2)*sin(6*d*x + 6*c) - 360*I*sqrt(2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 64*sqrt(2))*sin(3/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)))*sqrt(a) + (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*(((12*I*sqrt(2)*cos(6*d*x + 6*c) + 12*sqrt(2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (12*I*sqrt(2)*cos(6*d*x + 6*c) + 12*sqrt(2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (24*I*sqrt(2)*cos(6*d*x + 6*c) + 24*sqrt(2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 12*I*sqrt(2)*cos(6*d*x + 6*c) + 12*sqrt(2)*sin(6*d*x + 6*c))*cos(5/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + (-12*I*sqrt(2)*cos(6*d*x + 6*c) - 216*I*sqrt(2)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 288*I*sqrt(2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 12*sqrt(2)*sin(6*d*x + 6*c) - 216*sqrt(2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 288*sqrt(2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 768*I*sqrt(2))*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - 12*((sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*(sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*sin(5/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + (12*sqrt(2)*cos(6*d*x + 6*c) + 216*sqrt(2)*cos(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 288*sqrt(2)*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 12*I*sqrt(2)*sin(6*d*x + 6*c) - 216*I*sqrt(2)*sin(2/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 288*I*sqrt(2)*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 768*sqrt(2))*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)))*sqrt(a) - (630*sqrt(2)*arctan2((cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)), (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 1) - 630*sqrt(2)*arctan2((cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)), (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - 1) - 315*I*sqrt(2)*log(sqrt(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))^2 + sqrt(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))^2 + 2*(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 1) + 315*I*sqrt(2)*log(sqrt(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))^2 + sqrt(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))^2 - 2*(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 1))*sqrt(a))/(a^2*d)","B",0
362,1,94,0,0.366055," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(1155 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 10920 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a + 40040 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{2} - 68640 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{3} + 48048 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{4}\right)}}{15015 \, a^{9} d}"," ",0,"-2/15015*I*(1155*(I*a*tan(d*x + c) + a)^(13/2) - 10920*(I*a*tan(d*x + c) + a)^(11/2)*a + 40040*(I*a*tan(d*x + c) + a)^(9/2)*a^2 - 68640*(I*a*tan(d*x + c) + a)^(7/2)*a^3 + 48048*(I*a*tan(d*x + c) + a)^(5/2)*a^4)/(a^9*d)","A",0
363,1,76,0,0.598174," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(35 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 270 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 756 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 840 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3}\right)}}{315 \, a^{7} d}"," ",0,"2/315*I*(35*(I*a*tan(d*x + c) + a)^(9/2) - 270*(I*a*tan(d*x + c) + a)^(7/2)*a + 756*(I*a*tan(d*x + c) + a)^(5/2)*a^2 - 840*(I*a*tan(d*x + c) + a)^(3/2)*a^3)/(a^7*d)","A",0
364,1,58,0,0.319797," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 20 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 60 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}\right)}}{15 \, a^{5} d}"," ",0,"-2/15*I*(3*(I*a*tan(d*x + c) + a)^(5/2) - 20*(I*a*tan(d*x + c) + a)^(3/2)*a + 60*sqrt(I*a*tan(d*x + c) + a)*a^2)/(a^5*d)","A",0
365,1,44,0,0.448594," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{a^{2}} + \frac{2}{\sqrt{i \, a \tan\left(d x + c\right) + a} a}\right)}}{a d}"," ",0,"2*I*(sqrt(I*a*tan(d*x + c) + a)/a^2 + 2/(sqrt(I*a*tan(d*x + c) + a)*a))/(a*d)","A",0
366,1,21,0,0.558374," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 i}{3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a d}"," ",0,"2/3*I/((I*a*tan(d*x + c) + a)^(3/2)*a*d)","A",0
367,1,175,0,0.661416," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{4 \, {\left(315 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} - 420 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a - 168 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{2} - 144 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{3} - 160 \, a^{4}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2}} + \frac{315 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{3}{2}}}\right)}}{4480 \, a d}"," ",0,"1/4480*I*(4*(315*(I*a*tan(d*x + c) + a)^4 - 420*(I*a*tan(d*x + c) + a)^3*a - 168*(I*a*tan(d*x + c) + a)^2*a^2 - 144*(I*a*tan(d*x + c) + a)*a^3 - 160*a^4)/((I*a*tan(d*x + c) + a)^(9/2)*a - 2*(I*a*tan(d*x + c) + a)^(7/2)*a^2) + 315*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(3/2))/(a*d)","A",0
368,1,229,0,0.563489," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{4 \, {\left(45045 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{6} - 150150 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} a + 96096 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a^{2} + 27456 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{3} + 18304 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{4} + 16640 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{5} + 17920 \, a^{6}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} a - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{2} + 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{3}} + \frac{45045 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{3}{2}}}\right)}}{645120 \, a d}"," ",0,"1/645120*I*(4*(45045*(I*a*tan(d*x + c) + a)^6 - 150150*(I*a*tan(d*x + c) + a)^5*a + 96096*(I*a*tan(d*x + c) + a)^4*a^2 + 27456*(I*a*tan(d*x + c) + a)^3*a^3 + 18304*(I*a*tan(d*x + c) + a)^2*a^4 + 16640*(I*a*tan(d*x + c) + a)*a^5 + 17920*a^6)/((I*a*tan(d*x + c) + a)^(13/2)*a - 4*(I*a*tan(d*x + c) + a)^(11/2)*a^2 + 4*(I*a*tan(d*x + c) + a)^(9/2)*a^3) + 45045*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(3/2))/(a*d)","A",0
369,1,902,0,1.143041," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-2429 i \, \sqrt{a} - \frac{8850 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5122 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{45190 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{12924 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{152478 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{40470 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{397594 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{50065 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{722228 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{19380 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{936700 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{936700 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{19380 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{722228 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{50065 i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{397594 \, \sqrt{a} \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} + \frac{40470 i \, \sqrt{a} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} - \frac{152478 \, \sqrt{a} \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} + \frac{12924 i \, \sqrt{a} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} - \frac{45190 \, \sqrt{a} \sin\left(d x + c\right)^{21}}{{\left(\cos\left(d x + c\right) + 1\right)}^{21}} + \frac{5122 i \, \sqrt{a} \sin\left(d x + c\right)^{22}}{{\left(\cos\left(d x + c\right) + 1\right)}^{22}} - \frac{8850 \, \sqrt{a} \sin\left(d x + c\right)^{23}}{{\left(\cos\left(d x + c\right) + 1\right)}^{23}} + \frac{2429 i \, \sqrt{a} \sin\left(d x + c\right)^{24}}{{\left(\cos\left(d x + c\right) + 1\right)}^{24}}\right)} {\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}}}{20995 \, {\left(a^{3} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{66 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{220 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{495 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{792 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{924 \, a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{792 \, a^{3} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{495 \, a^{3} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{220 \, a^{3} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{66 \, a^{3} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{22}}{{\left(\cos\left(d x + c\right) + 1\right)}^{22}} + \frac{a^{3} \sin\left(d x + c\right)^{24}}{{\left(\cos\left(d x + c\right) + 1\right)}^{24}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}"," ",0,"-2/20995*(-2429*I*sqrt(a) - 8850*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 5122*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 45190*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 12924*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 152478*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 40470*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 397594*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 50065*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 722228*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 19380*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 936700*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 936700*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 19380*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 722228*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 50065*I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 397594*sqrt(a)*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 + 40470*I*sqrt(a)*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 - 152478*sqrt(a)*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 + 12924*I*sqrt(a)*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 - 45190*sqrt(a)*sin(d*x + c)^21/(cos(d*x + c) + 1)^21 + 5122*I*sqrt(a)*sin(d*x + c)^22/(cos(d*x + c) + 1)^22 - 8850*sqrt(a)*sin(d*x + c)^23/(cos(d*x + c) + 1)^23 + 2429*I*sqrt(a)*sin(d*x + c)^24/(cos(d*x + c) + 1)^24)*(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^3 - 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 66*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 220*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 495*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 792*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 924*a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 792*a^3*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 495*a^3*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 220*a^3*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + 66*a^3*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 - 12*a^3*sin(d*x + c)^22/(cos(d*x + c) + 1)^22 + a^3*sin(d*x + c)^24/(cos(d*x + c) + 1)^24)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2))","B",0
370,1,764,0,1.017784," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-263 i \, \sqrt{a} - \frac{830 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{760 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4270 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1085 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{11576 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2000 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{23000 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{2470 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{33540 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{33540 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{2470 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{23000 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{2000 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{11576 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{1085 i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{4270 \, \sqrt{a} \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} + \frac{760 i \, \sqrt{a} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} - \frac{830 \, \sqrt{a} \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} + \frac{263 i \, \sqrt{a} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}}\right)} {\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}}}{2145 \, {\left(a^{3} - \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{45 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{120 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{210 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{252 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{210 \, a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{120 \, a^{3} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{45 \, a^{3} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{10 \, a^{3} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{a^{3} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}"," ",0,"-2/2145*(-263*I*sqrt(a) - 830*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 760*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4270*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1085*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 11576*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2000*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 23000*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 2470*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 33540*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 33540*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 2470*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 23000*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 2000*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 11576*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 1085*I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 4270*sqrt(a)*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 + 760*I*sqrt(a)*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 - 830*sqrt(a)*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 + 263*I*sqrt(a)*sin(d*x + c)^20/(cos(d*x + c) + 1)^20)*(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^3 - 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 45*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 120*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 210*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 252*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 210*a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 120*a^3*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 45*a^3*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 10*a^3*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + a^3*sin(d*x + c)^20/(cos(d*x + c) + 1)^20)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2))","B",0
371,1,626,0,0.920516," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-13 i \, \sqrt{a} - \frac{34 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{46 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{174 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{54 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{394 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{22 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{550 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{550 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{22 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{394 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{54 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{174 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{46 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{34 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{13 i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}\right)} {\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}}}{99 \, {\left(a^{3} - \frac{8 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{56 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{56 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{8 \, a^{3} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a^{3} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}"," ",0,"-2/99*(-13*I*sqrt(a) - 34*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 46*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 174*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 54*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 394*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 22*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 550*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 550*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 22*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 394*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 54*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 174*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 46*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 34*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 13*I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16)*(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^3 - 8*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 56*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 56*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 8*a^3*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a^3*sin(d*x + c)^16/(cos(d*x + c) + 1)^16)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2))","B",0
372,1,488,0,0.995600," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-i \, \sqrt{a} - \frac{2 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{10 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{20 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{20 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{5 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{10 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{4 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{2 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} {\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}}}{7 \, {\left(a^{3} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{20 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}"," ",0,"-2/7*(-I*sqrt(a) - 2*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 10*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 20*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 20*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 5*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 10*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 4*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 2*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*(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^3 - 6*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 20*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 6*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2))","B",0
373,1,1070,0,1.212513," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \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 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 12 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 16 i \, \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) + 4 \, {\left(3 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 3 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left(6 \, {\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({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{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) - 6 \, {\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({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{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(-3 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - 3 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 6 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 3 i \, \sqrt{2}\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) + {\left(3 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 3 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 3 i \, \sqrt{2}\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)\right)} \sqrt{a}}{3 \, {\left(a^{3} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{3} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{3} \cos\left(2 \, d x + 2 \, c\right) + a^{3}\right)} d}"," ",0,"-1/3*((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*I*sqrt(2)*cos(2*d*x + 2*c) - 12*sqrt(2)*sin(2*d*x + 2*c) + 16*I*sqrt(2))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 4*(3*sqrt(2)*cos(2*d*x + 2*c) + 3*I*sqrt(2)*sin(2*d*x + 2*c) + 4*sqrt(2))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + (6*(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((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*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) - 6*(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((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*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) + (-3*I*sqrt(2)*cos(2*d*x + 2*c)^2 - 3*I*sqrt(2)*sin(2*d*x + 2*c)^2 - 6*I*sqrt(2)*cos(2*d*x + 2*c) - 3*I*sqrt(2))*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*I*sqrt(2)*cos(2*d*x + 2*c)^2 + 3*I*sqrt(2)*sin(2*d*x + 2*c)^2 + 6*I*sqrt(2)*cos(2*d*x + 2*c) + 3*I*sqrt(2))*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))*sqrt(a))/((a^3*cos(2*d*x + 2*c)^2 + a^3*sin(2*d*x + 2*c)^2 + 2*a^3*cos(2*d*x + 2*c) + a^3)*d)","B",0
374,1,826,0,0.990583," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(4 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 4 \, \sqrt{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) + 1\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left(2 \, \sqrt{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) - 2 \, \sqrt{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) - i \, \sqrt{2} \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) + i \, \sqrt{2} \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)\right)} \sqrt{a}}{8 \, a^{3} d}"," ",0,"1/8*((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*I*sqrt(2)*cos(2*d*x + 2*c) + 4*sqrt(2)*sin(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 4*(sqrt(2)*cos(2*d*x + 2*c) - I*sqrt(2)*sin(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + (2*sqrt(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) - 2*sqrt(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) - I*sqrt(2)*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) + I*sqrt(2)*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))*sqrt(a))/(a^3*d)","B",0
375,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
376,1,2297,0,1.225913," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left(544 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 544 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) - 544 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(-348 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 348 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + {\left(-348 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 348 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + {\left(-696 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 696 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) - 348 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 348 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + {\left(-228 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 228 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 192 i \, \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + 348 \, {\left({\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + 12 \, {\left(19 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 19 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) - 16 \, \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + {\left(210 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + 1\right) - 210 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) - 1\right) - 105 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + 1\right) + 105 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right)^{2} - 2 \, {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right), \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, d x + 6 \, c\right), \cos\left(6 \, d x + 6 \, c\right)\right)\right) + 1\right)\right) + 1\right)\right)} \sqrt{a}}{3072 \, a^{3} d}"," ",0,"-1/3072*((cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(3/4)*((544*I*sqrt(2)*cos(6*d*x + 6*c) + 544*sqrt(2)*sin(6*d*x + 6*c))*cos(3/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - 544*(sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*sin(3/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)))*sqrt(a) + (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*(((-348*I*sqrt(2)*cos(6*d*x + 6*c) - 348*sqrt(2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (-348*I*sqrt(2)*cos(6*d*x + 6*c) - 348*sqrt(2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (-696*I*sqrt(2)*cos(6*d*x + 6*c) - 696*sqrt(2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) - 348*I*sqrt(2)*cos(6*d*x + 6*c) - 348*sqrt(2)*sin(6*d*x + 6*c))*cos(5/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + (-228*I*sqrt(2)*cos(6*d*x + 6*c) - 228*sqrt(2)*sin(6*d*x + 6*c) + 192*I*sqrt(2))*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 348*((sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + (sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*(sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + sqrt(2)*cos(6*d*x + 6*c) - I*sqrt(2)*sin(6*d*x + 6*c))*sin(5/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 12*(19*sqrt(2)*cos(6*d*x + 6*c) - 19*I*sqrt(2)*sin(6*d*x + 6*c) - 16*sqrt(2))*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)))*sqrt(a) + (210*sqrt(2)*arctan2((cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)), (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 1) - 210*sqrt(2)*arctan2((cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)), (cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) - 1) - 105*I*sqrt(2)*log(sqrt(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))^2 + sqrt(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))^2 + 2*(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 1) + 105*I*sqrt(2)*log(sqrt(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))^2 + sqrt(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)*sin(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1))^2 - 2*(cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c)))^2 + 2*cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))), cos(1/3*arctan2(sin(6*d*x + 6*c), cos(6*d*x + 6*c))) + 1)) + 1))*sqrt(a))/(a^3*d)","B",0
377,1,3783,0,1.381618," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left({\left(60 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 60 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + {\left(60 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 60 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + {\left(120 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 120 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 60 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 60 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + {\left(-220 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 3840 i \, \sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 5184 i \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 220 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right) - 3840 \, \sqrt{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 5184 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 512 i \, \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) - {\left(60 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 60 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 120 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 60 \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 60 i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + {\left(220 \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 3840 \, \sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 5184 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 220 i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right) - 3840 i \, \sqrt{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 5184 i \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 512 \, \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(292 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 292 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + {\left(292 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 292 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + {\left(3168 i \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 3168 i \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 6336 i \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 3168 i \, \sqrt{2}\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + {\left(584 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 584 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 3168 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + \sqrt{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 292 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 292 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + {\left(60 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 1440 i \, \sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 4032 i \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 768 i \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 60 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 1440 \, \sqrt{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 4032 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 768 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 7680 i \, \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) - {\left(292 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 292 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 3168 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 584 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - {\left(3168 i \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 3168 i \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 6336 i \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 3168 i \, \sqrt{2}\right)} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 292 \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 292 i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) - {\left(60 \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 1440 \, \sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 4032 \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 768 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 60 i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right) - 1440 i \, \sqrt{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 4032 i \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 768 i \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 7680 \, \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} - {\left(6930 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + 1\right) - 6930 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) - 1\right) - 3465 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + 1\right) + 3465 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)^{2} - 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + 1\right)\right)} \sqrt{a}}{98304 \, a^{3} d}"," ",0,"1/98304*((cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(3/4)*(((60*I*sqrt(2)*cos(8*d*x + 8*c) + 60*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + (60*I*sqrt(2)*cos(8*d*x + 8*c) + 60*sqrt(2)*sin(8*d*x + 8*c))*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + (120*I*sqrt(2)*cos(8*d*x + 8*c) + 120*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 60*I*sqrt(2)*cos(8*d*x + 8*c) + 60*sqrt(2)*sin(8*d*x + 8*c))*cos(7/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + (-220*I*sqrt(2)*cos(8*d*x + 8*c) - 3840*I*sqrt(2)*cos(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 5184*I*sqrt(2)*cos(1/2*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 220*sqrt(2)*sin(8*d*x + 8*c) - 3840*sqrt(2)*sin(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 5184*sqrt(2)*sin(1/2*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 512*I*sqrt(2))*cos(3/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) - (60*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 60*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 120*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 60*sqrt(2)*cos(8*d*x + 8*c) - 60*I*sqrt(2)*sin(8*d*x + 8*c))*sin(7/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + (220*sqrt(2)*cos(8*d*x + 8*c) + 3840*sqrt(2)*cos(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 5184*sqrt(2)*cos(1/2*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 220*I*sqrt(2)*sin(8*d*x + 8*c) - 3840*I*sqrt(2)*sin(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 5184*I*sqrt(2)*sin(1/2*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 512*sqrt(2))*sin(3/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)))*sqrt(a) + (cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*(((292*I*sqrt(2)*cos(8*d*x + 8*c) + 292*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + (292*I*sqrt(2)*cos(8*d*x + 8*c) + 292*sqrt(2)*sin(8*d*x + 8*c))*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + (3168*I*sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 3168*I*sqrt(2)*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 6336*I*sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 3168*I*sqrt(2))*cos(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + (584*I*sqrt(2)*cos(8*d*x + 8*c) + 584*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 3168*(sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sqrt(2)*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + sqrt(2))*sin(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 292*I*sqrt(2)*cos(8*d*x + 8*c) + 292*sqrt(2)*sin(8*d*x + 8*c))*cos(5/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + (60*I*sqrt(2)*cos(8*d*x + 8*c) + 1440*I*sqrt(2)*cos(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 4032*I*sqrt(2)*cos(1/2*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 768*I*sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 60*sqrt(2)*sin(8*d*x + 8*c) + 1440*sqrt(2)*sin(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 4032*sqrt(2)*sin(1/2*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 768*sqrt(2)*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 7680*I*sqrt(2))*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) - (292*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 292*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 3168*(sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sqrt(2)*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + sqrt(2))*cos(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 584*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - (3168*I*sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 3168*I*sqrt(2)*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 6336*I*sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 3168*I*sqrt(2))*sin(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 292*sqrt(2)*cos(8*d*x + 8*c) - 292*I*sqrt(2)*sin(8*d*x + 8*c))*sin(5/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) - (60*sqrt(2)*cos(8*d*x + 8*c) + 1440*sqrt(2)*cos(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 4032*sqrt(2)*cos(1/2*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 768*sqrt(2)*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 60*I*sqrt(2)*sin(8*d*x + 8*c) - 1440*I*sqrt(2)*sin(3/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 4032*I*sqrt(2)*sin(1/2*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 768*I*sqrt(2)*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 7680*sqrt(2))*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)))*sqrt(a) - (6930*sqrt(2)*arctan2((cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)), (cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + 1) - 6930*sqrt(2)*arctan2((cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)), (cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) - 1) - 3465*I*sqrt(2)*log(sqrt(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1))^2 + sqrt(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1))^2 + 2*(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + 1) + 3465*I*sqrt(2)*log(sqrt(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1))^2 + sqrt(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1))^2 - 2*(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + 1))*sqrt(a))/(a^3*d)","B",0
378,1,94,0,0.737485," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(315 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 3080 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 11880 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2} - 22176 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{3} + 18480 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{4}\right)}}{3465 \, a^{9} d}"," ",0,"-2/3465*I*(315*(I*a*tan(d*x + c) + a)^(11/2) - 3080*(I*a*tan(d*x + c) + a)^(9/2)*a + 11880*(I*a*tan(d*x + c) + a)^(7/2)*a^2 - 22176*(I*a*tan(d*x + c) + a)^(5/2)*a^3 + 18480*(I*a*tan(d*x + c) + a)^(3/2)*a^4)/(a^9*d)","A",0
379,1,76,0,0.473674," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 42 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 140 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} - 280 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{3}\right)}}{35 \, a^{7} d}"," ",0,"2/35*I*(5*(I*a*tan(d*x + c) + a)^(7/2) - 42*(I*a*tan(d*x + c) + a)^(5/2)*a + 140*(I*a*tan(d*x + c) + a)^(3/2)*a^2 - 280*sqrt(I*a*tan(d*x + c) + a)*a^3)/(a^7*d)","A",0
380,1,62,0,0.351751," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(\frac{12}{\sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}} - \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 12 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a}{a^{4}}\right)}}{3 \, a d}"," ",0,"2/3*I*(12/(sqrt(I*a*tan(d*x + c) + a)*a^2) - ((I*a*tan(d*x + c) + a)^(3/2) - 12*sqrt(I*a*tan(d*x + c) + a)*a)/a^4)/(a*d)","A",0
381,1,32,0,0.341276," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(3 i \, a \tan\left(d x + c\right) + a\right)}}{3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} d}"," ",0,"-2/3*I*(3*I*a*tan(d*x + c) + a)/((I*a*tan(d*x + c) + a)^(3/2)*a^3*d)","A",0
382,1,21,0,0.317315," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 i}{5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a d}"," ",0,"2/5*I/((I*a*tan(d*x + c) + a)^(5/2)*a*d)","A",0
383,1,195,0,0.585137," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{4 \, {\left(3465 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} - 4620 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a - 1848 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{2} - 1584 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{3} - 1760 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} - 2240 \, a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{2} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{3}} + \frac{3465 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{5}{2}}}\right)}}{80640 \, a d}"," ",0,"1/80640*I*(4*(3465*(I*a*tan(d*x + c) + a)^5 - 4620*(I*a*tan(d*x + c) + a)^4*a - 1848*(I*a*tan(d*x + c) + a)^3*a^2 - 1584*(I*a*tan(d*x + c) + a)^2*a^3 - 1760*(I*a*tan(d*x + c) + a)*a^4 - 2240*a^5)/((I*a*tan(d*x + c) + a)^(11/2)*a^2 - 2*(I*a*tan(d*x + c) + a)^(9/2)*a^3) + 3465*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(5/2))/(a*d)","A",0
384,1,249,0,1.011661," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{4 \, {\left(45045 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{7} - 150150 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{6} a + 96096 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} a^{2} + 27456 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a^{3} + 18304 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{4} + 16640 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{5} + 17920 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{6} + 21504 \, a^{7}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{15}{2}} a^{2} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{13}{2}} a^{3} + 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{4}} + \frac{45045 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{5}{2}}}\right)}}{946176 \, a d}"," ",0,"1/946176*I*(4*(45045*(I*a*tan(d*x + c) + a)^7 - 150150*(I*a*tan(d*x + c) + a)^6*a + 96096*(I*a*tan(d*x + c) + a)^5*a^2 + 27456*(I*a*tan(d*x + c) + a)^4*a^3 + 18304*(I*a*tan(d*x + c) + a)^3*a^4 + 16640*(I*a*tan(d*x + c) + a)^2*a^5 + 17920*(I*a*tan(d*x + c) + a)*a^6 + 21504*a^7)/((I*a*tan(d*x + c) + a)^(15/2)*a^2 - 4*(I*a*tan(d*x + c) + a)^(13/2)*a^3 + 4*(I*a*tan(d*x + c) + a)^(11/2)*a^4) + 45045*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(5/2))/(a*d)","A",0
385,1,902,0,1.079817," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-331 i \, \sqrt{a} - \frac{998 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1838 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{7522 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{4836 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{27882 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8954 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{68926 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{12631 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{125052 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{10540 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{168980 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{168980 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{10540 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{125052 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{12631 i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{68926 \, \sqrt{a} \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} + \frac{8954 i \, \sqrt{a} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} - \frac{27882 \, \sqrt{a} \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} + \frac{4836 i \, \sqrt{a} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} - \frac{7522 \, \sqrt{a} \sin\left(d x + c\right)^{21}}{{\left(\cos\left(d x + c\right) + 1\right)}^{21}} + \frac{1838 i \, \sqrt{a} \sin\left(d x + c\right)^{22}}{{\left(\cos\left(d x + c\right) + 1\right)}^{22}} - \frac{998 \, \sqrt{a} \sin\left(d x + c\right)^{23}}{{\left(\cos\left(d x + c\right) + 1\right)}^{23}} + \frac{331 i \, \sqrt{a} \sin\left(d x + c\right)^{24}}{{\left(\cos\left(d x + c\right) + 1\right)}^{24}}\right)} {\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}}}{3315 \, {\left(a^{4} - \frac{12 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{66 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{220 \, a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{495 \, a^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{792 \, a^{4} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{924 \, a^{4} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{792 \, a^{4} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{495 \, a^{4} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{220 \, a^{4} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{66 \, a^{4} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} - \frac{12 \, a^{4} \sin\left(d x + c\right)^{22}}{{\left(\cos\left(d x + c\right) + 1\right)}^{22}} + \frac{a^{4} \sin\left(d x + c\right)^{24}}{{\left(\cos\left(d x + c\right) + 1\right)}^{24}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{7}{2}}}"," ",0,"-2/3315*(-331*I*sqrt(a) - 998*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 1838*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 7522*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 4836*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 27882*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8954*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 68926*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 12631*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 125052*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 10540*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 168980*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 168980*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 10540*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 125052*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 12631*I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 68926*sqrt(a)*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 + 8954*I*sqrt(a)*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 - 27882*sqrt(a)*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 + 4836*I*sqrt(a)*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 - 7522*sqrt(a)*sin(d*x + c)^21/(cos(d*x + c) + 1)^21 + 1838*I*sqrt(a)*sin(d*x + c)^22/(cos(d*x + c) + 1)^22 - 998*sqrt(a)*sin(d*x + c)^23/(cos(d*x + c) + 1)^23 + 331*I*sqrt(a)*sin(d*x + c)^24/(cos(d*x + c) + 1)^24)*(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^4 - 12*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 66*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 220*a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 495*a^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 792*a^4*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 924*a^4*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 792*a^4*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 495*a^4*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 220*a^4*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + 66*a^4*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 - 12*a^4*sin(d*x + c)^22/(cos(d*x + c) + 1)^22 + a^4*sin(d*x + c)^24/(cos(d*x + c) + 1)^24)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(7/2))","B",0
386,1,764,0,1.200779," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-15 i \, \sqrt{a} - \frac{38 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{88 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{278 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{213 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{920 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{272 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1848 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{182 i \, \sqrt{a} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2548 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2548 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{182 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{1848 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{272 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{920 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{213 i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{278 \, \sqrt{a} \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} + \frac{88 i \, \sqrt{a} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} - \frac{38 \, \sqrt{a} \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} + \frac{15 i \, \sqrt{a} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}}\right)} {\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}}}{143 \, {\left(a^{4} - \frac{10 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{45 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{120 \, a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{210 \, a^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{252 \, a^{4} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{210 \, a^{4} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{120 \, a^{4} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{45 \, a^{4} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{10 \, a^{4} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{a^{4} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{7}{2}}}"," ",0,"-2/143*(-15*I*sqrt(a) - 38*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 88*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 278*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 213*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 920*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 272*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 1848*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 182*I*sqrt(a)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2548*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2548*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 182*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 1848*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 272*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 920*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 213*I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 278*sqrt(a)*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 + 88*I*sqrt(a)*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 - 38*sqrt(a)*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 + 15*I*sqrt(a)*sin(d*x + c)^20/(cos(d*x + c) + 1)^20)*(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^4 - 10*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 45*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 120*a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 210*a^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 252*a^4*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 210*a^4*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 120*a^4*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 45*a^4*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 10*a^4*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + a^4*sin(d*x + c)^20/(cos(d*x + c) + 1)^20)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(7/2))","B",0
387,1,626,0,1.017449," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-i \, \sqrt{a} - \frac{2 \, \sqrt{a} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 i \, \sqrt{a} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{14 \, \sqrt{a} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 i \, \sqrt{a} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{42 \, \sqrt{a} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 i \, \sqrt{a} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{70 \, \sqrt{a} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{70 \, \sqrt{a} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{14 i \, \sqrt{a} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{42 \, \sqrt{a} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{14 i \, \sqrt{a} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{14 \, \sqrt{a} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{6 i \, \sqrt{a} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{2 \, \sqrt{a} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{i \, \sqrt{a} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}\right)} {\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}}}{9 \, {\left(a^{4} - \frac{8 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{56 \, a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{56 \, a^{4} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a^{4} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{8 \, a^{4} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a^{4} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}\right)} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{7}{2}}}"," ",0,"-2/9*(-I*sqrt(a) - 2*sqrt(a)*sin(d*x + c)/(cos(d*x + c) + 1) - 6*I*sqrt(a)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 14*sqrt(a)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*I*sqrt(a)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 42*sqrt(a)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*I*sqrt(a)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 70*sqrt(a)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 70*sqrt(a)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 14*I*sqrt(a)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 42*sqrt(a)*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 14*I*sqrt(a)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 14*sqrt(a)*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 6*I*sqrt(a)*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 2*sqrt(a)*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + I*sqrt(a)*sin(d*x + c)^16/(cos(d*x + c) + 1)^16)*(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^4 - 8*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 56*a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 56*a^4*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a^4*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 8*a^4*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a^4*sin(d*x + c)^16/(cos(d*x + c) + 1)^16)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(7/2))","B",0
388,1,1166,0,1.089979," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(60 \, {\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({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{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) - 60 \, {\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({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{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(30 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + 30 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + 60 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 30 i \, \sqrt{2}\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) - {\left(-30 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - 30 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - 60 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 30 i \, \sqrt{2}\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)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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} - {\left({\left(-120 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 280 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 120 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 280 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 184 i \, \sqrt{2}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - {\left(120 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 280 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 120 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 280 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 184 \, \sqrt{2}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{15 \, {\left(a^{4} \cos\left(2 \, d x + 2 \, c\right)^{2} + a^{4} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a^{4} \cos\left(2 \, d x + 2 \, c\right) + a^{4}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{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,"-1/15*((60*(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((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*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) - 60*(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((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*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) - (30*I*sqrt(2)*cos(2*d*x + 2*c)^2 + 30*I*sqrt(2)*sin(2*d*x + 2*c)^2 + 60*I*sqrt(2)*cos(2*d*x + 2*c) + 30*I*sqrt(2))*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) - (-30*I*sqrt(2)*cos(2*d*x + 2*c)^2 - 30*I*sqrt(2)*sin(2*d*x + 2*c)^2 - 60*I*sqrt(2)*cos(2*d*x + 2*c) - 30*I*sqrt(2))*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))*(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) - ((-120*I*sqrt(2)*cos(4*d*x + 4*c) - 280*I*sqrt(2)*cos(2*d*x + 2*c) + 120*sqrt(2)*sin(4*d*x + 4*c) + 280*sqrt(2)*sin(2*d*x + 2*c) - 184*I*sqrt(2))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - (120*sqrt(2)*cos(4*d*x + 4*c) + 280*sqrt(2)*cos(2*d*x + 2*c) + 120*I*sqrt(2)*sin(4*d*x + 4*c) + 280*I*sqrt(2)*sin(2*d*x + 2*c) + 184*sqrt(2))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a))/((a^4*cos(2*d*x + 2*c)^2 + a^4*sin(2*d*x + 2*c)^2 + 2*a^4*cos(2*d*x + 2*c) + a^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)*d)","B",0
389,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,1,976,0,1.010668," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, d x + 2 \, 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({\left(4 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left({\left(4 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 4 \, \sqrt{2} \sin\left(4 \, d x + 4 \, 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) - 4 \, {\left(\sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left(2 \, \sqrt{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) - 2 \, \sqrt{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) - i \, \sqrt{2} \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) + i \, \sqrt{2} \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)\right)} \sqrt{a}}{64 \, a^{4} d}"," ",0,"1/64*((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*I*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*sin(4*d*x + 4*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 4*(sqrt(2)*cos(4*d*x + 4*c) - I*sqrt(2)*sin(4*d*x + 4*c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/4)*((4*I*sqrt(2)*cos(4*d*x + 4*c) + 4*sqrt(2)*sin(4*d*x + 4*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 4*(sqrt(2)*cos(4*d*x + 4*c) - I*sqrt(2)*sin(4*d*x + 4*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)))*sqrt(a) + (2*sqrt(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) - 2*sqrt(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) - I*sqrt(2)*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) + I*sqrt(2)*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))*sqrt(a))/(a^4*d)","B",0
391,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(I*a*tan(d*x + c) + a)^(7/2), x)","F",0
392,1,2781,0,0.929627," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left({\left(1300 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 1300 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + {\left(1300 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 1300 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + {\left(2600 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 2600 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1300 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 1300 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + {\left(2572 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) + 2572 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) - {\left(1300 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 1300 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2600 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1300 \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 1300 i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) - 2572 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(-3060 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 3060 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + {\left(-3060 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 3060 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + {\left(-6120 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 6120 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) - 3060 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 3060 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + {\left(-748 i \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 748 \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right) - 512 i \, \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + {\left(3060 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 3060 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 6120 \, {\left(\sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 3060 \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 3060 i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + 4 \, {\left(187 \, \sqrt{2} \cos\left(8 \, d x + 8 \, c\right) - 187 i \, \sqrt{2} \sin\left(8 \, d x + 8 \, c\right) + 128 \, \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} - {\left(630 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + 1\right) - 630 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) - 1\right) - 315 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + 1\right) + 315 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right)^{2} - 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right), \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(8 \, d x + 8 \, c\right), \cos\left(8 \, d x + 8 \, c\right)\right)\right) + 1\right)\right) + 1\right)\right)} \sqrt{a}}{16384 \, a^{4} d}"," ",0,"1/16384*((cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(3/4)*(((1300*I*sqrt(2)*cos(8*d*x + 8*c) + 1300*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + (1300*I*sqrt(2)*cos(8*d*x + 8*c) + 1300*sqrt(2)*sin(8*d*x + 8*c))*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + (2600*I*sqrt(2)*cos(8*d*x + 8*c) + 2600*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1300*I*sqrt(2)*cos(8*d*x + 8*c) + 1300*sqrt(2)*sin(8*d*x + 8*c))*cos(7/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + (2572*I*sqrt(2)*cos(8*d*x + 8*c) + 2572*sqrt(2)*sin(8*d*x + 8*c))*cos(3/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) - (1300*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 1300*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2600*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1300*sqrt(2)*cos(8*d*x + 8*c) - 1300*I*sqrt(2)*sin(8*d*x + 8*c))*sin(7/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) - 2572*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*sin(3/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)))*sqrt(a) + (cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*(((-3060*I*sqrt(2)*cos(8*d*x + 8*c) - 3060*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + (-3060*I*sqrt(2)*cos(8*d*x + 8*c) - 3060*sqrt(2)*sin(8*d*x + 8*c))*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + (-6120*I*sqrt(2)*cos(8*d*x + 8*c) - 6120*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) - 3060*I*sqrt(2)*cos(8*d*x + 8*c) - 3060*sqrt(2)*sin(8*d*x + 8*c))*cos(5/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + (-748*I*sqrt(2)*cos(8*d*x + 8*c) - 748*sqrt(2)*sin(8*d*x + 8*c) - 512*I*sqrt(2))*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + (3060*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 3060*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 6120*(sqrt(2)*cos(8*d*x + 8*c) - I*sqrt(2)*sin(8*d*x + 8*c))*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 3060*sqrt(2)*cos(8*d*x + 8*c) - 3060*I*sqrt(2)*sin(8*d*x + 8*c))*sin(5/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + 4*(187*sqrt(2)*cos(8*d*x + 8*c) - 187*I*sqrt(2)*sin(8*d*x + 8*c) + 128*sqrt(2))*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)))*sqrt(a) - (630*sqrt(2)*arctan2((cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)), (cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + 1) - 630*sqrt(2)*arctan2((cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)), (cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) - 1) - 315*I*sqrt(2)*log(sqrt(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1))^2 + sqrt(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1))^2 + 2*(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + 1) + 315*I*sqrt(2)*log(sqrt(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1))^2 + sqrt(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)*sin(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1))^2 - 2*(cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c)))^2 + 2*cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))), cos(1/4*arctan2(sin(8*d*x + 8*c), cos(8*d*x + 8*c))) + 1)) + 1))*sqrt(a))/(a^4*d)","B",0
393,1,5803,0,1.640294," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left({\left({\left(3160 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 3160 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + {\left(3160 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 3160 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + {\left(33480 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 33480 i \, \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 66960 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 33480 i \, \sqrt{2}\right)} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + {\left(6320 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 6320 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 33480 \, {\left(\sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + \sqrt{2}\right)} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 3160 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 3160 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) + {\left(1960 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 46200 i \, \sqrt{2} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 130560 i \, \sqrt{2} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 24960 i \, \sqrt{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1960 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right) + 46200 \, \sqrt{2} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 130560 \, \sqrt{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 24960 \, \sqrt{2} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 5120 i \, \sqrt{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) - {\left(3160 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 3160 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 33480 \, {\left(\sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 6320 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - {\left(33480 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 33480 i \, \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 66960 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 33480 i \, \sqrt{2}\right)} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 3160 \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - 3160 i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) - {\left(1960 \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 46200 \, \sqrt{2} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 130560 \, \sqrt{2} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 24960 \, \sqrt{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 1960 i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right) - 46200 i \, \sqrt{2} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 130560 i \, \sqrt{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 24960 i \, \sqrt{2} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 5120 \, \sqrt{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} + {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(420 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 420 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{4} + {\left(420 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 420 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{4} + {\left(1680 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 1680 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{3} + {\left(2520 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 2520 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + {\left({\left(840 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 840 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + {\left(1680 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 1680 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 840 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 840 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + {\left(1680 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 1680 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 420 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 420 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) + {\left({\left(-3584 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - 3584 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + {\left(-3584 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - 3584 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + {\left(-61320 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} - 61320 i \, \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} - 122640 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 61320 i \, \sqrt{2}\right)} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + {\left(83520 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 83520 i \, \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 167040 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 83520 i \, \sqrt{2}\right)} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + {\left(-7168 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - 7168 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 61320 \, {\left(\sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + \sqrt{2}\right)} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 83520 \, {\left(\sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + \sqrt{2}\right)} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 3584 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - 3584 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) + {\left(-420 i \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - 12600 i \, \sqrt{2} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 54720 i \, \sqrt{2} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 21120 i \, \sqrt{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 420 \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right) - 12600 \, \sqrt{2} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 54720 \, \sqrt{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 21120 \, \sqrt{2} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 92160 i \, \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) - 420 \, {\left({\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{4} + {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{4} + 4 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{3} + 6 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, {\left({\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) + {\left(3584 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 3584 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 61320 \, {\left(\sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 83520 \, {\left(\sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + \sqrt{2}\right)} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 7168 \, {\left(\sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + {\left(-61320 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} - 61320 i \, \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} - 122640 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 61320 i \, \sqrt{2}\right)} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + {\left(83520 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 83520 i \, \sqrt{2} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 167040 i \, \sqrt{2} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 83520 i \, \sqrt{2}\right)} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 3584 \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) - 3584 i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) + {\left(420 \, \sqrt{2} \cos\left(10 \, d x + 10 \, c\right) + 12600 \, \sqrt{2} \cos\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 54720 \, \sqrt{2} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 21120 \, \sqrt{2} \cos\left(\frac{2}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 420 i \, \sqrt{2} \sin\left(10 \, d x + 10 \, c\right) - 12600 i \, \sqrt{2} \sin\left(\frac{4}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 54720 i \, \sqrt{2} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) - 21120 i \, \sqrt{2} \sin\left(\frac{2}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 92160 \, \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right)\right)} \sqrt{a} - {\left(90090 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) + 1\right) - 90090 \, \sqrt{2} \arctan\left({\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) - 1\right) - 45045 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) + 1\right) + 45045 i \, \sqrt{2} \log\left(\sqrt{\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right)^{2} + \sqrt{\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right)^{2} - 2 \, {\left(\cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right), \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(10 \, d x + 10 \, c\right), \cos\left(10 \, d x + 10 \, c\right)\right)\right) + 1\right)\right) + 1\right)\right)} \sqrt{a}}{1966080 \, a^{4} d}"," ",0,"1/1966080*((cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)^(3/4)*(((3160*I*sqrt(2)*cos(10*d*x + 10*c) + 3160*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + (3160*I*sqrt(2)*cos(10*d*x + 10*c) + 3160*sqrt(2)*sin(10*d*x + 10*c))*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + (33480*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 33480*I*sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 66960*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 33480*I*sqrt(2))*cos(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + (6320*I*sqrt(2)*cos(10*d*x + 10*c) + 6320*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 33480*(sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + sqrt(2))*sin(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 3160*I*sqrt(2)*cos(10*d*x + 10*c) + 3160*sqrt(2)*sin(10*d*x + 10*c))*cos(7/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) + (1960*I*sqrt(2)*cos(10*d*x + 10*c) + 46200*I*sqrt(2)*cos(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 130560*I*sqrt(2)*cos(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 24960*I*sqrt(2)*cos(2/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1960*sqrt(2)*sin(10*d*x + 10*c) + 46200*sqrt(2)*sin(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 130560*sqrt(2)*sin(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 24960*sqrt(2)*sin(2/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 5120*I*sqrt(2))*cos(3/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) - (3160*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 3160*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 33480*(sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + sqrt(2))*cos(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 6320*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - (33480*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 33480*I*sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 66960*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 33480*I*sqrt(2))*sin(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 3160*sqrt(2)*cos(10*d*x + 10*c) - 3160*I*sqrt(2)*sin(10*d*x + 10*c))*sin(7/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) - (1960*sqrt(2)*cos(10*d*x + 10*c) + 46200*sqrt(2)*cos(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 130560*sqrt(2)*cos(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 24960*sqrt(2)*cos(2/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 1960*I*sqrt(2)*sin(10*d*x + 10*c) - 46200*I*sqrt(2)*sin(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 130560*I*sqrt(2)*sin(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 24960*I*sqrt(2)*sin(2/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 5120*sqrt(2))*sin(3/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)))*sqrt(a) + (cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)^(1/4)*(((420*I*sqrt(2)*cos(10*d*x + 10*c) + 420*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^4 + (420*I*sqrt(2)*cos(10*d*x + 10*c) + 420*sqrt(2)*sin(10*d*x + 10*c))*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^4 + (1680*I*sqrt(2)*cos(10*d*x + 10*c) + 1680*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^3 + (2520*I*sqrt(2)*cos(10*d*x + 10*c) + 2520*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + ((840*I*sqrt(2)*cos(10*d*x + 10*c) + 840*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + (1680*I*sqrt(2)*cos(10*d*x + 10*c) + 1680*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 840*I*sqrt(2)*cos(10*d*x + 10*c) + 840*sqrt(2)*sin(10*d*x + 10*c))*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + (1680*I*sqrt(2)*cos(10*d*x + 10*c) + 1680*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 420*I*sqrt(2)*cos(10*d*x + 10*c) + 420*sqrt(2)*sin(10*d*x + 10*c))*cos(9/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) + ((-3584*I*sqrt(2)*cos(10*d*x + 10*c) - 3584*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + (-3584*I*sqrt(2)*cos(10*d*x + 10*c) - 3584*sqrt(2)*sin(10*d*x + 10*c))*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + (-61320*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 - 61320*I*sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 - 122640*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 61320*I*sqrt(2))*cos(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + (83520*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 83520*I*sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 167040*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 83520*I*sqrt(2))*cos(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + (-7168*I*sqrt(2)*cos(10*d*x + 10*c) - 7168*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 61320*(sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + sqrt(2))*sin(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 83520*(sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + sqrt(2))*sin(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 3584*I*sqrt(2)*cos(10*d*x + 10*c) - 3584*sqrt(2)*sin(10*d*x + 10*c))*cos(5/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) + (-420*I*sqrt(2)*cos(10*d*x + 10*c) - 12600*I*sqrt(2)*cos(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 54720*I*sqrt(2)*cos(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 21120*I*sqrt(2)*cos(2/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 420*sqrt(2)*sin(10*d*x + 10*c) - 12600*sqrt(2)*sin(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 54720*sqrt(2)*sin(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 21120*sqrt(2)*sin(2/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 92160*I*sqrt(2))*cos(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) - 420*((sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^4 + (sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^4 + 4*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^3 + 6*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*((sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 4*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*sin(9/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) + (3584*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 3584*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 61320*(sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + sqrt(2))*cos(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 83520*(sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + sqrt(2))*cos(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 7168*(sqrt(2)*cos(10*d*x + 10*c) - I*sqrt(2)*sin(10*d*x + 10*c))*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + (-61320*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 - 61320*I*sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 - 122640*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 61320*I*sqrt(2))*sin(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + (83520*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 83520*I*sqrt(2)*sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 167040*I*sqrt(2)*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 83520*I*sqrt(2))*sin(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 3584*sqrt(2)*cos(10*d*x + 10*c) - 3584*I*sqrt(2)*sin(10*d*x + 10*c))*sin(5/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) + (420*sqrt(2)*cos(10*d*x + 10*c) + 12600*sqrt(2)*cos(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 54720*sqrt(2)*cos(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 21120*sqrt(2)*cos(2/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 420*I*sqrt(2)*sin(10*d*x + 10*c) - 12600*I*sqrt(2)*sin(4/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 54720*I*sqrt(2)*sin(3/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) - 21120*I*sqrt(2)*sin(2/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 92160*sqrt(2))*sin(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)))*sqrt(a) - (90090*sqrt(2)*arctan2((cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)), (cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) + 1) - 90090*sqrt(2)*arctan2((cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)^(1/4)*sin(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)), (cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) - 1) - 45045*I*sqrt(2)*log(sqrt(cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)*cos(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1))^2 + sqrt(cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)*sin(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1))^2 + 2*(cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) + 1) + 45045*I*sqrt(2)*log(sqrt(cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)*cos(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1))^2 + sqrt(cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)*sin(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1))^2 - 2*(cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c)))^2 + 2*cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)^(1/4)*cos(1/2*arctan2(sin(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))), cos(1/5*arctan2(sin(10*d*x + 10*c), cos(10*d*x + 10*c))) + 1)) + 1))*sqrt(a))/(a^4*d)","B",0
394,1,1875,0,1.209044," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(16 \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 16 i \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 16 i \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 16 i \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 16 i \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(16 i \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) - 16 \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 16 i \, \sqrt{2} e\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(-16 i \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) - 16 i \, \sqrt{2} e\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 128 \, e \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + {\left(8 \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 8 i \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 8 \, \sqrt{2} e\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(8 \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 8 i \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 8 \, \sqrt{2} e\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(8 i \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) - 8 \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 8 i \, \sqrt{2} e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-8 i \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 8 \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) - 8 i \, \sqrt{2} e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(8 i \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) - 8 \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) + 8 i \, \sqrt{2} e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-8 i \, \sqrt{2} e \cos\left(2 \, d x + 2 \, c\right) + 8 \, \sqrt{2} e \sin\left(2 \, d x + 2 \, c\right) - 8 i \, \sqrt{2} e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 128 i \, e \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{d {\left(-64 i \, \cos\left(2 \, d x + 2 \, c\right) + 64 \, \sin\left(2 \, d x + 2 \, c\right) - 64 i\right)}}"," ",0,"-((16*sqrt(2)*e*cos(2*d*x + 2*c) + 16*I*sqrt(2)*e*sin(2*d*x + 2*c) + 16*sqrt(2)*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (16*sqrt(2)*e*cos(2*d*x + 2*c) + 16*I*sqrt(2)*e*sin(2*d*x + 2*c) + 16*sqrt(2)*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (16*sqrt(2)*e*cos(2*d*x + 2*c) + 16*I*sqrt(2)*e*sin(2*d*x + 2*c) + 16*sqrt(2)*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (16*sqrt(2)*e*cos(2*d*x + 2*c) + 16*I*sqrt(2)*e*sin(2*d*x + 2*c) + 16*sqrt(2)*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (16*I*sqrt(2)*e*cos(2*d*x + 2*c) - 16*sqrt(2)*e*sin(2*d*x + 2*c) + 16*I*sqrt(2)*e)*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) + (-16*I*sqrt(2)*e*cos(2*d*x + 2*c) + 16*sqrt(2)*e*sin(2*d*x + 2*c) - 16*I*sqrt(2)*e)*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) - 128*e*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + (8*sqrt(2)*e*cos(2*d*x + 2*c) + 8*I*sqrt(2)*e*sin(2*d*x + 2*c) + 8*sqrt(2)*e)*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (8*sqrt(2)*e*cos(2*d*x + 2*c) + 8*I*sqrt(2)*e*sin(2*d*x + 2*c) + 8*sqrt(2)*e)*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (8*I*sqrt(2)*e*cos(2*d*x + 2*c) - 8*sqrt(2)*e*sin(2*d*x + 2*c) + 8*I*sqrt(2)*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-8*I*sqrt(2)*e*cos(2*d*x + 2*c) + 8*sqrt(2)*e*sin(2*d*x + 2*c) - 8*I*sqrt(2)*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (8*I*sqrt(2)*e*cos(2*d*x + 2*c) - 8*sqrt(2)*e*sin(2*d*x + 2*c) + 8*I*sqrt(2)*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-8*I*sqrt(2)*e*cos(2*d*x + 2*c) + 8*sqrt(2)*e*sin(2*d*x + 2*c) - 8*I*sqrt(2)*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 128*I*e*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)*sqrt(e)/(d*(-64*I*cos(2*d*x + 2*c) + 64*sin(2*d*x + 2*c) - 64*I))","B",0
395,1,1400,0,0.843545," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(-2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \arctan\left(\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 2 \, \sqrt{2} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + i \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - i \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right)\right)} \sqrt{a} \sqrt{e}}{4 \, d}"," ",0,"1/4*(-2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*arctan2(sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 2*sqrt(2)*arctan2(-sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), -sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + I*sqrt(2)*log(2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - I*sqrt(2)*log(-2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + sqrt(2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - sqrt(2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + sqrt(2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - sqrt(2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2))*sqrt(a)*sqrt(e)/d","B",0
396,1,76,0,0.490653," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, \sqrt{a} \sqrt{-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}{d \sqrt{e} \sqrt{-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}"," ",0,"-2*I*sqrt(a)*sqrt(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(d*sqrt(e)*sqrt(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
397,1,54,0,0.924614," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{a} {\left(-i \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 i \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{3 \, d e^{\frac{3}{2}}}"," ",0,"1/3*sqrt(a)*(-I*cos(3/2*d*x + 3/2*c) + 3*I*cos(1/2*d*x + 1/2*c) + sin(3/2*d*x + 3/2*c) + 3*sin(1/2*d*x + 1/2*c))/(d*e^(3/2))","A",0
398,1,130,0,0.718732," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{a} {\left(5 i \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 i \, \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 30 i \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 5 \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)}}{30 \, d e^{\frac{5}{2}}}"," ",0,"1/30*sqrt(a)*(5*I*cos(3/2*d*x + 3/2*c) - 3*I*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 30*I*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*sin(3/2*d*x + 3/2*c) + 3*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 30*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))/(d*e^(5/2))","A",0
399,1,178,0,0.876513," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{\sqrt{a} {\left(7 i \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 i \, \cos\left(\frac{7}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 35 i \, \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 105 i \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 7 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{7}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 105 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)}}{140 \, d e^{\frac{7}{2}}}"," ",0,"1/140*sqrt(a)*(7*I*cos(5/2*d*x + 5/2*c) - 5*I*cos(7/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 35*I*cos(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 105*I*cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 7*sin(5/2*d*x + 5/2*c) + 5*sin(7/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 35*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 105*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))/(d*e^(7/2))","A",0
400,1,3015,0,1.419881," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(64512 \, a e^{2} \cos\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 55296 \, a e^{2} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 21504 \, a e^{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 64512 i \, a e^{2} \sin\left(\frac{11}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 55296 i \, a e^{2} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 21504 i \, a e^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + {\left(8064 \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 24192 \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 24192 \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 8064 i \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 8064 \, \sqrt{2} a e^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(8064 \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 24192 \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 24192 \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 8064 i \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 8064 \, \sqrt{2} a e^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(8064 \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 24192 \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 24192 \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 8064 i \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 8064 \, \sqrt{2} a e^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(8064 \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 24192 \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 24192 \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 8064 i \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 8064 \, \sqrt{2} a e^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(8064 i \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 24192 i \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) - 8064 \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) - 24192 \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) - 24192 \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 8064 i \, \sqrt{2} a e^{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(-8064 i \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) - 24192 i \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) - 24192 i \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 8064 \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 24192 \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 24192 \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) - 8064 i \, \sqrt{2} a e^{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(4032 \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 12096 \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 12096 \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 4032 i \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 12096 i \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 12096 i \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 4032 \, \sqrt{2} a e^{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(4032 \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 12096 \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 12096 \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 4032 i \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 12096 i \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 12096 i \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 4032 \, \sqrt{2} a e^{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(-4032 i \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) - 12096 i \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) - 12096 i \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 4032 \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 12096 \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 12096 \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) - 4032 i \, \sqrt{2} a e^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(4032 i \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 12096 i \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 12096 i \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) - 4032 \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) - 12096 \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) - 12096 \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 4032 i \, \sqrt{2} a e^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(-4032 i \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) - 12096 i \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) - 12096 i \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) + 4032 \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) + 12096 \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) + 12096 \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) - 4032 i \, \sqrt{2} a e^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(4032 i \, \sqrt{2} a e^{2} \cos\left(6 \, d x + 6 \, c\right) + 12096 i \, \sqrt{2} a e^{2} \cos\left(4 \, d x + 4 \, c\right) + 12096 i \, \sqrt{2} a e^{2} \cos\left(2 \, d x + 2 \, c\right) - 4032 \, \sqrt{2} a e^{2} \sin\left(6 \, d x + 6 \, c\right) - 12096 \, \sqrt{2} a e^{2} \sin\left(4 \, d x + 4 \, c\right) - 12096 \, \sqrt{2} a e^{2} \sin\left(2 \, d x + 2 \, c\right) + 4032 i \, \sqrt{2} a e^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right)\right)} \sqrt{a} \sqrt{e}}{d {\left(-36864 i \, \cos\left(6 \, d x + 6 \, c\right) - 110592 i \, \cos\left(4 \, d x + 4 \, c\right) - 110592 i \, \cos\left(2 \, d x + 2 \, c\right) + 36864 \, \sin\left(6 \, d x + 6 \, c\right) + 110592 \, \sin\left(4 \, d x + 4 \, c\right) + 110592 \, \sin\left(2 \, d x + 2 \, c\right) - 36864 i\right)}}"," ",0,"-(64512*a*e^2*cos(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 55296*a*e^2*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 21504*a*e^2*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 64512*I*a*e^2*sin(11/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 55296*I*a*e^2*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 21504*I*a*e^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + (8064*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 24192*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 24192*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 8064*I*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 24192*I*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 24192*I*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 8064*sqrt(2)*a*e^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (8064*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 24192*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 24192*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 8064*I*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 24192*I*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 24192*I*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 8064*sqrt(2)*a*e^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (8064*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 24192*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 24192*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 8064*I*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 24192*I*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 24192*I*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 8064*sqrt(2)*a*e^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (8064*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 24192*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 24192*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 8064*I*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 24192*I*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 24192*I*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 8064*sqrt(2)*a*e^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (8064*I*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 24192*I*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 24192*I*sqrt(2)*a*e^2*cos(2*d*x + 2*c) - 8064*sqrt(2)*a*e^2*sin(6*d*x + 6*c) - 24192*sqrt(2)*a*e^2*sin(4*d*x + 4*c) - 24192*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 8064*I*sqrt(2)*a*e^2)*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) - (-8064*I*sqrt(2)*a*e^2*cos(6*d*x + 6*c) - 24192*I*sqrt(2)*a*e^2*cos(4*d*x + 4*c) - 24192*I*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 8064*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 24192*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 24192*sqrt(2)*a*e^2*sin(2*d*x + 2*c) - 8064*I*sqrt(2)*a*e^2)*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) - (4032*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 12096*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 12096*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 4032*I*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 12096*I*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 12096*I*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 4032*sqrt(2)*a*e^2)*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (4032*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 12096*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 12096*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 4032*I*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 12096*I*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 12096*I*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 4032*sqrt(2)*a*e^2)*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (-4032*I*sqrt(2)*a*e^2*cos(6*d*x + 6*c) - 12096*I*sqrt(2)*a*e^2*cos(4*d*x + 4*c) - 12096*I*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 4032*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 12096*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 12096*sqrt(2)*a*e^2*sin(2*d*x + 2*c) - 4032*I*sqrt(2)*a*e^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (4032*I*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 12096*I*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 12096*I*sqrt(2)*a*e^2*cos(2*d*x + 2*c) - 4032*sqrt(2)*a*e^2*sin(6*d*x + 6*c) - 12096*sqrt(2)*a*e^2*sin(4*d*x + 4*c) - 12096*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 4032*I*sqrt(2)*a*e^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (-4032*I*sqrt(2)*a*e^2*cos(6*d*x + 6*c) - 12096*I*sqrt(2)*a*e^2*cos(4*d*x + 4*c) - 12096*I*sqrt(2)*a*e^2*cos(2*d*x + 2*c) + 4032*sqrt(2)*a*e^2*sin(6*d*x + 6*c) + 12096*sqrt(2)*a*e^2*sin(4*d*x + 4*c) + 12096*sqrt(2)*a*e^2*sin(2*d*x + 2*c) - 4032*I*sqrt(2)*a*e^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (4032*I*sqrt(2)*a*e^2*cos(6*d*x + 6*c) + 12096*I*sqrt(2)*a*e^2*cos(4*d*x + 4*c) + 12096*I*sqrt(2)*a*e^2*cos(2*d*x + 2*c) - 4032*sqrt(2)*a*e^2*sin(6*d*x + 6*c) - 12096*sqrt(2)*a*e^2*sin(4*d*x + 4*c) - 12096*sqrt(2)*a*e^2*sin(2*d*x + 2*c) + 4032*I*sqrt(2)*a*e^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2))*sqrt(a)*sqrt(e)/(d*(-36864*I*cos(6*d*x + 6*c) - 110592*I*cos(4*d*x + 4*c) - 110592*I*cos(2*d*x + 2*c) + 36864*sin(6*d*x + 6*c) + 110592*sin(4*d*x + 4*c) + 110592*sin(2*d*x + 2*c) - 36864*I))","B",0
401,1,2380,0,1.105739," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\left(4608 \, a e \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2560 \, a e \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 4608 i \, a e \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2560 i \, a e \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(320 \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 640 \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 320 i \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 640 i \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 320 \, \sqrt{2} a e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(320 \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 640 \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 320 i \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 640 i \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 320 \, \sqrt{2} a e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(320 \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 640 \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 320 i \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 640 i \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 320 \, \sqrt{2} a e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(320 \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 640 \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 320 i \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 640 i \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 320 \, \sqrt{2} a e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(320 i \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 640 i \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) - 320 \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) - 640 \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 320 i \, \sqrt{2} a e\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(-320 i \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) - 640 i \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 320 \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 640 \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) - 320 i \, \sqrt{2} a e\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(160 \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 320 \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 160 i \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 320 i \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 160 \, \sqrt{2} a e\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(160 \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 320 \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 160 i \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 320 i \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 160 \, \sqrt{2} a e\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(160 i \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 320 i \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) - 160 \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) - 320 \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 160 i \, \sqrt{2} a e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(-160 i \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) - 320 i \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 160 \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 320 \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) - 160 i \, \sqrt{2} a e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(160 i \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) + 320 i \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) - 160 \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) - 320 \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) + 160 i \, \sqrt{2} a e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(-160 i \, \sqrt{2} a e \cos\left(4 \, d x + 4 \, c\right) - 320 i \, \sqrt{2} a e \cos\left(2 \, d x + 2 \, c\right) + 160 \, \sqrt{2} a e \sin\left(4 \, d x + 4 \, c\right) + 320 \, \sqrt{2} a e \sin\left(2 \, d x + 2 \, c\right) - 160 i \, \sqrt{2} a e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right)\right)} \sqrt{a} \sqrt{e}}{d {\left(-1024 i \, \cos\left(4 \, d x + 4 \, c\right) - 2048 i \, \cos\left(2 \, d x + 2 \, c\right) + 1024 \, \sin\left(4 \, d x + 4 \, c\right) + 2048 \, \sin\left(2 \, d x + 2 \, c\right) - 1024 i\right)}}"," ",0,"(4608*a*e*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2560*a*e*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 4608*I*a*e*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2560*I*a*e*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (320*sqrt(2)*a*e*cos(4*d*x + 4*c) + 640*sqrt(2)*a*e*cos(2*d*x + 2*c) + 320*I*sqrt(2)*a*e*sin(4*d*x + 4*c) + 640*I*sqrt(2)*a*e*sin(2*d*x + 2*c) + 320*sqrt(2)*a*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (320*sqrt(2)*a*e*cos(4*d*x + 4*c) + 640*sqrt(2)*a*e*cos(2*d*x + 2*c) + 320*I*sqrt(2)*a*e*sin(4*d*x + 4*c) + 640*I*sqrt(2)*a*e*sin(2*d*x + 2*c) + 320*sqrt(2)*a*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (320*sqrt(2)*a*e*cos(4*d*x + 4*c) + 640*sqrt(2)*a*e*cos(2*d*x + 2*c) + 320*I*sqrt(2)*a*e*sin(4*d*x + 4*c) + 640*I*sqrt(2)*a*e*sin(2*d*x + 2*c) + 320*sqrt(2)*a*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (320*sqrt(2)*a*e*cos(4*d*x + 4*c) + 640*sqrt(2)*a*e*cos(2*d*x + 2*c) + 320*I*sqrt(2)*a*e*sin(4*d*x + 4*c) + 640*I*sqrt(2)*a*e*sin(2*d*x + 2*c) + 320*sqrt(2)*a*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (320*I*sqrt(2)*a*e*cos(4*d*x + 4*c) + 640*I*sqrt(2)*a*e*cos(2*d*x + 2*c) - 320*sqrt(2)*a*e*sin(4*d*x + 4*c) - 640*sqrt(2)*a*e*sin(2*d*x + 2*c) + 320*I*sqrt(2)*a*e)*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) - (-320*I*sqrt(2)*a*e*cos(4*d*x + 4*c) - 640*I*sqrt(2)*a*e*cos(2*d*x + 2*c) + 320*sqrt(2)*a*e*sin(4*d*x + 4*c) + 640*sqrt(2)*a*e*sin(2*d*x + 2*c) - 320*I*sqrt(2)*a*e)*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) - (160*sqrt(2)*a*e*cos(4*d*x + 4*c) + 320*sqrt(2)*a*e*cos(2*d*x + 2*c) + 160*I*sqrt(2)*a*e*sin(4*d*x + 4*c) + 320*I*sqrt(2)*a*e*sin(2*d*x + 2*c) + 160*sqrt(2)*a*e)*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (160*sqrt(2)*a*e*cos(4*d*x + 4*c) + 320*sqrt(2)*a*e*cos(2*d*x + 2*c) + 160*I*sqrt(2)*a*e*sin(4*d*x + 4*c) + 320*I*sqrt(2)*a*e*sin(2*d*x + 2*c) + 160*sqrt(2)*a*e)*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (160*I*sqrt(2)*a*e*cos(4*d*x + 4*c) + 320*I*sqrt(2)*a*e*cos(2*d*x + 2*c) - 160*sqrt(2)*a*e*sin(4*d*x + 4*c) - 320*sqrt(2)*a*e*sin(2*d*x + 2*c) + 160*I*sqrt(2)*a*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (-160*I*sqrt(2)*a*e*cos(4*d*x + 4*c) - 320*I*sqrt(2)*a*e*cos(2*d*x + 2*c) + 160*sqrt(2)*a*e*sin(4*d*x + 4*c) + 320*sqrt(2)*a*e*sin(2*d*x + 2*c) - 160*I*sqrt(2)*a*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (160*I*sqrt(2)*a*e*cos(4*d*x + 4*c) + 320*I*sqrt(2)*a*e*cos(2*d*x + 2*c) - 160*sqrt(2)*a*e*sin(4*d*x + 4*c) - 320*sqrt(2)*a*e*sin(2*d*x + 2*c) + 160*I*sqrt(2)*a*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (-160*I*sqrt(2)*a*e*cos(4*d*x + 4*c) - 320*I*sqrt(2)*a*e*cos(2*d*x + 2*c) + 160*sqrt(2)*a*e*sin(4*d*x + 4*c) + 320*sqrt(2)*a*e*sin(2*d*x + 2*c) - 160*I*sqrt(2)*a*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2))*sqrt(a)*sqrt(e)/(d*(-1024*I*cos(4*d*x + 4*c) - 2048*I*cos(2*d*x + 2*c) + 1024*sin(4*d*x + 4*c) + 2048*sin(2*d*x + 2*c) - 1024*I))","B",0
402,1,1881,0,1.132608," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(48 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 48 i \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 48 \, \sqrt{2} a\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(48 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 48 i \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 48 \, \sqrt{2} a\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(48 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 48 i \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 48 \, \sqrt{2} a\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(48 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 48 i \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 48 \, \sqrt{2} a\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(48 i \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) - 48 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 48 i \, \sqrt{2} a\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(-48 i \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 48 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) - 48 i \, \sqrt{2} a\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 128 \, a \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(24 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 24 i \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 24 \, \sqrt{2} a\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(24 \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 24 i \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 24 \, \sqrt{2} a\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(-24 i \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 24 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) - 24 i \, \sqrt{2} a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(24 i \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) - 24 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 24 i \, \sqrt{2} a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(-24 i \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) + 24 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) - 24 i \, \sqrt{2} a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(24 i \, \sqrt{2} a \cos\left(2 \, d x + 2 \, c\right) - 24 \, \sqrt{2} a \sin\left(2 \, d x + 2 \, c\right) + 24 i \, \sqrt{2} a\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 128 i \, a \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{d {\left(-64 i \, \cos\left(2 \, d x + 2 \, c\right) + 64 \, \sin\left(2 \, d x + 2 \, c\right) - 64 i\right)}}"," ",0,"-((48*sqrt(2)*a*cos(2*d*x + 2*c) + 48*I*sqrt(2)*a*sin(2*d*x + 2*c) + 48*sqrt(2)*a)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (48*sqrt(2)*a*cos(2*d*x + 2*c) + 48*I*sqrt(2)*a*sin(2*d*x + 2*c) + 48*sqrt(2)*a)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (48*sqrt(2)*a*cos(2*d*x + 2*c) + 48*I*sqrt(2)*a*sin(2*d*x + 2*c) + 48*sqrt(2)*a)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (48*sqrt(2)*a*cos(2*d*x + 2*c) + 48*I*sqrt(2)*a*sin(2*d*x + 2*c) + 48*sqrt(2)*a)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (48*I*sqrt(2)*a*cos(2*d*x + 2*c) - 48*sqrt(2)*a*sin(2*d*x + 2*c) + 48*I*sqrt(2)*a)*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) - (-48*I*sqrt(2)*a*cos(2*d*x + 2*c) + 48*sqrt(2)*a*sin(2*d*x + 2*c) - 48*I*sqrt(2)*a)*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) - 128*a*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (24*sqrt(2)*a*cos(2*d*x + 2*c) + 24*I*sqrt(2)*a*sin(2*d*x + 2*c) + 24*sqrt(2)*a)*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (24*sqrt(2)*a*cos(2*d*x + 2*c) + 24*I*sqrt(2)*a*sin(2*d*x + 2*c) + 24*sqrt(2)*a)*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (-24*I*sqrt(2)*a*cos(2*d*x + 2*c) + 24*sqrt(2)*a*sin(2*d*x + 2*c) - 24*I*sqrt(2)*a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (24*I*sqrt(2)*a*cos(2*d*x + 2*c) - 24*sqrt(2)*a*sin(2*d*x + 2*c) + 24*I*sqrt(2)*a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (-24*I*sqrt(2)*a*cos(2*d*x + 2*c) + 24*sqrt(2)*a*sin(2*d*x + 2*c) - 24*I*sqrt(2)*a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (24*I*sqrt(2)*a*cos(2*d*x + 2*c) - 24*sqrt(2)*a*sin(2*d*x + 2*c) + 24*I*sqrt(2)*a)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 128*I*a*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)*sqrt(e)/(d*(-64*I*cos(2*d*x + 2*c) + 64*sin(2*d*x + 2*c) - 64*I))","B",0
403,1,1462,0,0.904049," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 i \, \sqrt{2} a \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 2 i \, \sqrt{2} a \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 2 i \, \sqrt{2} a \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 2 i \, \sqrt{2} a \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} a \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 2 \, \sqrt{2} a \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + i \, \sqrt{2} a \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - i \, \sqrt{2} a \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + \sqrt{2} a \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 16 i \, a \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 16 \, a \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a}}{4 \, d \sqrt{e}}"," ",0,"1/4*(2*I*sqrt(2)*a*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 2*I*sqrt(2)*a*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 2*I*sqrt(2)*a*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 2*I*sqrt(2)*a*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 2*sqrt(2)*a*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) + 2*sqrt(2)*a*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) + I*sqrt(2)*a*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - I*sqrt(2)*a*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - sqrt(2)*a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + sqrt(2)*a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - sqrt(2)*a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + sqrt(2)*a*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 16*I*a*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 16*a*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)/(d*sqrt(e))","B",0
404,1,76,0,0.867162," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, a^{\frac{3}{2}} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}{3 \, d e^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}"," ",0,"-2/3*I*a^(3/2)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2)/(d*e^(3/2)*(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2))","B",0
405,1,59,0,0.956890," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(-i \, a \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 i \, a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}}{5 \, d e^{\frac{5}{2}}}"," ",0,"1/5*(-I*a*cos(5/2*d*x + 5/2*c) - 5*I*a*cos(1/2*d*x + 1/2*c) + a*sin(5/2*d*x + 5/2*c) + 5*a*sin(1/2*d*x + 1/2*c))*sqrt(a)/(d*e^(5/2))","A",0
406,1,84,0,1.073752," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{{\left(-3 i \, a \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 14 i \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 21 i \, a \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 14 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 21 \, a \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}}{42 \, d e^{\frac{7}{2}}}"," ",0,"1/42*(-3*I*a*cos(7/2*d*x + 7/2*c) - 14*I*a*cos(3/2*d*x + 3/2*c) + 21*I*a*cos(1/2*d*x + 1/2*c) + 3*a*sin(7/2*d*x + 7/2*c) + 14*a*sin(3/2*d*x + 3/2*c) + 21*a*sin(1/2*d*x + 1/2*c))*sqrt(a)/(d*e^(7/2))","A",0
407,1,160,0,1.383215," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(9/2),x, algorithm=""maxima"")","\frac{{\left(-5 i \, a \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 15 i \, a \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 27 i \, a \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 135 i \, a \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 5 \, a \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 15 \, a \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 27 \, a \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 135 \, a \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sqrt{a}}{180 \, d e^{\frac{9}{2}}}"," ",0,"1/180*(-5*I*a*cos(9/2*d*x + 9/2*c) + 15*I*a*cos(3/2*d*x + 3/2*c) - 27*I*a*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 135*I*a*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*a*sin(9/2*d*x + 9/2*c) + 15*a*sin(3/2*d*x + 3/2*c) + 27*a*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 135*a*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sqrt(a)/(d*e^(9/2))","A",0
408,1,3018,0,1.502464," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(347136 \, a^{2} e \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 387072 \, a^{2} e \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 138240 \, a^{2} e \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 347136 i \, a^{2} e \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 387072 i \, a^{2} e \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 138240 i \, a^{2} e \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(17280 \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 51840 \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 51840 \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 17280 i \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 17280 \, \sqrt{2} a^{2} e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(17280 \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 51840 \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 51840 \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 17280 i \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 17280 \, \sqrt{2} a^{2} e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(17280 \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 51840 \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 51840 \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 17280 i \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 17280 \, \sqrt{2} a^{2} e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(17280 \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 51840 \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 51840 \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 17280 i \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 17280 \, \sqrt{2} a^{2} e\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(17280 i \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 51840 i \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) - 17280 \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) - 51840 \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) - 51840 \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 17280 i \, \sqrt{2} a^{2} e\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(-17280 i \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) - 51840 i \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) - 51840 i \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 17280 \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 51840 \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 51840 \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) - 17280 i \, \sqrt{2} a^{2} e\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(8640 \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 25920 \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 25920 \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 8640 i \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 25920 i \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 25920 i \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 8640 \, \sqrt{2} a^{2} e\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(8640 \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 25920 \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 25920 \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 8640 i \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 25920 i \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 25920 i \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 8640 \, \sqrt{2} a^{2} e\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(8640 i \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 25920 i \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 25920 i \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) - 8640 \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) - 25920 \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) - 25920 \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 8640 i \, \sqrt{2} a^{2} e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(-8640 i \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) - 25920 i \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) - 25920 i \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 8640 \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 25920 \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 25920 \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) - 8640 i \, \sqrt{2} a^{2} e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(8640 i \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) + 25920 i \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) + 25920 i \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) - 8640 \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) - 25920 \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) - 25920 \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) + 8640 i \, \sqrt{2} a^{2} e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(-8640 i \, \sqrt{2} a^{2} e \cos\left(6 \, d x + 6 \, c\right) - 25920 i \, \sqrt{2} a^{2} e \cos\left(4 \, d x + 4 \, c\right) - 25920 i \, \sqrt{2} a^{2} e \cos\left(2 \, d x + 2 \, c\right) + 8640 \, \sqrt{2} a^{2} e \sin\left(6 \, d x + 6 \, c\right) + 25920 \, \sqrt{2} a^{2} e \sin\left(4 \, d x + 4 \, c\right) + 25920 \, \sqrt{2} a^{2} e \sin\left(2 \, d x + 2 \, c\right) - 8640 i \, \sqrt{2} a^{2} e\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right)\right)} \sqrt{a} \sqrt{e}}{d {\left(-36864 i \, \cos\left(6 \, d x + 6 \, c\right) - 110592 i \, \cos\left(4 \, d x + 4 \, c\right) - 110592 i \, \cos\left(2 \, d x + 2 \, c\right) + 36864 \, \sin\left(6 \, d x + 6 \, c\right) + 110592 \, \sin\left(4 \, d x + 4 \, c\right) + 110592 \, \sin\left(2 \, d x + 2 \, c\right) - 36864 i\right)}}"," ",0,"(347136*a^2*e*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 387072*a^2*e*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 138240*a^2*e*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 347136*I*a^2*e*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 387072*I*a^2*e*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 138240*I*a^2*e*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (17280*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 51840*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 51840*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 17280*I*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 51840*I*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 51840*I*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 17280*sqrt(2)*a^2*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (17280*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 51840*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 51840*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 17280*I*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 51840*I*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 51840*I*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 17280*sqrt(2)*a^2*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (17280*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 51840*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 51840*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 17280*I*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 51840*I*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 51840*I*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 17280*sqrt(2)*a^2*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (17280*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 51840*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 51840*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 17280*I*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 51840*I*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 51840*I*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 17280*sqrt(2)*a^2*e)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (17280*I*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 51840*I*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 51840*I*sqrt(2)*a^2*e*cos(2*d*x + 2*c) - 17280*sqrt(2)*a^2*e*sin(6*d*x + 6*c) - 51840*sqrt(2)*a^2*e*sin(4*d*x + 4*c) - 51840*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 17280*I*sqrt(2)*a^2*e)*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) - (-17280*I*sqrt(2)*a^2*e*cos(6*d*x + 6*c) - 51840*I*sqrt(2)*a^2*e*cos(4*d*x + 4*c) - 51840*I*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 17280*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 51840*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 51840*sqrt(2)*a^2*e*sin(2*d*x + 2*c) - 17280*I*sqrt(2)*a^2*e)*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) - (8640*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 25920*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 25920*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 8640*I*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 25920*I*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 25920*I*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 8640*sqrt(2)*a^2*e)*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (8640*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 25920*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 25920*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 8640*I*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 25920*I*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 25920*I*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 8640*sqrt(2)*a^2*e)*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (8640*I*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 25920*I*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 25920*I*sqrt(2)*a^2*e*cos(2*d*x + 2*c) - 8640*sqrt(2)*a^2*e*sin(6*d*x + 6*c) - 25920*sqrt(2)*a^2*e*sin(4*d*x + 4*c) - 25920*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 8640*I*sqrt(2)*a^2*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (-8640*I*sqrt(2)*a^2*e*cos(6*d*x + 6*c) - 25920*I*sqrt(2)*a^2*e*cos(4*d*x + 4*c) - 25920*I*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 8640*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 25920*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 25920*sqrt(2)*a^2*e*sin(2*d*x + 2*c) - 8640*I*sqrt(2)*a^2*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (8640*I*sqrt(2)*a^2*e*cos(6*d*x + 6*c) + 25920*I*sqrt(2)*a^2*e*cos(4*d*x + 4*c) + 25920*I*sqrt(2)*a^2*e*cos(2*d*x + 2*c) - 8640*sqrt(2)*a^2*e*sin(6*d*x + 6*c) - 25920*sqrt(2)*a^2*e*sin(4*d*x + 4*c) - 25920*sqrt(2)*a^2*e*sin(2*d*x + 2*c) + 8640*I*sqrt(2)*a^2*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (-8640*I*sqrt(2)*a^2*e*cos(6*d*x + 6*c) - 25920*I*sqrt(2)*a^2*e*cos(4*d*x + 4*c) - 25920*I*sqrt(2)*a^2*e*cos(2*d*x + 2*c) + 8640*sqrt(2)*a^2*e*sin(6*d*x + 6*c) + 25920*sqrt(2)*a^2*e*sin(4*d*x + 4*c) + 25920*sqrt(2)*a^2*e*sin(2*d*x + 2*c) - 8640*I*sqrt(2)*a^2*e)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2))*sqrt(a)*sqrt(e)/(d*(-36864*I*cos(6*d*x + 6*c) - 110592*I*cos(4*d*x + 4*c) - 110592*I*cos(2*d*x + 2*c) + 36864*sin(6*d*x + 6*c) + 110592*sin(4*d*x + 4*c) + 110592*sin(2*d*x + 2*c) - 36864*I))","B",0
409,1,2438,0,1.622216," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(5632 \, a^{2} \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3584 \, a^{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 5632 i \, a^{2} \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 3584 i \, a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - {\left(1344 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2688 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 1344 i \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2688 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 1344 \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(1344 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2688 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 1344 i \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2688 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 1344 \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(1344 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2688 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 1344 i \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2688 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 1344 \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(1344 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2688 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 1344 i \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2688 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 1344 \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(1344 i \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 2688 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 1344 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) - 2688 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 1344 i \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(-1344 i \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) - 2688 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 1344 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 2688 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) - 1344 i \, \sqrt{2} a^{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(672 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 1344 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 672 i \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 1344 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 672 \, \sqrt{2} a^{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(672 \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 1344 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 672 i \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 1344 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 672 \, \sqrt{2} a^{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(-672 i \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) - 1344 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 672 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 1344 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) - 672 i \, \sqrt{2} a^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(672 i \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 1344 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 672 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) - 1344 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 672 i \, \sqrt{2} a^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-672 i \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) - 1344 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 672 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) + 1344 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) - 672 i \, \sqrt{2} a^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(672 i \, \sqrt{2} a^{2} \cos\left(4 \, d x + 4 \, c\right) + 1344 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 672 \, \sqrt{2} a^{2} \sin\left(4 \, d x + 4 \, c\right) - 1344 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 672 i \, \sqrt{2} a^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right)\right)} \sqrt{a} \sqrt{e}}{d {\left(-1024 i \, \cos\left(4 \, d x + 4 \, c\right) - 2048 i \, \cos\left(2 \, d x + 2 \, c\right) + 1024 \, \sin\left(4 \, d x + 4 \, c\right) + 2048 \, \sin\left(2 \, d x + 2 \, c\right) - 1024 i\right)}}"," ",0,"(5632*a^2*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3584*a^2*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 5632*I*a^2*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 3584*I*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - (1344*sqrt(2)*a^2*cos(4*d*x + 4*c) + 2688*sqrt(2)*a^2*cos(2*d*x + 2*c) + 1344*I*sqrt(2)*a^2*sin(4*d*x + 4*c) + 2688*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 1344*sqrt(2)*a^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (1344*sqrt(2)*a^2*cos(4*d*x + 4*c) + 2688*sqrt(2)*a^2*cos(2*d*x + 2*c) + 1344*I*sqrt(2)*a^2*sin(4*d*x + 4*c) + 2688*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 1344*sqrt(2)*a^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (1344*sqrt(2)*a^2*cos(4*d*x + 4*c) + 2688*sqrt(2)*a^2*cos(2*d*x + 2*c) + 1344*I*sqrt(2)*a^2*sin(4*d*x + 4*c) + 2688*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 1344*sqrt(2)*a^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (1344*sqrt(2)*a^2*cos(4*d*x + 4*c) + 2688*sqrt(2)*a^2*cos(2*d*x + 2*c) + 1344*I*sqrt(2)*a^2*sin(4*d*x + 4*c) + 2688*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 1344*sqrt(2)*a^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (1344*I*sqrt(2)*a^2*cos(4*d*x + 4*c) + 2688*I*sqrt(2)*a^2*cos(2*d*x + 2*c) - 1344*sqrt(2)*a^2*sin(4*d*x + 4*c) - 2688*sqrt(2)*a^2*sin(2*d*x + 2*c) + 1344*I*sqrt(2)*a^2)*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) + (-1344*I*sqrt(2)*a^2*cos(4*d*x + 4*c) - 2688*I*sqrt(2)*a^2*cos(2*d*x + 2*c) + 1344*sqrt(2)*a^2*sin(4*d*x + 4*c) + 2688*sqrt(2)*a^2*sin(2*d*x + 2*c) - 1344*I*sqrt(2)*a^2)*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) + (672*sqrt(2)*a^2*cos(4*d*x + 4*c) + 1344*sqrt(2)*a^2*cos(2*d*x + 2*c) + 672*I*sqrt(2)*a^2*sin(4*d*x + 4*c) + 1344*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 672*sqrt(2)*a^2)*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (672*sqrt(2)*a^2*cos(4*d*x + 4*c) + 1344*sqrt(2)*a^2*cos(2*d*x + 2*c) + 672*I*sqrt(2)*a^2*sin(4*d*x + 4*c) + 1344*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 672*sqrt(2)*a^2)*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (-672*I*sqrt(2)*a^2*cos(4*d*x + 4*c) - 1344*I*sqrt(2)*a^2*cos(2*d*x + 2*c) + 672*sqrt(2)*a^2*sin(4*d*x + 4*c) + 1344*sqrt(2)*a^2*sin(2*d*x + 2*c) - 672*I*sqrt(2)*a^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (672*I*sqrt(2)*a^2*cos(4*d*x + 4*c) + 1344*I*sqrt(2)*a^2*cos(2*d*x + 2*c) - 672*sqrt(2)*a^2*sin(4*d*x + 4*c) - 1344*sqrt(2)*a^2*sin(2*d*x + 2*c) + 672*I*sqrt(2)*a^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-672*I*sqrt(2)*a^2*cos(4*d*x + 4*c) - 1344*I*sqrt(2)*a^2*cos(2*d*x + 2*c) + 672*sqrt(2)*a^2*sin(4*d*x + 4*c) + 1344*sqrt(2)*a^2*sin(2*d*x + 2*c) - 672*I*sqrt(2)*a^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (672*I*sqrt(2)*a^2*cos(4*d*x + 4*c) + 1344*I*sqrt(2)*a^2*cos(2*d*x + 2*c) - 672*sqrt(2)*a^2*sin(4*d*x + 4*c) - 1344*sqrt(2)*a^2*sin(2*d*x + 2*c) + 672*I*sqrt(2)*a^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2))*sqrt(a)*sqrt(e)/(d*(-1024*I*cos(4*d*x + 4*c) - 2048*I*cos(2*d*x + 2*c) + 1024*sin(4*d*x + 4*c) + 2048*sin(2*d*x + 2*c) - 1024*I))","B",0
410,1,2015,0,1.350776," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(80 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 80 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 80 \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(80 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 80 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 80 \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(80 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 80 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 80 \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(80 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 80 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 80 \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(80 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 80 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 80 i \, \sqrt{2} a^{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(-80 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 80 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) - 80 i \, \sqrt{2} a^{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(512 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 512 i \, a^{2} \sin\left(2 \, d x + 2 \, c\right) + 640 \, a^{2}\right)} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + {\left(40 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 40 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 40 \, \sqrt{2} a^{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(40 \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 40 i \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 40 \, \sqrt{2} a^{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(40 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 40 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 40 i \, \sqrt{2} a^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-40 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 40 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) - 40 i \, \sqrt{2} a^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(40 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) - 40 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) + 40 i \, \sqrt{2} a^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-40 i \, \sqrt{2} a^{2} \cos\left(2 \, d x + 2 \, c\right) + 40 \, \sqrt{2} a^{2} \sin\left(2 \, d x + 2 \, c\right) - 40 i \, \sqrt{2} a^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-512 i \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 512 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 640 i \, a^{2}\right)} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{{\left(-64 i \, e \cos\left(2 \, d x + 2 \, c\right) + 64 \, e \sin\left(2 \, d x + 2 \, c\right) - 64 i \, e\right)} d}"," ",0,"((80*sqrt(2)*a^2*cos(2*d*x + 2*c) + 80*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 80*sqrt(2)*a^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (80*sqrt(2)*a^2*cos(2*d*x + 2*c) + 80*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 80*sqrt(2)*a^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (80*sqrt(2)*a^2*cos(2*d*x + 2*c) + 80*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 80*sqrt(2)*a^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (80*sqrt(2)*a^2*cos(2*d*x + 2*c) + 80*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 80*sqrt(2)*a^2)*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (80*I*sqrt(2)*a^2*cos(2*d*x + 2*c) - 80*sqrt(2)*a^2*sin(2*d*x + 2*c) + 80*I*sqrt(2)*a^2)*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) + (-80*I*sqrt(2)*a^2*cos(2*d*x + 2*c) + 80*sqrt(2)*a^2*sin(2*d*x + 2*c) - 80*I*sqrt(2)*a^2)*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) - (512*a^2*cos(2*d*x + 2*c) + 512*I*a^2*sin(2*d*x + 2*c) + 640*a^2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + (40*sqrt(2)*a^2*cos(2*d*x + 2*c) + 40*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 40*sqrt(2)*a^2)*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (40*sqrt(2)*a^2*cos(2*d*x + 2*c) + 40*I*sqrt(2)*a^2*sin(2*d*x + 2*c) + 40*sqrt(2)*a^2)*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (40*I*sqrt(2)*a^2*cos(2*d*x + 2*c) - 40*sqrt(2)*a^2*sin(2*d*x + 2*c) + 40*I*sqrt(2)*a^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-40*I*sqrt(2)*a^2*cos(2*d*x + 2*c) + 40*sqrt(2)*a^2*sin(2*d*x + 2*c) - 40*I*sqrt(2)*a^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (40*I*sqrt(2)*a^2*cos(2*d*x + 2*c) - 40*sqrt(2)*a^2*sin(2*d*x + 2*c) + 40*I*sqrt(2)*a^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-40*I*sqrt(2)*a^2*cos(2*d*x + 2*c) + 40*sqrt(2)*a^2*sin(2*d*x + 2*c) - 40*I*sqrt(2)*a^2)*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-512*I*a^2*cos(2*d*x + 2*c) + 512*a^2*sin(2*d*x + 2*c) - 640*I*a^2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)*sqrt(e)/((-64*I*e*cos(2*d*x + 2*c) + 64*e*sin(2*d*x + 2*c) - 64*I*e)*d)","B",0
411,1,1492,0,1.004884," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(-6 i \, \sqrt{2} a^{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 6 i \, \sqrt{2} a^{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 6 i \, \sqrt{2} a^{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 6 i \, \sqrt{2} a^{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 6 \, \sqrt{2} a^{2} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 6 \, \sqrt{2} a^{2} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 i \, \sqrt{2} a^{2} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 3 i \, \sqrt{2} a^{2} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} a^{2} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 16 i \, a^{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 16 \, a^{2} \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a}}{12 \, d e^{\frac{3}{2}}}"," ",0,"-1/12*(-6*I*sqrt(2)*a^2*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 6*I*sqrt(2)*a^2*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 6*I*sqrt(2)*a^2*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 6*I*sqrt(2)*a^2*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 6*sqrt(2)*a^2*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) + 6*sqrt(2)*a^2*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) + 3*I*sqrt(2)*a^2*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 3*I*sqrt(2)*a^2*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 3*sqrt(2)*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 3*sqrt(2)*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 3*sqrt(2)*a^2*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 16*I*a^2*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 16*a^2*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)/(d*e^(3/2))","B",0
412,1,76,0,0.889319," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, a^{\frac{5}{2}} {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}{5 \, d e^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}"," ",0,"-2/5*I*a^(5/2)*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2)/(d*e^(5/2)*(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2))","B",0
413,1,94,0,1.054477," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{{\left(-7 i \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 i \, a^{2} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 7 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, a^{2} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sqrt{a}}{21 \, d e^{\frac{7}{2}}}"," ",0,"1/21*(-7*I*a^2*cos(3/2*d*x + 3/2*c) - 3*I*a^2*cos(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 7*a^2*sin(3/2*d*x + 3/2*c) + 3*a^2*sin(7/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sqrt(a)/(d*e^(7/2))","A",0
414,1,96,0,1.156887," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(9/2),x, algorithm=""maxima"")","\frac{{\left(-5 i \, a^{2} \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 18 i \, a^{2} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 45 i \, a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 5 \, a^{2} \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 18 \, a^{2} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 45 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}}{90 \, d e^{\frac{9}{2}}}"," ",0,"1/90*(-5*I*a^2*cos(9/2*d*x + 9/2*c) - 18*I*a^2*cos(5/2*d*x + 5/2*c) - 45*I*a^2*cos(1/2*d*x + 1/2*c) + 5*a^2*sin(9/2*d*x + 9/2*c) + 18*a^2*sin(5/2*d*x + 5/2*c) + 45*a^2*sin(1/2*d*x + 1/2*c))*sqrt(a)/(d*e^(9/2))","A",0
415,1,124,0,1.105117," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(11/2),x, algorithm=""maxima"")","\frac{{\left(-7 i \, a^{2} \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) - 33 i \, a^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 77 i \, a^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 77 i \, a^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7 \, a^{2} \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 33 \, a^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 77 \, a^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 77 \, a^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}}{308 \, d e^{\frac{11}{2}}}"," ",0,"1/308*(-7*I*a^2*cos(11/2*d*x + 11/2*c) - 33*I*a^2*cos(7/2*d*x + 7/2*c) - 77*I*a^2*cos(3/2*d*x + 3/2*c) + 77*I*a^2*cos(1/2*d*x + 1/2*c) + 7*a^2*sin(11/2*d*x + 11/2*c) + 33*a^2*sin(7/2*d*x + 7/2*c) + 77*a^2*sin(3/2*d*x + 3/2*c) + 77*a^2*sin(1/2*d*x + 1/2*c))*sqrt(a)/(d*e^(11/2))","A",0
416,1,2273,0,0.967632," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(128 \, e^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 128 i \, e^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + {\left(16 \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} e^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} e^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} e^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} e^{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(16 i \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 16 \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} e^{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(-16 i \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 16 i \, \sqrt{2} e^{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(8 \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 i \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, \sqrt{2} e^{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + {\left(8 \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 i \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, \sqrt{2} e^{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(-8 i \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 i \, \sqrt{2} e^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - {\left(8 i \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 i \, \sqrt{2} e^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - {\left(-8 i \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 i \, \sqrt{2} e^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - {\left(8 i \, \sqrt{2} e^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, \sqrt{2} e^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 i \, \sqrt{2} e^{2}\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right)\right)} \sqrt{a} \sqrt{e}}{{\left(-64 i \, a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 64 \, a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 64 i \, a\right)} d}"," ",0,"-(128*e^2*cos(3/2*d*x + 3/2*c) + 128*I*e^2*sin(3/2*d*x + 3/2*c) + (16*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*e^2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (16*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*e^2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (16*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*e^2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (16*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*e^2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (16*I*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 16*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*e^2)*arctan2(sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (-16*I*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 16*I*sqrt(2)*e^2)*arctan2(-sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), -sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (8*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*I*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*sqrt(2)*e^2)*log(2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (8*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*I*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*sqrt(2)*e^2)*log(-2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (-8*I*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*I*sqrt(2)*e^2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - (8*I*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*I*sqrt(2)*e^2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - (-8*I*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*I*sqrt(2)*e^2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - (8*I*sqrt(2)*e^2*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*sqrt(2)*e^2*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*I*sqrt(2)*e^2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2))*sqrt(a)*sqrt(e)/((-64*I*a*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 64*a*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 64*I*a)*d)","B",0
417,1,726,0,1.049449," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(2 i \, \sqrt{2} e \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} e \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} e \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} e \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 2 \, \sqrt{2} e \arctan\left(\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) + 2 \, \sqrt{2} e \arctan\left(-\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), -\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) + i \, \sqrt{2} e \log\left(2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - i \, \sqrt{2} e \log\left(-2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} e \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} e \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} e \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} e \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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{e}}{4 \, \sqrt{a} d}"," ",0,"-1/4*(2*I*sqrt(2)*e*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*e*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*e*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*e*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 2*sqrt(2)*e*arctan2(sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) + 2*sqrt(2)*e*arctan2(-sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), -sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) + I*sqrt(2)*e*log(2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) + 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) - I*sqrt(2)*e*log(-2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) - sqrt(2)*e*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*e*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*e*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*e*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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(e)/(sqrt(a)*d)","A",0
418,1,76,0,0.668479," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 i \, \sqrt{e} \sqrt{-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}{\sqrt{a} d \sqrt{-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}"," ",0,"2*I*sqrt(e)*sqrt(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(sqrt(a)*d*sqrt(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
419,1,80,0,1.019547," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 i \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)}{3 \, \sqrt{a} d \sqrt{e}}"," ",0,"1/3*(I*cos(3/2*d*x + 3/2*c) - 3*I*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))/(sqrt(a)*d*sqrt(e))","A",0
420,1,130,0,0.860871," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{3 i \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 i \, \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 i \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 3 \, \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)}{30 \, \sqrt{a} d e^{\frac{3}{2}}}"," ",0,"1/30*(3*I*cos(5/2*d*x + 5/2*c) - 5*I*cos(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*I*cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 3*sin(5/2*d*x + 5/2*c) + 5*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))/(sqrt(a)*d*e^(3/2))","A",0
421,1,178,0,1.025426," ","integrate(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{5 i \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 7 i \, \cos\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 i \, \cos\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 105 i \, \cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 5 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 105 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)}{140 \, \sqrt{a} d e^{\frac{5}{2}}}"," ",0,"1/140*(5*I*cos(7/2*d*x + 7/2*c) - 7*I*cos(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*I*cos(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 105*I*cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 5*sin(7/2*d*x + 7/2*c) + 7*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 105*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))/(sqrt(a)*d*e^(5/2))","A",0
422,1,226,0,1.139720," ","integrate(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{35 i \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) - 45 i \, \cos\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 252 i \, \cos\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 420 i \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1890 i \, \cos\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 45 \, \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 252 \, \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 420 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 1890 \, \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)}{2520 \, \sqrt{a} d e^{\frac{7}{2}}}"," ",0,"1/2520*(35*I*cos(9/2*d*x + 9/2*c) - 45*I*cos(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 252*I*cos(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 420*I*cos(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1890*I*cos(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 35*sin(9/2*d*x + 9/2*c) + 45*sin(7/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 252*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 420*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 1890*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))/(sqrt(a)*d*e^(7/2))","A",0
423,1,1819,0,1.247645," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(48 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 24 i \, \sqrt{2} e^{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) - 24 i \, \sqrt{2} e^{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) + 24 i \, \sqrt{2} e^{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) - 24 i \, \sqrt{2} e^{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) + 128 \, e^{3} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 128 i \, e^{3} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + {\left(48 i \, \sqrt{2} e^{3} \cos\left(2 \, d x + 2 \, c\right) - 48 \, \sqrt{2} e^{3} \sin\left(2 \, d x + 2 \, c\right) + 48 i \, \sqrt{2} e^{3}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) + {\left(-48 i \, \sqrt{2} e^{3} \cos\left(2 \, d x + 2 \, c\right) + 48 \, \sqrt{2} e^{3} \sin\left(2 \, d x + 2 \, c\right) - 48 i \, \sqrt{2} e^{3}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), -\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) + {\left(48 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 24 i \, \sqrt{2} e^{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) - 24 i \, \sqrt{2} e^{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) + 24 i \, \sqrt{2} e^{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) - 24 i \, \sqrt{2} e^{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) + {\left(24 \, \sqrt{2} e^{3} \cos\left(2 \, d x + 2 \, c\right) + 24 i \, \sqrt{2} e^{3} \sin\left(2 \, d x + 2 \, c\right) + 24 \, \sqrt{2} e^{3}\right)} \log\left(2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - {\left(24 \, \sqrt{2} e^{3} \cos\left(2 \, d x + 2 \, c\right) + 24 i \, \sqrt{2} e^{3} \sin\left(2 \, d x + 2 \, c\right) + 24 \, \sqrt{2} e^{3}\right)} \log\left(-2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + {\left(48 i \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 i \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 i \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 48 i \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 24 \, \sqrt{2} e^{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) + 24 \, \sqrt{2} e^{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) - 24 \, \sqrt{2} e^{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) + 24 \, \sqrt{2} e^{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)} \sin\left(2 \, d x + 2 \, c\right)\right)} \sqrt{a} \sqrt{e}}{{\left(-64 i \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + 64 \, a^{2} \sin\left(2 \, d x + 2 \, c\right) - 64 i \, a^{2}\right)} d}"," ",0,"-(48*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 24*I*sqrt(2)*e^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) - 24*I*sqrt(2)*e^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) + 24*I*sqrt(2)*e^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) - 24*I*sqrt(2)*e^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) + 128*e^3*cos(1/2*d*x + 1/2*c) + 128*I*e^3*sin(1/2*d*x + 1/2*c) + (48*I*sqrt(2)*e^3*cos(2*d*x + 2*c) - 48*sqrt(2)*e^3*sin(2*d*x + 2*c) + 48*I*sqrt(2)*e^3)*arctan2(sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) + (-48*I*sqrt(2)*e^3*cos(2*d*x + 2*c) + 48*sqrt(2)*e^3*sin(2*d*x + 2*c) - 48*I*sqrt(2)*e^3)*arctan2(-sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), -sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) + (48*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 24*I*sqrt(2)*e^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) - 24*I*sqrt(2)*e^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) + 24*I*sqrt(2)*e^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) - 24*I*sqrt(2)*e^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) + (24*sqrt(2)*e^3*cos(2*d*x + 2*c) + 24*I*sqrt(2)*e^3*sin(2*d*x + 2*c) + 24*sqrt(2)*e^3)*log(2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) + 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) - (24*sqrt(2)*e^3*cos(2*d*x + 2*c) + 24*I*sqrt(2)*e^3*sin(2*d*x + 2*c) + 24*sqrt(2)*e^3)*log(-2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) + (48*I*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*I*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*I*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 48*I*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 24*sqrt(2)*e^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) + 24*sqrt(2)*e^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) - 24*sqrt(2)*e^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) + 24*sqrt(2)*e^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))*sin(2*d*x + 2*c))*sqrt(a)*sqrt(e)/((-64*I*a^2*cos(2*d*x + 2*c) + 64*a^2*sin(2*d*x + 2*c) - 64*I*a^2)*d)","B",0
424,1,778,0,1.317995," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(2 i \, \sqrt{2} e^{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} e^{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} e^{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} e^{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 \, \sqrt{2} e^{2} \arctan\left(\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) - 2 \, \sqrt{2} e^{2} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), -\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) + i \, \sqrt{2} e^{2} \log\left(2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - i \, \sqrt{2} e^{2} \log\left(-2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + \sqrt{2} e^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} e^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} e^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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} e^{2} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 16 i \, e^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 \, e^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{e}}{4 \, a^{\frac{3}{2}} d}"," ",0,"-1/4*(2*I*sqrt(2)*e^2*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*e^2*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*e^2*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*e^2*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*sqrt(2)*e^2*arctan2(sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) - 2*sqrt(2)*e^2*arctan2(-sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), -sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) + I*sqrt(2)*e^2*log(2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) + 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) - I*sqrt(2)*e^2*log(-2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) + sqrt(2)*e^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*e^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*e^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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)*e^2*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 16*I*e^2*cos(1/2*d*x + 1/2*c) - 16*e^2*sin(1/2*d*x + 1/2*c))*sqrt(e)/(a^(3/2)*d)","B",0
425,1,76,0,0.785532," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, e^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}{3 \, a^{\frac{3}{2}} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{3}{2}}}"," ",0,"2/3*I*e^(3/2)*(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2)/(a^(3/2)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(3/2))","B",0
426,1,80,0,0.941005," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{e} {\left(i \, \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 i \, \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)}}{5 \, a^{\frac{3}{2}} d}"," ",0,"1/5*sqrt(e)*(I*cos(5/2*d*x + 5/2*c) + 5*I*cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + sin(5/2*d*x + 5/2*c) + 5*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))/(a^(3/2)*d)","A",0
427,1,130,0,0.957864," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{3 i \, \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 14 i \, \cos\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 21 i \, \cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 3 \, \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 14 \, \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 21 \, \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)}{42 \, a^{\frac{3}{2}} d \sqrt{e}}"," ",0,"1/42*(3*I*cos(7/2*d*x + 7/2*c) + 14*I*cos(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 21*I*cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 3*sin(7/2*d*x + 7/2*c) + 14*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 21*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))/(a^(3/2)*d*sqrt(e))","A",0
428,1,178,0,1.171638," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{5 i \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 27 i \, \cos\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) - 15 i \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 135 i \, \cos\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 5 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 27 \, \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 15 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 135 \, \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)}{180 \, a^{\frac{3}{2}} d e^{\frac{3}{2}}}"," ",0,"1/180*(5*I*cos(9/2*d*x + 9/2*c) + 27*I*cos(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) - 15*I*cos(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 135*I*cos(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 5*sin(9/2*d*x + 9/2*c) + 27*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 15*sin(1/3*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 135*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))/(a^(3/2)*d*e^(3/2))","A",0
429,1,226,0,1.158466," ","integrate(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{35 i \, \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 220 i \, \cos\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 77 i \, \cos\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 770 i \, \cos\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 1540 i \, \cos\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 35 \, \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 220 \, \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 77 \, \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 770 \, \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 1540 \, \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)}{3080 \, a^{\frac{3}{2}} d e^{\frac{5}{2}}}"," ",0,"1/3080*(35*I*cos(11/2*d*x + 11/2*c) + 220*I*cos(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 77*I*cos(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 770*I*cos(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 1540*I*cos(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 35*sin(11/2*d*x + 11/2*c) + 220*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 77*sin(5/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 770*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 1540*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))/(a^(3/2)*d*e^(5/2))","A",0
430,1,2453,0,1.292513," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(64 \, e^{4} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 64 \, e^{4} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, e^{4} + {\left(10 i \, \sqrt{2} e^{4} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 10 i \, \sqrt{2} e^{4} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 10 \, \sqrt{2} e^{4} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 10 \, \sqrt{2} e^{4} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) + {\left(-10 i \, \sqrt{2} e^{4} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 10 i \, \sqrt{2} e^{4} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 10 \, \sqrt{2} e^{4} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 10 \, \sqrt{2} e^{4} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), -\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) - {\left(10 \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 5 i \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 5 i \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 5 i \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 5 i \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 64 \, e^{4} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 64 i \, e^{4} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - {\left(10 \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 5 i \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 5 i \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 5 i \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 5 i \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - {\left(5 \, \sqrt{2} e^{4} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 \, \sqrt{2} e^{4} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 i \, \sqrt{2} e^{4} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 i \, \sqrt{2} e^{4} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \log\left(2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + {\left(5 \, \sqrt{2} e^{4} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 \, \sqrt{2} e^{4} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 i \, \sqrt{2} e^{4} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 5 i \, \sqrt{2} e^{4} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \log\left(-2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + {\left(10 i \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 i \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 i \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 10 i \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 5 \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 5 \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 5 \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 5 \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 64 i \, e^{4} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 64 \, e^{4} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + {\left(-10 i \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 10 i \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 10 i \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 10 i \, \sqrt{2} e^{4} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 5 \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 5 \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) - 5 \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2\right) + 5 \, \sqrt{2} e^{4} \log\left(2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, 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(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a} \sqrt{e}}{{\left(8 i \, a^{3} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 8 i \, a^{3} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a^{3} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 8 \, a^{3} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} d}"," ",0,"-(64*e^4*cos(1/2*d*x + 1/2*c)^2 + 64*e^4*sin(1/2*d*x + 1/2*c)^2 + 16*e^4 + (10*I*sqrt(2)*e^4*cos(3/2*d*x + 3/2*c) + 10*I*sqrt(2)*e^4*cos(1/2*d*x + 1/2*c) + 10*sqrt(2)*e^4*sin(3/2*d*x + 3/2*c) - 10*sqrt(2)*e^4*sin(1/2*d*x + 1/2*c))*arctan2(sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) + (-10*I*sqrt(2)*e^4*cos(3/2*d*x + 3/2*c) - 10*I*sqrt(2)*e^4*cos(1/2*d*x + 1/2*c) - 10*sqrt(2)*e^4*sin(3/2*d*x + 3/2*c) + 10*sqrt(2)*e^4*sin(1/2*d*x + 1/2*c))*arctan2(-sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), -sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) - (10*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 5*I*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 5*I*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 5*I*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 5*I*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 64*e^4*cos(1/2*d*x + 1/2*c) + 64*I*e^4*sin(1/2*d*x + 1/2*c))*cos(3/2*d*x + 3/2*c) - (10*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 5*I*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 5*I*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 5*I*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 5*I*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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(1/2*d*x + 1/2*c) - (5*sqrt(2)*e^4*cos(3/2*d*x + 3/2*c) + 5*sqrt(2)*e^4*cos(1/2*d*x + 1/2*c) - 5*I*sqrt(2)*e^4*sin(3/2*d*x + 3/2*c) + 5*I*sqrt(2)*e^4*sin(1/2*d*x + 1/2*c))*log(2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) + 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) + (5*sqrt(2)*e^4*cos(3/2*d*x + 3/2*c) + 5*sqrt(2)*e^4*cos(1/2*d*x + 1/2*c) - 5*I*sqrt(2)*e^4*sin(3/2*d*x + 3/2*c) + 5*I*sqrt(2)*e^4*sin(1/2*d*x + 1/2*c))*log(-2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) + (10*I*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*I*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*I*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 10*I*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 5*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 5*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 5*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 5*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 64*I*e^4*cos(1/2*d*x + 1/2*c) - 64*e^4*sin(1/2*d*x + 1/2*c))*sin(3/2*d*x + 3/2*c) + (-10*I*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 10*I*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 10*I*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 10*I*sqrt(2)*e^4*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 5*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 5*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) - 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) - 5*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 2*sqrt(2)*sin(1/2*d*x + 1/2*c) + 2) + 5*sqrt(2)*e^4*log(2*cos(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c)^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(1/2*d*x + 1/2*c))*sqrt(a)*sqrt(e)/((8*I*a^3*cos(3/2*d*x + 3/2*c) + 8*I*a^3*cos(1/2*d*x + 1/2*c) + 8*a^3*sin(3/2*d*x + 3/2*c) - 8*a^3*sin(1/2*d*x + 1/2*c))*d)","B",0
431,1,1466,0,1.032533," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(6 i \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 6 i \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 6 i \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 6 i \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 6 \, \sqrt{2} e^{3} \arctan\left(\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 6 \, \sqrt{2} e^{3} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 3 i \, \sqrt{2} e^{3} \log\left(2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 3 i \, \sqrt{2} e^{3} \log\left(-2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 3 \, \sqrt{2} e^{3} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 3 \, \sqrt{2} e^{3} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - 3 \, \sqrt{2} e^{3} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 3 \, \sqrt{2} e^{3} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 16 i \, e^{3} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 16 \, e^{3} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sqrt{e}}{12 \, a^{\frac{5}{2}} d}"," ",0,"1/12*(6*I*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 6*I*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 6*I*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 6*I*sqrt(2)*e^3*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 6*sqrt(2)*e^3*arctan2(sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 6*sqrt(2)*e^3*arctan2(-sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), -sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 3*I*sqrt(2)*e^3*log(2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 3*I*sqrt(2)*e^3*log(-2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 3*sqrt(2)*e^3*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 3*sqrt(2)*e^3*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - 3*sqrt(2)*e^3*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 3*sqrt(2)*e^3*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 16*I*e^3*cos(3/2*d*x + 3/2*c) + 16*e^3*sin(3/2*d*x + 3/2*c))*sqrt(e)/(a^(5/2)*d)","B",0
432,1,76,0,0.908911," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, e^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}{5 \, a^{\frac{5}{2}} d {\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)}^{\frac{5}{2}}}"," ",0,"2/5*I*e^(5/2)*(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2)/(a^(5/2)*d*(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)^(5/2))","B",0
433,1,86,0,0.612810," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(3 i \, e \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 i \, e \cos\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 3 \, e \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, e \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} \sqrt{e}}{21 \, a^{\frac{5}{2}} d}"," ",0,"1/21*(3*I*e*cos(7/2*d*x + 7/2*c) + 7*I*e*cos(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 3*e*sin(7/2*d*x + 7/2*c) + 7*e*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*sqrt(e)/(a^(5/2)*d)","A",0
434,1,130,0,1.116754," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{e} {\left(5 i \, \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 18 i \, \cos\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 45 i \, \cos\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 5 \, \sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right) + 18 \, \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right) + 45 \, \sin\left(\frac{1}{9} \, \arctan\left(\sin\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right), \cos\left(\frac{9}{2} \, d x + \frac{9}{2} \, c\right)\right)\right)\right)}}{90 \, a^{\frac{5}{2}} d}"," ",0,"1/90*sqrt(e)*(5*I*cos(9/2*d*x + 9/2*c) + 18*I*cos(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 45*I*cos(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 5*sin(9/2*d*x + 9/2*c) + 18*sin(5/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))) + 45*sin(1/9*arctan2(sin(9/2*d*x + 9/2*c), cos(9/2*d*x + 9/2*c))))/(a^(5/2)*d)","A",0
435,1,178,0,1.047705," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{7 i \, \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 33 i \, \cos\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 77 i \, \cos\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) - 77 i \, \cos\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 7 \, \sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right) + 33 \, \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 77 \, \sin\left(\frac{3}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right) + 77 \, \sin\left(\frac{1}{11} \, \arctan\left(\sin\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right), \cos\left(\frac{11}{2} \, d x + \frac{11}{2} \, c\right)\right)\right)}{308 \, a^{\frac{5}{2}} d \sqrt{e}}"," ",0,"1/308*(7*I*cos(11/2*d*x + 11/2*c) + 33*I*cos(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 77*I*cos(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) - 77*I*cos(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 7*sin(11/2*d*x + 11/2*c) + 33*sin(7/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 77*sin(3/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))) + 77*sin(1/11*arctan2(sin(11/2*d*x + 11/2*c), cos(11/2*d*x + 11/2*c))))/(a^(5/2)*d*sqrt(e))","A",0
436,1,226,0,0.970188," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{45 i \, \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 260 i \, \cos\left(\frac{9}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 702 i \, \cos\left(\frac{5}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) - 195 i \, \cos\left(\frac{3}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 2340 i \, \cos\left(\frac{1}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 45 \, \sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right) + 260 \, \sin\left(\frac{9}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 702 \, \sin\left(\frac{5}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 195 \, \sin\left(\frac{3}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right) + 2340 \, \sin\left(\frac{1}{13} \, \arctan\left(\sin\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right), \cos\left(\frac{13}{2} \, d x + \frac{13}{2} \, c\right)\right)\right)}{4680 \, a^{\frac{5}{2}} d e^{\frac{3}{2}}}"," ",0,"1/4680*(45*I*cos(13/2*d*x + 13/2*c) + 260*I*cos(9/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 702*I*cos(5/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) - 195*I*cos(3/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 2340*I*cos(1/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 45*sin(13/2*d*x + 13/2*c) + 260*sin(9/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 702*sin(5/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 195*sin(3/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))) + 2340*sin(1/13*arctan2(sin(13/2*d*x + 13/2*c), cos(13/2*d*x + 13/2*c))))/(a^(5/2)*d*e^(3/2))","A",0
437,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(7/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
438,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
439,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(2/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
440,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(1/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
441,0,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}} \sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*sec(d*x + c))^(1/3)*sqrt(I*a*tan(d*x + c) + a)), x)","F",0
442,0,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\left(e \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*sec(d*x + c))^(4/3)*sqrt(I*a*tan(d*x + c) + a)), x)","F",0
443,1,3905,0,1.746424," ","integrate((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(7/3),x, algorithm=""maxima"")","\frac{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{5}{6}} {\left(48 \, {\left(i \cdot 2^{\frac{1}{3}} \cos\left(4 \, f x + 4 \, e\right) + 2^{\frac{1}{3}} \sin\left(4 \, f x + 4 \, e\right)\right)} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) - {\left(48 \cdot 2^{\frac{1}{3}} \cos\left(4 \, f x + 4 \, e\right) - 48 i \cdot 2^{\frac{1}{3}} \sin\left(4 \, f x + 4 \, e\right)\right)} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)\right)} d^{\frac{2}{3}} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} {\left(30 \, {\left(-i \cdot 2^{\frac{1}{3}} \cos\left(4 \, f x + 4 \, e\right) - 2^{\frac{1}{3}} \sin\left(4 \, f x + 4 \, e\right)\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + {\left(30 \cdot 2^{\frac{1}{3}} \cos\left(4 \, f x + 4 \, e\right) - 30 i \cdot 2^{\frac{1}{3}} \sin\left(4 \, f x + 4 \, e\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)\right)} d^{\frac{2}{3}} - {\left(10 i \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + \frac{1}{3} \, \sqrt{3}, \frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + \sqrt{3}\right)}\right) + 10 i \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + \frac{1}{3} \, \sqrt{3}, -\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) - \sqrt{3}\right)}\right) - 5 \, \sqrt{3} 2^{\frac{1}{3}} \log\left(\frac{4}{3} \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2}\right)} + \frac{4}{3} \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} {\left(\sqrt{3} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)\right)} + \frac{4}{3}\right) + 5 \, \sqrt{3} 2^{\frac{1}{3}} \log\left(\frac{4}{3} \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2}\right)} - \frac{4}{3} \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} {\left(\sqrt{3} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)\right)} + \frac{4}{3}\right) + 10 \cdot 2^{\frac{1}{3}} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + 1\right) - 20 \cdot 2^{\frac{1}{3}} \arctan\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right), {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) - 1\right) + 10 i \cdot 2^{\frac{1}{3}} \log\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2} - 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + 1\right) - 5 i \cdot 2^{\frac{1}{3}} \log\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{2}{3}} {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2}\right)} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)^{2}\right)} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{3}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)\right)} + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right)\right)} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)}^{\frac{1}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right), \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, f x + 4 \, e\right), \cos\left(4 \, f x + 4 \, e\right)\right)\right) + 1\right)\right) + 1\right)\right)} d^{\frac{2}{3}}}{288 \, a^{\frac{7}{3}} f}"," ",0,"1/288*((cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(5/6)*(48*(I*2^(1/3)*cos(4*f*x + 4*e) + 2^(1/3)*sin(4*f*x + 4*e))*cos(5/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) - (48*2^(1/3)*cos(4*f*x + 4*e) - 48*I*2^(1/3)*sin(4*f*x + 4*e))*sin(5/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)))*d^(2/3) + (cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*(30*(-I*2^(1/3)*cos(4*f*x + 4*e) - 2^(1/3)*sin(4*f*x + 4*e))*cos(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + (30*2^(1/3)*cos(4*f*x + 4*e) - 30*I*2^(1/3)*sin(4*f*x + 4*e))*sin(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)))*d^(2/3) - (10*I*sqrt(3)*2^(1/3)*arctan2(2/3*sqrt(3)*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + 1/3*sqrt(3), 1/3*sqrt(3)*(2*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + sqrt(3))) + 10*I*sqrt(3)*2^(1/3)*arctan2(2/3*sqrt(3)*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + 1/3*sqrt(3), -1/3*sqrt(3)*(2*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) - sqrt(3))) - 5*sqrt(3)*2^(1/3)*log(4/3*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*(cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2 + sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2) + 4/3*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*(sqrt(3)*sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))) + 4/3) + 5*sqrt(3)*2^(1/3)*log(4/3*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*(cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2 + sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2) - 4/3*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*(sqrt(3)*sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) - cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))) + 4/3) + 10*2^(1/3)*arctan2((cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*sin(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + (cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)), (cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*cos(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + (cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + 1) - 20*2^(1/3)*arctan2((cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)), (cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) - 1) + 10*I*2^(1/3)*log((cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2 + (cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2 - 2*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + 1) - 5*I*2^(1/3)*log((cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(2/3)*(cos(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2 + sin(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2) + (cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*(cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2 + sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))^2) + 2*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/3)*((cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*(cos(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))*cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + sin(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))*sin(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))) + cos(2/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1))) + 2*(cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e)))^2 + 2*cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)^(1/6)*cos(1/3*arctan2(sin(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))), cos(1/2*arctan2(sin(4*f*x + 4*e), cos(4*f*x + 4*e))) + 1)) + 1))*d^(2/3))/(a^(7/3)*f)","B",0
444,1,1907,0,0.945038," ","integrate((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(4/3),x, algorithm=""maxima"")","-\frac{{\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}{3}} {\left(6 \, {\left(-i \cdot 2^{\frac{1}{3}} \cos\left(2 \, f x + 2 \, e\right) - 2^{\frac{1}{3}} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + {\left(6 \cdot 2^{\frac{1}{3}} \cos\left(2 \, f x + 2 \, e\right) - 6 i \cdot 2^{\frac{1}{3}} \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} d^{\frac{2}{3}} - {\left(-2 i \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \frac{1}{3} \, \sqrt{3}, \frac{1}{3} \, \sqrt{3} {\left(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}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \sqrt{3}\right)}\right) - 2 i \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \frac{1}{3} \, \sqrt{3}, -\frac{1}{3} \, \sqrt{3} {\left(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}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - \sqrt{3}\right)}\right) + \sqrt{3} 2^{\frac{1}{3}} \log\left(\frac{4}{3} \, {\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}{3}} {\left(\cos\left(\frac{1}{3} \, \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}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2}\right)} + \frac{4}{3} \, {\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}{6}} {\left(\sqrt{3} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} + \frac{4}{3}\right) - \sqrt{3} 2^{\frac{1}{3}} \log\left(\frac{4}{3} \, {\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}{3}} {\left(\cos\left(\frac{1}{3} \, \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}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2}\right)} - \frac{4}{3} \, {\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}{6}} {\left(\sqrt{3} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} + \frac{4}{3}\right) - 2 \cdot 2^{\frac{1}{3}} \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}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right) + 4 \cdot 2^{\frac{1}{3}} \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}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 1\right) - 2 i \cdot 2^{\frac{1}{3}} \log\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}{3}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{3}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2} - 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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right) + i \cdot 2^{\frac{1}{3}} \log\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{2}{3}} {\left(\cos\left(\frac{2}{3} \, \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{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2}\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}{3}} {\left(\cos\left(\frac{1}{3} \, \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}{3} \, \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}{3}} {\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}{6}} {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right)\right)} d^{\frac{2}{3}}}{24 \, a^{\frac{4}{3}} f}"," ",0,"-1/24*((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*(6*(-I*2^(1/3)*cos(2*f*x + 2*e) - 2^(1/3)*sin(2*f*x + 2*e))*cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + (6*2^(1/3)*cos(2*f*x + 2*e) - 6*I*2^(1/3)*sin(2*f*x + 2*e))*sin(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*d^(2/3) - (-2*I*sqrt(3)*2^(1/3)*arctan2(2/3*sqrt(3)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1/3*sqrt(3), 1/3*sqrt(3)*(2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + sqrt(3))) - 2*I*sqrt(3)*2^(1/3)*arctan2(2/3*sqrt(3)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1/3*sqrt(3), -1/3*sqrt(3)*(2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - sqrt(3))) + sqrt(3)*2^(1/3)*log(4/3*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*(cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2) + 4/3*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*(sqrt(3)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))) + 4/3) - sqrt(3)*2^(1/3)*log(4/3*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*(cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2) - 4/3*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*(sqrt(3)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))) + 4/3) - 2*2^(1/3)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*sin(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1) + 4*2^(1/3)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 1) - 2*I*2^(1/3)*log((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*sin(1/3*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)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1) + I*2^(1/3)*log((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(2/3)*(cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2) + (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*(cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(1/3*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)^(1/3)*((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*(cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + sin(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))) + cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))) + 2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1))*d^(2/3))/(a^(4/3)*f)","B",0
445,1,1753,0,1.096862," ","integrate((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(1/3),x, algorithm=""maxima"")","\frac{{\left(-2 i \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \frac{1}{3} \, \sqrt{3}, \frac{1}{3} \, \sqrt{3} {\left(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}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \sqrt{3}\right)}\right) - 2 i \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \frac{1}{3} \, \sqrt{3}, -\frac{1}{3} \, \sqrt{3} {\left(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}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - \sqrt{3}\right)}\right) + \sqrt{3} 2^{\frac{1}{3}} \log\left(\frac{4}{3} \, {\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}{3}} {\left(\cos\left(\frac{1}{3} \, \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}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2}\right)} + \frac{4}{3} \, {\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}{6}} {\left(\sqrt{3} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} + \frac{4}{3}\right) - \sqrt{3} 2^{\frac{1}{3}} \log\left(\frac{4}{3} \, {\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}{3}} {\left(\cos\left(\frac{1}{3} \, \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}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2}\right)} - \frac{4}{3} \, {\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}{6}} {\left(\sqrt{3} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} + \frac{4}{3}\right) - 2 \cdot 2^{\frac{1}{3}} \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}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right) + 4 \cdot 2^{\frac{1}{3}} \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}{6}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 1\right) - 2 i \cdot 2^{\frac{1}{3}} \log\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}{3}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\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}{3}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2} - 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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right) + i \cdot 2^{\frac{1}{3}} \log\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{2}{3}} {\left(\cos\left(\frac{2}{3} \, \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{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)^{2}\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}{3}} {\left(\cos\left(\frac{1}{3} \, \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}{3} \, \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}{3}} {\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}{6}} {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\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}{6}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 1\right)\right)} d^{\frac{2}{3}}}{8 \, a^{\frac{1}{3}} f}"," ",0,"1/8*(-2*I*sqrt(3)*2^(1/3)*arctan2(2/3*sqrt(3)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1/3*sqrt(3), 1/3*sqrt(3)*(2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + sqrt(3))) - 2*I*sqrt(3)*2^(1/3)*arctan2(2/3*sqrt(3)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1/3*sqrt(3), -1/3*sqrt(3)*(2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - sqrt(3))) + sqrt(3)*2^(1/3)*log(4/3*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*(cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2) + 4/3*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*(sqrt(3)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))) + 4/3) - sqrt(3)*2^(1/3)*log(4/3*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*(cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2) - 4/3*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*(sqrt(3)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))) + 4/3) - 2*2^(1/3)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*sin(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1) + 4*2^(1/3)*arctan2((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)), (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 1) - 2*I*2^(1/3)*log((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*sin(1/3*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)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1) + I*2^(1/3)*log((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(2/3)*(cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2) + (cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/3)*(cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))^2 + sin(1/3*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)^(1/3)*((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*(cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + sin(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))) + cos(2/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1))) + 2*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 1))*d^(2/3)/(a^(1/3)*f)","B",0
446,1,106,0,1.145133," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(2/3),x, algorithm=""maxima"")","\frac{{\left(3 i \cdot 2^{\frac{1}{3}} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 3 \cdot 2^{\frac{1}{3}} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} a^{\frac{2}{3}} d^{\frac{2}{3}}}{{\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}{6}} f}"," ",0,"(3*I*2^(1/3)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 3*2^(1/3)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*a^(2/3)*d^(2/3)/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*f)","B",0
447,1,318,0,1.296551," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(5/3),x, algorithm=""maxima"")","\frac{3 \, {\left(-i \cdot 2^{\frac{1}{3}} a \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 2^{\frac{1}{3}} a \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} \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} a^{\frac{2}{3}} d^{\frac{2}{3}} - {\left({\left(-12 i \cdot 2^{\frac{1}{3}} a \cos\left(2 \, f x + 2 \, e\right)^{2} - 12 i \cdot 2^{\frac{1}{3}} a \sin\left(2 \, f x + 2 \, e\right)^{2} - 24 i \cdot 2^{\frac{1}{3}} a \cos\left(2 \, f x + 2 \, e\right) - 12 i \cdot 2^{\frac{1}{3}} a\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 12 \, {\left(2^{\frac{1}{3}} a \cos\left(2 \, f x + 2 \, e\right)^{2} + 2^{\frac{1}{3}} a \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \cdot 2^{\frac{1}{3}} a \cos\left(2 \, f x + 2 \, e\right) + 2^{\frac{1}{3}} a\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} a^{\frac{2}{3}} d^{\frac{2}{3}}}{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{7}{6}} f}"," ",0,"1/2*(3*(-I*2^(1/3)*a*cos(4/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 2^(1/3)*a*sin(4/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*sqrt(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*a^(2/3)*d^(2/3) - ((-12*I*2^(1/3)*a*cos(2*f*x + 2*e)^2 - 12*I*2^(1/3)*a*sin(2*f*x + 2*e)^2 - 24*I*2^(1/3)*a*cos(2*f*x + 2*e) - 12*I*2^(1/3)*a)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 12*(2^(1/3)*a*cos(2*f*x + 2*e)^2 + 2^(1/3)*a*sin(2*f*x + 2*e)^2 + 2*2^(1/3)*a*cos(2*f*x + 2*e) + 2^(1/3)*a)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*a^(2/3)*d^(2/3))/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(7/6)*f)","B",0
448,1,402,0,1.092300," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(8/3),x, algorithm=""maxima"")","\frac{42 \, {\left(-i \cdot 2^{\frac{1}{3}} a^{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 2^{\frac{1}{3}} a^{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} \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} a^{\frac{2}{3}} d^{\frac{2}{3}} - {\left(-12 i \cdot 2^{\frac{1}{3}} a^{2} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 12 \cdot 2^{\frac{1}{3}} a^{2} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + {\left(-84 i \cdot 2^{\frac{1}{3}} a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} - 84 i \cdot 2^{\frac{1}{3}} a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} - 168 i \cdot 2^{\frac{1}{3}} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 84 i \cdot 2^{\frac{1}{3}} a^{2}\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 84 \, {\left(2^{\frac{1}{3}} a^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2^{\frac{1}{3}} a^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \cdot 2^{\frac{1}{3}} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 2^{\frac{1}{3}} a^{2}\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} a^{\frac{2}{3}} d^{\frac{2}{3}}}{7 \, {\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{7}{6}} f}"," ",0,"1/7*(42*(-I*2^(1/3)*a^2*cos(4/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 2^(1/3)*a^2*sin(4/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*sqrt(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*a^(2/3)*d^(2/3) - (-12*I*2^(1/3)*a^2*cos(7/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 12*2^(1/3)*a^2*sin(7/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + (-84*I*2^(1/3)*a^2*cos(2*f*x + 2*e)^2 - 84*I*2^(1/3)*a^2*sin(2*f*x + 2*e)^2 - 168*I*2^(1/3)*a^2*cos(2*f*x + 2*e) - 84*I*2^(1/3)*a^2)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 84*(2^(1/3)*a^2*cos(2*f*x + 2*e)^2 + 2^(1/3)*a^2*sin(2*f*x + 2*e)^2 + 2*2^(1/3)*a^2*cos(2*f*x + 2*e) + 2^(1/3)*a^2)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*a^(2/3)*d^(2/3))/((cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(7/6)*f)","B",0
449,1,977,0,1.081499," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(11/3),x, algorithm=""maxima"")","-\frac{{\left(84 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(\frac{10}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 84 \cdot 2^{\frac{1}{3}} a^{3} \sin\left(\frac{10}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + {\left(630 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 630 i \cdot 2^{\frac{1}{3}} a^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 1260 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 630 i \cdot 2^{\frac{1}{3}} a^{3}\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 630 \, {\left(2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2^{\frac{1}{3}} a^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 2^{\frac{1}{3}} a^{3}\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} \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} a^{\frac{2}{3}} d^{\frac{2}{3}} + {\left({\left(-360 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} - 360 i \cdot 2^{\frac{1}{3}} a^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} - 720 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 360 i \cdot 2^{\frac{1}{3}} a^{3}\right)} \cos\left(\frac{7}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + {\left(-840 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{4} - 840 i \cdot 2^{\frac{1}{3}} a^{3} \sin\left(2 \, f x + 2 \, e\right)^{4} - 3360 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{3} - 5040 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} - 3360 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 840 i \cdot 2^{\frac{1}{3}} a^{3} + {\left(-1680 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} - 3360 i \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 1680 i \cdot 2^{\frac{1}{3}} a^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2}\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 360 \, {\left(2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2^{\frac{1}{3}} a^{3} \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 2^{\frac{1}{3}} a^{3}\right)} \sin\left(\frac{7}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 840 \, {\left(2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{4} + 2^{\frac{1}{3}} a^{3} \sin\left(2 \, f x + 2 \, e\right)^{4} + 4 \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{3} + 6 \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 2^{\frac{1}{3}} a^{3} + 2 \, {\left(2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \cdot 2^{\frac{1}{3}} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 2^{\frac{1}{3}} a^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2}\right)} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right)\right)} a^{\frac{2}{3}} d^{\frac{2}{3}}}{35 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{4} + \sin\left(2 \, f x + 2 \, e\right)^{4} + 4 \, \cos\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \cos\left(2 \, f x + 2 \, e\right) + 1\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}{6}} f}"," ",0,"-1/35*((84*I*2^(1/3)*a^3*cos(10/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 84*2^(1/3)*a^3*sin(10/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + (630*I*2^(1/3)*a^3*cos(2*f*x + 2*e)^2 + 630*I*2^(1/3)*a^3*sin(2*f*x + 2*e)^2 + 1260*I*2^(1/3)*a^3*cos(2*f*x + 2*e) + 630*I*2^(1/3)*a^3)*cos(4/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 630*(2^(1/3)*a^3*cos(2*f*x + 2*e)^2 + 2^(1/3)*a^3*sin(2*f*x + 2*e)^2 + 2*2^(1/3)*a^3*cos(2*f*x + 2*e) + 2^(1/3)*a^3)*sin(4/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*sqrt(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*a^(2/3)*d^(2/3) + ((-360*I*2^(1/3)*a^3*cos(2*f*x + 2*e)^2 - 360*I*2^(1/3)*a^3*sin(2*f*x + 2*e)^2 - 720*I*2^(1/3)*a^3*cos(2*f*x + 2*e) - 360*I*2^(1/3)*a^3)*cos(7/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + (-840*I*2^(1/3)*a^3*cos(2*f*x + 2*e)^4 - 840*I*2^(1/3)*a^3*sin(2*f*x + 2*e)^4 - 3360*I*2^(1/3)*a^3*cos(2*f*x + 2*e)^3 - 5040*I*2^(1/3)*a^3*cos(2*f*x + 2*e)^2 - 3360*I*2^(1/3)*a^3*cos(2*f*x + 2*e) - 840*I*2^(1/3)*a^3 + (-1680*I*2^(1/3)*a^3*cos(2*f*x + 2*e)^2 - 3360*I*2^(1/3)*a^3*cos(2*f*x + 2*e) - 1680*I*2^(1/3)*a^3)*sin(2*f*x + 2*e)^2)*cos(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 360*(2^(1/3)*a^3*cos(2*f*x + 2*e)^2 + 2^(1/3)*a^3*sin(2*f*x + 2*e)^2 + 2*2^(1/3)*a^3*cos(2*f*x + 2*e) + 2^(1/3)*a^3)*sin(7/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 840*(2^(1/3)*a^3*cos(2*f*x + 2*e)^4 + 2^(1/3)*a^3*sin(2*f*x + 2*e)^4 + 4*2^(1/3)*a^3*cos(2*f*x + 2*e)^3 + 6*2^(1/3)*a^3*cos(2*f*x + 2*e)^2 + 4*2^(1/3)*a^3*cos(2*f*x + 2*e) + 2^(1/3)*a^3 + 2*(2^(1/3)*a^3*cos(2*f*x + 2*e)^2 + 2*2^(1/3)*a^3*cos(2*f*x + 2*e) + 2^(1/3)*a^3)*sin(2*f*x + 2*e)^2)*sin(1/3*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))*a^(2/3)*d^(2/3))/((cos(2*f*x + 2*e)^4 + sin(2*f*x + 2*e)^4 + 4*cos(2*f*x + 2*e)^3 + 2*(cos(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)*sin(2*f*x + 2*e)^2 + 6*cos(2*f*x + 2*e)^2 + 4*cos(2*f*x + 2*e) + 1)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/6)*f)","B",0
450,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^5,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^5*(e*sec(d*x + c))^m, x)","F",0
451,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3*(e*sec(d*x + c))^m, x)","F",0
452,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2*(e*sec(d*x + c))^m, x)","F",0
453,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)*(e*sec(d*x + c))^m, x)","F",0
454,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
455,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
456,-2,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(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
457,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*(e*sec(d*x + c))^m, x)","F",0
458,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*(e*sec(d*x + c))^m, x)","F",0
459,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*(e*sec(d*x + c))^m, x)","F",0
460,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*(e*sec(d*x + c))^m, x)","F",0
461,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{m}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m/sqrt(I*a*tan(d*x + c) + a), x)","F",0
462,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
463,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
464,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{m} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m*(I*a*tan(d*x + c) + a)^n, x)","F",0
465,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^6, x)","F",0
466,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^4, x)","F",0
467,1,28,0,0.384083," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","-\frac{i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n + 1}}{a d {\left(n + 1\right)}}"," ",0,"-I*(I*a*tan(d*x + c) + a)^(n + 1)/(a*d*(n + 1))","A",0
468,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^2, x)","F",0
469,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^4, x)","F",0
470,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^6, x)","F",0
471,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^5, x)","F",0
472,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^3, x)","F",0
473,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c), x)","F",0
474,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c), x)","F",0
475,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^3, x)","F",0
476,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^5, x)","F",0
477,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
478,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
479,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a)^n, x)","F",0
480,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\sqrt{e \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/sqrt(e*sec(d*x + c)), x)","F",0
481,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/(e*sec(d*x + c))^(3/2), x)","F",0
482,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/(e*sec(d*x + c))^(5/2), x)","F",0
483,1,432,0,1.266415," ","integrate((e*sec(d*x+c))^(-4-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{{\left(-i \, a^{n} n^{4} + 4 i \, a^{n} n^{3} + 4 i \, a^{n} n^{2} - 16 i \, a^{n} n\right)} \cos\left({\left(d x + c\right)} {\left(n + 4\right)}\right) + {\left(-4 i \, a^{n} n^{4} + 8 i \, a^{n} n^{3} + 64 i \, a^{n} n^{2} - 128 i \, a^{n} n\right)} \cos\left({\left(d x + c\right)} {\left(n + 2\right)}\right) + {\left(-4 i \, a^{n} n^{4} - 8 i \, a^{n} n^{3} + 64 i \, a^{n} n^{2} + 128 i \, a^{n} n\right)} \cos\left({\left(d x + c\right)} {\left(n - 2\right)}\right) + {\left(-i \, a^{n} n^{4} - 4 i \, a^{n} n^{3} + 4 i \, a^{n} n^{2} + 16 i \, a^{n} n\right)} \cos\left({\left(d x + c\right)} {\left(n - 4\right)}\right) + {\left(-6 i \, a^{n} n^{4} + 120 i \, a^{n} n^{2} - 384 i \, a^{n}\right)} \cos\left({\left(d x + c\right)} n\right) + {\left(a^{n} n^{4} - 4 \, a^{n} n^{3} - 4 \, a^{n} n^{2} + 16 \, a^{n} n\right)} \sin\left({\left(d x + c\right)} {\left(n + 4\right)}\right) + 4 \, {\left(a^{n} n^{4} - 2 \, a^{n} n^{3} - 16 \, a^{n} n^{2} + 32 \, a^{n} n\right)} \sin\left({\left(d x + c\right)} {\left(n + 2\right)}\right) + 4 \, {\left(a^{n} n^{4} + 2 \, a^{n} n^{3} - 16 \, a^{n} n^{2} - 32 \, a^{n} n\right)} \sin\left({\left(d x + c\right)} {\left(n - 2\right)}\right) + {\left(a^{n} n^{4} + 4 \, a^{n} n^{3} - 4 \, a^{n} n^{2} - 16 \, a^{n} n\right)} \sin\left({\left(d x + c\right)} {\left(n - 4\right)}\right) + 6 \, {\left(a^{n} n^{4} - 20 \, a^{n} n^{2} + 64 \, a^{n}\right)} \sin\left({\left(d x + c\right)} n\right)}{16 \, {\left(e^{n + 4} n^{5} - 20 \, e^{n + 4} n^{3} + 64 \, e^{n + 4} n\right)} d}"," ",0,"1/16*((-I*a^n*n^4 + 4*I*a^n*n^3 + 4*I*a^n*n^2 - 16*I*a^n*n)*cos((d*x + c)*(n + 4)) + (-4*I*a^n*n^4 + 8*I*a^n*n^3 + 64*I*a^n*n^2 - 128*I*a^n*n)*cos((d*x + c)*(n + 2)) + (-4*I*a^n*n^4 - 8*I*a^n*n^3 + 64*I*a^n*n^2 + 128*I*a^n*n)*cos((d*x + c)*(n - 2)) + (-I*a^n*n^4 - 4*I*a^n*n^3 + 4*I*a^n*n^2 + 16*I*a^n*n)*cos((d*x + c)*(n - 4)) + (-6*I*a^n*n^4 + 120*I*a^n*n^2 - 384*I*a^n)*cos((d*x + c)*n) + (a^n*n^4 - 4*a^n*n^3 - 4*a^n*n^2 + 16*a^n*n)*sin((d*x + c)*(n + 4)) + 4*(a^n*n^4 - 2*a^n*n^3 - 16*a^n*n^2 + 32*a^n*n)*sin((d*x + c)*(n + 2)) + 4*(a^n*n^4 + 2*a^n*n^3 - 16*a^n*n^2 - 32*a^n*n)*sin((d*x + c)*(n - 2)) + (a^n*n^4 + 4*a^n*n^3 - 4*a^n*n^2 - 16*a^n*n)*sin((d*x + c)*(n - 4)) + 6*(a^n*n^4 - 20*a^n*n^2 + 64*a^n)*sin((d*x + c)*n))/((e^(n + 4)*n^5 - 20*e^(n + 4)*n^3 + 64*e^(n + 4)*n)*d)","A",0
484,1,344,0,1.087898," ","integrate((e*sec(d*x+c))^(-3-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{{\left(-i \, a^{n} n^{3} + 3 i \, a^{n} n^{2} + i \, a^{n} n - 3 i \, a^{n}\right)} \cos\left({\left(d x + c\right)} {\left(n + 3\right)}\right) + {\left(-3 i \, a^{n} n^{3} + 3 i \, a^{n} n^{2} + 27 i \, a^{n} n - 27 i \, a^{n}\right)} \cos\left({\left(d x + c\right)} {\left(n + 1\right)}\right) + {\left(-3 i \, a^{n} n^{3} - 3 i \, a^{n} n^{2} + 27 i \, a^{n} n + 27 i \, a^{n}\right)} \cos\left({\left(d x + c\right)} {\left(n - 1\right)}\right) + {\left(-i \, a^{n} n^{3} - 3 i \, a^{n} n^{2} + i \, a^{n} n + 3 i \, a^{n}\right)} \cos\left({\left(d x + c\right)} {\left(n - 3\right)}\right) + {\left(a^{n} n^{3} - 3 \, a^{n} n^{2} - a^{n} n + 3 \, a^{n}\right)} \sin\left({\left(d x + c\right)} {\left(n + 3\right)}\right) + 3 \, {\left(a^{n} n^{3} - a^{n} n^{2} - 9 \, a^{n} n + 9 \, a^{n}\right)} \sin\left({\left(d x + c\right)} {\left(n + 1\right)}\right) + 3 \, {\left(a^{n} n^{3} + a^{n} n^{2} - 9 \, a^{n} n - 9 \, a^{n}\right)} \sin\left({\left(d x + c\right)} {\left(n - 1\right)}\right) + {\left(a^{n} n^{3} + 3 \, a^{n} n^{2} - a^{n} n - 3 \, a^{n}\right)} \sin\left({\left(d x + c\right)} {\left(n - 3\right)}\right)}{8 \, {\left(e^{n + 3} n^{4} - 10 \, e^{n + 3} n^{2} + 9 \, e^{n + 3}\right)} d}"," ",0,"1/8*((-I*a^n*n^3 + 3*I*a^n*n^2 + I*a^n*n - 3*I*a^n)*cos((d*x + c)*(n + 3)) + (-3*I*a^n*n^3 + 3*I*a^n*n^2 + 27*I*a^n*n - 27*I*a^n)*cos((d*x + c)*(n + 1)) + (-3*I*a^n*n^3 - 3*I*a^n*n^2 + 27*I*a^n*n + 27*I*a^n)*cos((d*x + c)*(n - 1)) + (-I*a^n*n^3 - 3*I*a^n*n^2 + I*a^n*n + 3*I*a^n)*cos((d*x + c)*(n - 3)) + (a^n*n^3 - 3*a^n*n^2 - a^n*n + 3*a^n)*sin((d*x + c)*(n + 3)) + 3*(a^n*n^3 - a^n*n^2 - 9*a^n*n + 9*a^n)*sin((d*x + c)*(n + 1)) + 3*(a^n*n^3 + a^n*n^2 - 9*a^n*n - 9*a^n)*sin((d*x + c)*(n - 1)) + (a^n*n^3 + 3*a^n*n^2 - a^n*n - 3*a^n)*sin((d*x + c)*(n - 3)))/((e^(n + 3)*n^4 - 10*e^(n + 3)*n^2 + 9*e^(n + 3))*d)","A",0
485,1,174,0,0.729521," ","integrate((e*sec(d*x+c))^(-2-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{{\left(-i \, a^{n} n^{2} + 2 i \, a^{n} n\right)} \cos\left({\left(d x + c\right)} {\left(n + 2\right)}\right) + {\left(-i \, a^{n} n^{2} - 2 i \, a^{n} n\right)} \cos\left({\left(d x + c\right)} {\left(n - 2\right)}\right) + {\left(-2 i \, a^{n} n^{2} + 8 i \, a^{n}\right)} \cos\left({\left(d x + c\right)} n\right) + {\left(a^{n} n^{2} - 2 \, a^{n} n\right)} \sin\left({\left(d x + c\right)} {\left(n + 2\right)}\right) + {\left(a^{n} n^{2} + 2 \, a^{n} n\right)} \sin\left({\left(d x + c\right)} {\left(n - 2\right)}\right) + 2 \, {\left(a^{n} n^{2} - 4 \, a^{n}\right)} \sin\left({\left(d x + c\right)} n\right)}{4 \, {\left(e^{n + 2} n^{3} - 4 \, e^{n + 2} n\right)} d}"," ",0,"1/4*((-I*a^n*n^2 + 2*I*a^n*n)*cos((d*x + c)*(n + 2)) + (-I*a^n*n^2 - 2*I*a^n*n)*cos((d*x + c)*(n - 2)) + (-2*I*a^n*n^2 + 8*I*a^n)*cos((d*x + c)*n) + (a^n*n^2 - 2*a^n*n)*sin((d*x + c)*(n + 2)) + (a^n*n^2 + 2*a^n*n)*sin((d*x + c)*(n - 2)) + 2*(a^n*n^2 - 4*a^n)*sin((d*x + c)*n))/((e^(n + 2)*n^3 - 4*e^(n + 2)*n)*d)","A",0
486,1,113,0,1.102867," ","integrate((e*sec(d*x+c))^(-1-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{{\left(-i \, a^{n} n + i \, a^{n}\right)} \cos\left({\left(d x + c\right)} {\left(n + 1\right)}\right) + {\left(-i \, a^{n} n - i \, a^{n}\right)} \cos\left({\left(d x + c\right)} {\left(n - 1\right)}\right) + {\left(a^{n} n - a^{n}\right)} \sin\left({\left(d x + c\right)} {\left(n + 1\right)}\right) + {\left(a^{n} n + a^{n}\right)} \sin\left({\left(d x + c\right)} {\left(n - 1\right)}\right)}{2 \, {\left(e^{n + 1} n^{2} - e^{n + 1}\right)} d}"," ",0,"1/2*((-I*a^n*n + I*a^n)*cos((d*x + c)*(n + 1)) + (-I*a^n*n - I*a^n)*cos((d*x + c)*(n - 1)) + (a^n*n - a^n)*sin((d*x + c)*(n + 1)) + (a^n*n + a^n)*sin((d*x + c)*(n - 1)))/((e^(n + 1)*n^2 - e^(n + 1))*d)","A",0
487,1,86,0,0.901078," ","integrate((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^n),x, algorithm=""maxima"")","-\frac{i \, a^{n} e^{\left(n \log\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right) - n \log\left(-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)\right)}}{d e^{n} n}"," ",0,"-I*a^n*e^(n*log(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1) - n*log(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))/(d*e^n*n)","B",0
488,-1,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,-1,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,1,1062,0,3.280016," ","integrate((e*sec(d*x+c))^(6-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","-\frac{64 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} a^{n} e^{6} \cos\left(n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 64 i \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} a^{n} e^{6} \sin\left(n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 32 \, {\left(a^{n} e^{6} n^{2} - 9 \, a^{n} e^{6} n + 20 \, a^{n} e^{6}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} \cos\left(4 \, d x + n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right) + 4 \, c\right) - 64 \, {\left(a^{n} e^{6} n - 5 \, a^{n} e^{6}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} \cos\left(2 \, d x + n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right) + 2 \, c\right) + {\left(32 i \, a^{n} e^{6} n^{2} - 288 i \, a^{n} e^{6} n + 640 i \, a^{n} e^{6}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} \sin\left(4 \, d x + n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right) + 4 \, c\right) + {\left(-64 i \, a^{n} e^{6} n + 320 i \, a^{n} e^{6}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} \sin\left(2 \, d x + n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right) + 2 \, c\right)}{{\left({\left(-i \, e^{2 \, n} n^{3} + 12 i \, e^{2 \, n} n^{2} - 47 i \, e^{2 \, n} n + 60 i \, e^{2 \, n}\right)} 2^{n} \cos\left(10 \, d x + 10 \, c\right) + {\left(-5 i \, e^{2 \, n} n^{3} + 60 i \, e^{2 \, n} n^{2} - 235 i \, e^{2 \, n} n + 300 i \, e^{2 \, n}\right)} 2^{n} \cos\left(8 \, d x + 8 \, c\right) + {\left(-10 i \, e^{2 \, n} n^{3} + 120 i \, e^{2 \, n} n^{2} - 470 i \, e^{2 \, n} n + 600 i \, e^{2 \, n}\right)} 2^{n} \cos\left(6 \, d x + 6 \, c\right) + {\left(-10 i \, e^{2 \, n} n^{3} + 120 i \, e^{2 \, n} n^{2} - 470 i \, e^{2 \, n} n + 600 i \, e^{2 \, n}\right)} 2^{n} \cos\left(4 \, d x + 4 \, c\right) + {\left(-5 i \, e^{2 \, n} n^{3} + 60 i \, e^{2 \, n} n^{2} - 235 i \, e^{2 \, n} n + 300 i \, e^{2 \, n}\right)} 2^{n} \cos\left(2 \, d x + 2 \, c\right) + {\left(e^{2 \, n} n^{3} - 12 \, e^{2 \, n} n^{2} + 47 \, e^{2 \, n} n - 60 \, e^{2 \, n}\right)} 2^{n} \sin\left(10 \, d x + 10 \, c\right) + 5 \, {\left(e^{2 \, n} n^{3} - 12 \, e^{2 \, n} n^{2} + 47 \, e^{2 \, n} n - 60 \, e^{2 \, n}\right)} 2^{n} \sin\left(8 \, d x + 8 \, c\right) + 10 \, {\left(e^{2 \, n} n^{3} - 12 \, e^{2 \, n} n^{2} + 47 \, e^{2 \, n} n - 60 \, e^{2 \, n}\right)} 2^{n} \sin\left(6 \, d x + 6 \, c\right) + 10 \, {\left(e^{2 \, n} n^{3} - 12 \, e^{2 \, n} n^{2} + 47 \, e^{2 \, n} n - 60 \, e^{2 \, n}\right)} 2^{n} \sin\left(4 \, d x + 4 \, c\right) + 5 \, {\left(e^{2 \, n} n^{3} - 12 \, e^{2 \, n} n^{2} + 47 \, e^{2 \, n} n - 60 \, e^{2 \, n}\right)} 2^{n} \sin\left(2 \, d x + 2 \, c\right) + {\left(-i \, e^{2 \, n} n^{3} + 12 i \, e^{2 \, n} n^{2} - 47 i \, e^{2 \, n} n + 60 i \, e^{2 \, n}\right)} 2^{n}\right)} d}"," ",0,"-(64*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*a^n*e^6*cos(n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 64*I*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*a^n*e^6*sin(n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 32*(a^n*e^6*n^2 - 9*a^n*e^6*n + 20*a^n*e^6)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*cos(4*d*x + n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1) + 4*c) - 64*(a^n*e^6*n - 5*a^n*e^6)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*cos(2*d*x + n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1) + 2*c) + (32*I*a^n*e^6*n^2 - 288*I*a^n*e^6*n + 640*I*a^n*e^6)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*sin(4*d*x + n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1) + 4*c) + (-64*I*a^n*e^6*n + 320*I*a^n*e^6)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*sin(2*d*x + n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1) + 2*c))/(((-I*e^(2*n)*n^3 + 12*I*e^(2*n)*n^2 - 47*I*e^(2*n)*n + 60*I*e^(2*n))*2^n*cos(10*d*x + 10*c) + (-5*I*e^(2*n)*n^3 + 60*I*e^(2*n)*n^2 - 235*I*e^(2*n)*n + 300*I*e^(2*n))*2^n*cos(8*d*x + 8*c) + (-10*I*e^(2*n)*n^3 + 120*I*e^(2*n)*n^2 - 470*I*e^(2*n)*n + 600*I*e^(2*n))*2^n*cos(6*d*x + 6*c) + (-10*I*e^(2*n)*n^3 + 120*I*e^(2*n)*n^2 - 470*I*e^(2*n)*n + 600*I*e^(2*n))*2^n*cos(4*d*x + 4*c) + (-5*I*e^(2*n)*n^3 + 60*I*e^(2*n)*n^2 - 235*I*e^(2*n)*n + 300*I*e^(2*n))*2^n*cos(2*d*x + 2*c) + (e^(2*n)*n^3 - 12*e^(2*n)*n^2 + 47*e^(2*n)*n - 60*e^(2*n))*2^n*sin(10*d*x + 10*c) + 5*(e^(2*n)*n^3 - 12*e^(2*n)*n^2 + 47*e^(2*n)*n - 60*e^(2*n))*2^n*sin(8*d*x + 8*c) + 10*(e^(2*n)*n^3 - 12*e^(2*n)*n^2 + 47*e^(2*n)*n - 60*e^(2*n))*2^n*sin(6*d*x + 6*c) + 10*(e^(2*n)*n^3 - 12*e^(2*n)*n^2 + 47*e^(2*n)*n - 60*e^(2*n))*2^n*sin(4*d*x + 4*c) + 5*(e^(2*n)*n^3 - 12*e^(2*n)*n^2 + 47*e^(2*n)*n - 60*e^(2*n))*2^n*sin(2*d*x + 2*c) + (-I*e^(2*n)*n^3 + 12*I*e^(2*n)*n^2 - 47*I*e^(2*n)*n + 60*I*e^(2*n))*2^n)*d)","B",0
492,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 5} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 5)*(I*a*tan(d*x + c) + a)^n, x)","F",0
493,1,594,0,1.262674," ","integrate((e*sec(d*x+c))^(4-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} a^{n} e^{4} \cos\left(n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + 8 i \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} a^{n} e^{4} \sin\left(n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - 8 \, {\left(a^{n} e^{4} n - 3 \, a^{n} e^{4}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} \cos\left(2 \, d x + n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right) + 2 \, c\right) - {\left(8 i \, a^{n} e^{4} n - 24 i \, a^{n} e^{4}\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{2} \, n} \sin\left(2 \, d x + n \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) + 1\right) + 2 \, c\right)}{{\left({\left(-i \, e^{2 \, n} n^{2} + 5 i \, e^{2 \, n} n - 6 i \, e^{2 \, n}\right)} 2^{n} \cos\left(6 \, d x + 6 \, c\right) + {\left(-3 i \, e^{2 \, n} n^{2} + 15 i \, e^{2 \, n} n - 18 i \, e^{2 \, n}\right)} 2^{n} \cos\left(4 \, d x + 4 \, c\right) + {\left(-3 i \, e^{2 \, n} n^{2} + 15 i \, e^{2 \, n} n - 18 i \, e^{2 \, n}\right)} 2^{n} \cos\left(2 \, d x + 2 \, c\right) + {\left(e^{2 \, n} n^{2} - 5 \, e^{2 \, n} n + 6 \, e^{2 \, n}\right)} 2^{n} \sin\left(6 \, d x + 6 \, c\right) + 3 \, {\left(e^{2 \, n} n^{2} - 5 \, e^{2 \, n} n + 6 \, e^{2 \, n}\right)} 2^{n} \sin\left(4 \, d x + 4 \, c\right) + 3 \, {\left(e^{2 \, n} n^{2} - 5 \, e^{2 \, n} n + 6 \, e^{2 \, n}\right)} 2^{n} \sin\left(2 \, d x + 2 \, c\right) + {\left(-i \, e^{2 \, n} n^{2} + 5 i \, e^{2 \, n} n - 6 i \, e^{2 \, n}\right)} 2^{n}\right)} d}"," ",0,"(8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*a^n*e^4*cos(n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) + 8*I*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*a^n*e^4*sin(n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1)) - 8*(a^n*e^4*n - 3*a^n*e^4)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*cos(2*d*x + n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1) + 2*c) - (8*I*a^n*e^4*n - 24*I*a^n*e^4)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 + 2*cos(2*d*x + 2*c) + 1)^(1/2*n)*sin(2*d*x + n*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) + 1) + 2*c))/(((-I*e^(2*n)*n^2 + 5*I*e^(2*n)*n - 6*I*e^(2*n))*2^n*cos(6*d*x + 6*c) + (-3*I*e^(2*n)*n^2 + 15*I*e^(2*n)*n - 18*I*e^(2*n))*2^n*cos(4*d*x + 4*c) + (-3*I*e^(2*n)*n^2 + 15*I*e^(2*n)*n - 18*I*e^(2*n))*2^n*cos(2*d*x + 2*c) + (e^(2*n)*n^2 - 5*e^(2*n)*n + 6*e^(2*n))*2^n*sin(6*d*x + 6*c) + 3*(e^(2*n)*n^2 - 5*e^(2*n)*n + 6*e^(2*n))*2^n*sin(4*d*x + 4*c) + 3*(e^(2*n)*n^2 - 5*e^(2*n)*n + 6*e^(2*n))*2^n*sin(2*d*x + 2*c) + (-I*e^(2*n)*n^2 + 5*I*e^(2*n)*n - 6*I*e^(2*n))*2^n)*d)","B",0
494,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 3} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 3)*(I*a*tan(d*x + c) + a)^n, x)","F",0
495,1,217,0,0.837418," ","integrate((e*sec(d*x+c))^(2-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{{\left(-i \, a^{n} e^{2} - \frac{2 \, a^{n} e^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{i \, a^{n} e^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} e^{\left(n \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right) + n \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right) + n \log\left(-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right) - 2 \, n \log\left(-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)\right)}}{{\left(e^{2 \, n} {\left(n - 1\right)} - \frac{e^{2 \, n} {\left(n - 1\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d}"," ",0,"(-I*a^n*e^2 - 2*a^n*e^2*sin(d*x + c)/(cos(d*x + c) + 1) + I*a^n*e^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*e^(n*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1) + n*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1) + n*log(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1) - 2*n*log(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))/((e^(2*n)*(n - 1) - e^(2*n)*(n - 1)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d)","B",0
496,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 1} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 1)*(I*a*tan(d*x + c) + a)^n, x)","F",0
497,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^(2*n)),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\left(e \sec\left(d x + c\right)\right)^{2 \, n}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/(e*sec(d*x + c))^(2*n), x)","F",0
498,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-1-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n - 1} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n - 1)*(I*a*tan(d*x + c) + a)^n, x)","F",0
499,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-2-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n - 2} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n - 2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
500,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-3-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n - 3} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n - 3)*(I*a*tan(d*x + c) + a)^n, x)","F",0
501,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-2-n),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
502,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-1-n),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
503,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)/((a+I*a*tan(f*x+e))^n),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{2 \, n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{n}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2*n)/(I*a*tan(f*x + e) + a)^n, x)","F",0
504,1,137,0,0.492056," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(1-n),x, algorithm=""maxima"")","\frac{i \, a^{-n + 1} d^{2 \, n} e^{\left(-n \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - n \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right) - n \log\left(-\frac{2 i \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right) + 2 \, n \log\left(-\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)\right)}}{f n}"," ",0,"I*a^(-n + 1)*d^(2*n)*e^(-n*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - n*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1) - n*log(-2*I*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1) + 2*n*log(-sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1))/(f*n)","B",0
505,1,304,0,0.676287," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(2-n),x, algorithm=""maxima"")","\frac{2^{n + 1} a^{2} d^{2 \, n} \cos\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - i \cdot 2^{n + 1} a^{2} d^{2 \, n} \sin\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 2 \, {\left(a^{2} d^{2 \, n} n + a^{2} d^{2 \, n}\right)} 2^{n} \cos\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right) - {\left(2 i \, a^{2} d^{2 \, n} n + 2 i \, a^{2} d^{2 \, n}\right)} 2^{n} \sin\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right)}{{\left(-i \, a^{n} n^{2} - i \, a^{n} n + {\left(-i \, a^{n} n^{2} - i \, a^{n} n\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(a^{n} n^{2} + a^{n} n\right)} \sin\left(2 \, f x + 2 \, e\right)\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}{2} \, n} f}"," ",0,"(2^(n + 1)*a^2*d^(2*n)*cos(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - I*2^(n + 1)*a^2*d^(2*n)*sin(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 2*(a^2*d^(2*n)*n + a^2*d^(2*n))*2^n*cos(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e) - (2*I*a^2*d^(2*n)*n + 2*I*a^2*d^(2*n))*2^n*sin(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e))/((-I*a^n*n^2 - I*a^n*n + (-I*a^n*n^2 - I*a^n*n)*cos(2*f*x + 2*e) + (a^n*n^2 + a^n*n)*sin(2*f*x + 2*e))*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*f)","B",0
506,1,617,0,1.590892," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(3-n),x, algorithm=""maxima"")","\frac{2^{n + 3} a^{3} d^{2 \, n} \cos\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - i \cdot 2^{n + 3} a^{3} d^{2 \, n} \sin\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 8 \, {\left(a^{3} d^{2 \, n} n + 2 \, a^{3} d^{2 \, n}\right)} 2^{n} \cos\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right) + 4 \, {\left(a^{3} d^{2 \, n} n^{2} + 3 \, a^{3} d^{2 \, n} n + 2 \, a^{3} d^{2 \, n}\right)} 2^{n} \cos\left(-4 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, e\right) - {\left(8 i \, a^{3} d^{2 \, n} n + 16 i \, a^{3} d^{2 \, n}\right)} 2^{n} \sin\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right) - {\left(4 i \, a^{3} d^{2 \, n} n^{2} + 12 i \, a^{3} d^{2 \, n} n + 8 i \, a^{3} d^{2 \, n}\right)} 2^{n} \sin\left(-4 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, e\right)}{{\left({\left(-i \, a^{n} n^{3} - 3 i \, a^{n} n^{2} - 2 i \, a^{n} n\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}{2} \, n} \cos\left(4 \, f x + 4 \, e\right) + {\left(a^{n} n^{3} + 3 \, a^{n} n^{2} + 2 \, a^{n} n\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}{2} \, n} \sin\left(4 \, f x + 4 \, e\right) + {\left(-i \, a^{n} n^{3} - 3 i \, a^{n} n^{2} - 2 i \, a^{n} n + {\left(-2 i \, a^{n} n^{3} - 6 i \, a^{n} n^{2} - 4 i \, a^{n} n\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(a^{n} n^{3} + 3 \, a^{n} n^{2} + 2 \, a^{n} n\right)} \sin\left(2 \, f x + 2 \, e\right)\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}{2} \, n}\right)} f}"," ",0,"(2^(n + 3)*a^3*d^(2*n)*cos(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - I*2^(n + 3)*a^3*d^(2*n)*sin(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 8*(a^3*d^(2*n)*n + 2*a^3*d^(2*n))*2^n*cos(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e) + 4*(a^3*d^(2*n)*n^2 + 3*a^3*d^(2*n)*n + 2*a^3*d^(2*n))*2^n*cos(-4*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*e) - (8*I*a^3*d^(2*n)*n + 16*I*a^3*d^(2*n))*2^n*sin(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e) - (4*I*a^3*d^(2*n)*n^2 + 12*I*a^3*d^(2*n)*n + 8*I*a^3*d^(2*n))*2^n*sin(-4*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*e))/(((-I*a^n*n^3 - 3*I*a^n*n^2 - 2*I*a^n*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*cos(4*f*x + 4*e) + (a^n*n^3 + 3*a^n*n^2 + 2*a^n*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*sin(4*f*x + 4*e) + (-I*a^n*n^3 - 3*I*a^n*n^2 - 2*I*a^n*n + (-2*I*a^n*n^3 - 6*I*a^n*n^2 - 4*I*a^n*n)*cos(2*f*x + 2*e) + 2*(a^n*n^3 + 3*a^n*n^2 + 2*a^n*n)*sin(2*f*x + 2*e))*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n))*f)","B",0
507,1,70,0,0.327993," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{5 \, b \tan\left(d x + c\right)^{6} + 6 \, a \tan\left(d x + c\right)^{5} + 15 \, b \tan\left(d x + c\right)^{4} + 20 \, a \tan\left(d x + c\right)^{3} + 15 \, b \tan\left(d x + c\right)^{2} + 30 \, a \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(5*b*tan(d*x + c)^6 + 6*a*tan(d*x + c)^5 + 15*b*tan(d*x + c)^4 + 20*a*tan(d*x + c)^3 + 15*b*tan(d*x + c)^2 + 30*a*tan(d*x + c))/d","A",0
508,1,86,0,0.329686," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, 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)} - \frac{16 \, b}{\cos\left(d x + c\right)^{5}}}{80 \, d}"," ",0,"-1/80*(5*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)) - 16*b/cos(d*x + c)^5)/d","A",0
509,1,48,0,0.328840," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, b \tan\left(d x + c\right)^{4} + 4 \, a \tan\left(d x + c\right)^{3} + 6 \, b \tan\left(d x + c\right)^{2} + 12 \, a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*b*tan(d*x + c)^4 + 4*a*tan(d*x + c)^3 + 6*b*tan(d*x + c)^2 + 12*a*tan(d*x + c))/d","A",0
510,1,61,0,0.337588," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{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)} - \frac{4 \, b}{\cos\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(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)) - 4*b/cos(d*x + c)^3)/d","A",0
511,1,20,0,0.332677," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}{2 \, b d}"," ",0,"1/2*(b*tan(d*x + c) + a)^2/(b*d)","A",0
512,1,31,0,0.334038," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) + \frac{b}{\cos\left(d x + c\right)}}{d}"," ",0,"(a*log(sec(d*x + c) + tan(d*x + c)) + b/cos(d*x + c))/d","A",0
513,1,23,0,0.326133," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{b \cos\left(d x + c\right) - a \sin\left(d x + c\right)}{d}"," ",0,"-(b*cos(d*x + c) - a*sin(d*x + c))/d","A",0
514,1,38,0,0.428257," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} a + \frac{a \tan\left(d x + c\right) - b}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*((d*x + c)*a + (a*tan(d*x + c) - b)/(tan(d*x + c)^2 + 1))/d","A",0
515,1,35,0,0.326068," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{b \cos\left(d x + c\right)^{3} + {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a}{3 \, d}"," ",0,"-1/3*(b*cos(d*x + c)^3 + (sin(d*x + c)^3 - 3*sin(d*x + c))*a)/d","A",0
516,1,61,0,0.425004," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(d x + c\right)} a + \frac{3 \, a \tan\left(d x + c\right)^{3} + 5 \, a \tan\left(d x + c\right) - 2 \, b}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*(3*(d*x + c)*a + (3*a*tan(d*x + c)^3 + 5*a*tan(d*x + c) - 2*b)/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
517,1,133,0,0.334847," ","integrate(sec(d*x+c)^8*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{140 \, b^{2} \tan\left(d x + c\right)^{9} + 315 \, a b \tan\left(d x + c\right)^{8} + 1260 \, a b \tan\left(d x + c\right)^{6} + 180 \, {\left(a^{2} + 3 \, b^{2}\right)} \tan\left(d x + c\right)^{7} + 1890 \, a b \tan\left(d x + c\right)^{4} + 756 \, {\left(a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{5} + 1260 \, a b \tan\left(d x + c\right)^{2} + 420 \, {\left(3 \, a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{3} + 1260 \, a^{2} \tan\left(d x + c\right)}{1260 \, d}"," ",0,"1/1260*(140*b^2*tan(d*x + c)^9 + 315*a*b*tan(d*x + c)^8 + 1260*a*b*tan(d*x + c)^6 + 180*(a^2 + 3*b^2)*tan(d*x + c)^7 + 1890*a*b*tan(d*x + c)^4 + 756*(a^2 + b^2)*tan(d*x + c)^5 + 1260*a*b*tan(d*x + c)^2 + 420*(3*a^2 + b^2)*tan(d*x + c)^3 + 1260*a^2*tan(d*x + c))/d","A",0
518,1,104,0,0.330549," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{15 \, b^{2} \tan\left(d x + c\right)^{7} + 35 \, a b \tan\left(d x + c\right)^{6} + 105 \, a b \tan\left(d x + c\right)^{4} + 21 \, {\left(a^{2} + 2 \, b^{2}\right)} \tan\left(d x + c\right)^{5} + 105 \, a b \tan\left(d x + c\right)^{2} + 35 \, {\left(2 \, a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{3} + 105 \, a^{2} \tan\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*b^2*tan(d*x + c)^7 + 35*a*b*tan(d*x + c)^6 + 105*a*b*tan(d*x + c)^4 + 21*(a^2 + 2*b^2)*tan(d*x + c)^5 + 105*a*b*tan(d*x + c)^2 + 35*(2*a^2 + b^2)*tan(d*x + c)^3 + 105*a^2*tan(d*x + c))/d","A",0
519,1,71,0,0.337795," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, b^{2} \tan\left(d x + c\right)^{5} + 15 \, a b \tan\left(d x + c\right)^{4} + 30 \, a b \tan\left(d x + c\right)^{2} + 10 \, {\left(a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{3} + 30 \, a^{2} \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(6*b^2*tan(d*x + c)^5 + 15*a*b*tan(d*x + c)^4 + 30*a*b*tan(d*x + c)^2 + 10*(a^2 + b^2)*tan(d*x + c)^3 + 30*a^2*tan(d*x + c))/d","A",0
520,1,20,0,0.331101," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{3 \, b d}"," ",0,"1/3*(b*tan(d*x + c) + a)^3/(b*d)","A",0
521,1,55,0,0.427061," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} + b^{2}\right)} {\left(d x + c\right)} - \frac{2 \, a b - {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*((a^2 + b^2)*(d*x + c) - (2*a*b - (a^2 - b^2)*tan(d*x + c))/(tan(d*x + c)^2 + 1))/d","A",0
522,1,85,0,0.432491," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{2} + b^{2}\right)} {\left(d x + c\right)} + \frac{{\left(3 \, a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{3} - 4 \, a b + {\left(5 \, a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*((3*a^2 + b^2)*(d*x + c) + ((3*a^2 + b^2)*tan(d*x + c)^3 - 4*a*b + (5*a^2 - b^2)*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
523,1,220,0,0.345409," ","integrate(sec(d*x+c)^7*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{7 \, b^{2} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 55 \, \sin\left(d x + c\right)^{5} + 73 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{8} - 4 \, \sin\left(d x + c\right)^{6} + 6 \, \sin\left(d x + c\right)^{4} - 4 \, \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)} - 56 \, a^{2} {\left(\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{1536 \, a b}{\cos\left(d x + c\right)^{7}}}{5376 \, d}"," ",0,"1/5376*(7*b^2*(2*(15*sin(d*x + c)^7 - 55*sin(d*x + c)^5 + 73*sin(d*x + c)^3 + 15*sin(d*x + c))/(sin(d*x + c)^8 - 4*sin(d*x + c)^6 + 6*sin(d*x + c)^4 - 4*sin(d*x + c)^2 + 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) - 56*a^2*(2*(15*sin(d*x + c)^5 - 40*sin(d*x + c)^3 + 33*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 15*log(sin(d*x + c) + 1) + 15*log(sin(d*x + c) - 1)) + 1536*a*b/cos(d*x + c)^7)/d","A",0
524,1,180,0,0.345922," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{5 \, b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 8 \, \sin\left(d x + c\right)^{3} - 3 \, \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} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 30 \, a^{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)} + \frac{192 \, a b}{\cos\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(5*b^2*(2*(3*sin(d*x + c)^5 - 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 30*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)) + 192*a*b/cos(d*x + c)^5)/d","A",0
525,1,129,0,0.330306," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\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} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right) + 1\right) + \log\left(\sin\left(d x + c\right) - 1\right)\right)} + \frac{32 \, a b}{\cos\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(3*b^2*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + 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)) + 32*a*b/cos(d*x + c)^3)/d","A",0
526,1,82,0,0.324611," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 4 \, a^{2} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - \frac{8 \, a b}{\cos\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 4*a^2*log(sec(d*x + c) + tan(d*x + c)) - 8*a*b/cos(d*x + c))/d","A",0
527,1,60,0,0.332104," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} - 4 \, a b \cos\left(d x + c\right) + 2 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) - 4*a*b*cos(d*x + c) + 2*a^2*sin(d*x + c))/d","A",0
528,1,52,0,0.331075," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, a b \cos\left(d x + c\right)^{3} - b^{2} \sin\left(d x + c\right)^{3} + {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{2}}{3 \, d}"," ",0,"-1/3*(2*a*b*cos(d*x + c)^3 - b^2*sin(d*x + c)^3 + (sin(d*x + c)^3 - 3*sin(d*x + c))*a^2)/d","A",0
529,1,77,0,0.328340," ","integrate(cos(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, a b \cos\left(d x + c\right)^{5} - {\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} + {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} b^{2}}{15 \, d}"," ",0,"-1/15*(6*a*b*cos(d*x + c)^5 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^2 + (3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*b^2)/d","A",0
530,1,98,0,0.330973," ","integrate(cos(d*x+c)^7*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{30 \, a b \cos\left(d x + c\right)^{7} + 3 \, {\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^{2} - {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} b^{2}}{105 \, d}"," ",0,"-1/105*(30*a*b*cos(d*x + c)^7 + 3*(5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^2 - (15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*b^2)/d","A",0
531,1,176,0,0.358249," ","integrate(sec(d*x+c)^8*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{84 \, b^{3} \tan\left(d x + c\right)^{10} + 280 \, a b^{2} \tan\left(d x + c\right)^{9} + 315 \, {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)^{8} + 120 \, {\left(a^{3} + 9 \, a b^{2}\right)} \tan\left(d x + c\right)^{7} + 420 \, {\left(3 \, a^{2} b + b^{3}\right)} \tan\left(d x + c\right)^{6} + 504 \, {\left(a^{3} + 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{5} + 1260 \, a^{2} b \tan\left(d x + c\right)^{2} + 210 \, {\left(9 \, a^{2} b + b^{3}\right)} \tan\left(d x + c\right)^{4} + 840 \, a^{3} \tan\left(d x + c\right) + 840 \, {\left(a^{3} + a b^{2}\right)} \tan\left(d x + c\right)^{3}}{840 \, d}"," ",0,"1/840*(84*b^3*tan(d*x + c)^10 + 280*a*b^2*tan(d*x + c)^9 + 315*(a^2*b + b^3)*tan(d*x + c)^8 + 120*(a^3 + 9*a*b^2)*tan(d*x + c)^7 + 420*(3*a^2*b + b^3)*tan(d*x + c)^6 + 504*(a^3 + 3*a*b^2)*tan(d*x + c)^5 + 1260*a^2*b*tan(d*x + c)^2 + 210*(9*a^2*b + b^3)*tan(d*x + c)^4 + 840*a^3*tan(d*x + c) + 840*(a^3 + a*b^2)*tan(d*x + c)^3)/d","A",0
532,1,142,0,0.332558," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{105 \, b^{3} \tan\left(d x + c\right)^{8} + 360 \, a b^{2} \tan\left(d x + c\right)^{7} + 140 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \tan\left(d x + c\right)^{6} + 168 \, {\left(a^{3} + 6 \, a b^{2}\right)} \tan\left(d x + c\right)^{5} + 1260 \, a^{2} b \tan\left(d x + c\right)^{2} + 210 \, {\left(6 \, a^{2} b + b^{3}\right)} \tan\left(d x + c\right)^{4} + 840 \, a^{3} \tan\left(d x + c\right) + 280 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{3}}{840 \, d}"," ",0,"1/840*(105*b^3*tan(d*x + c)^8 + 360*a*b^2*tan(d*x + c)^7 + 140*(3*a^2*b + 2*b^3)*tan(d*x + c)^6 + 168*(a^3 + 6*a*b^2)*tan(d*x + c)^5 + 1260*a^2*b*tan(d*x + c)^2 + 210*(6*a^2*b + b^3)*tan(d*x + c)^4 + 840*a^3*tan(d*x + c) + 280*(2*a^3 + 3*a*b^2)*tan(d*x + c)^3)/d","A",0
533,1,98,0,0.378550," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{10 \, b^{3} \tan\left(d x + c\right)^{6} + 36 \, a b^{2} \tan\left(d x + c\right)^{5} + 90 \, a^{2} b \tan\left(d x + c\right)^{2} + 15 \, {\left(3 \, a^{2} b + b^{3}\right)} \tan\left(d x + c\right)^{4} + 60 \, a^{3} \tan\left(d x + c\right) + 20 \, {\left(a^{3} + 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{3}}{60 \, d}"," ",0,"1/60*(10*b^3*tan(d*x + c)^6 + 36*a*b^2*tan(d*x + c)^5 + 90*a^2*b*tan(d*x + c)^2 + 15*(3*a^2*b + b^3)*tan(d*x + c)^4 + 60*a^3*tan(d*x + c) + 20*(a^3 + 3*a*b^2)*tan(d*x + c)^3)/d","A",0
534,1,20,0,0.342787," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{4}}{4 \, b d}"," ",0,"1/4*(b*tan(d*x + c) + a)^4/(b*d)","A",0
535,1,81,0,0.433494," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + {\left(a^{3} + 3 \, a b^{2}\right)} {\left(d x + c\right)} - \frac{3 \, a^{2} b - b^{3} - {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*(b^3*log(tan(d*x + c)^2 + 1) + (a^3 + 3*a*b^2)*(d*x + c) - (3*a^2*b - b^3 - (a^3 - 3*a*b^2)*tan(d*x + c))/(tan(d*x + c)^2 + 1))/d","A",0
536,1,110,0,0.436117," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, {\left(a^{3} + a b^{2}\right)} {\left(d x + c\right)} - \frac{4 \, b^{3} \tan\left(d x + c\right)^{2} - 3 \, {\left(a^{3} + a b^{2}\right)} \tan\left(d x + c\right)^{3} + 6 \, a^{2} b + 2 \, b^{3} - {\left(5 \, a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*(3*(a^3 + a*b^2)*(d*x + c) - (4*b^3*tan(d*x + c)^2 - 3*(a^3 + a*b^2)*tan(d*x + c)^3 + 6*a^2*b + 2*b^3 - (5*a^3 - 3*a*b^2)*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1))/d","A",0
537,1,208,0,0.387364," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{35 \, a b^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 8 \, \sin\left(d x + c\right)^{3} - 3 \, \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} - 3 \, \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 70 \, 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)} + \frac{672 \, a^{2} b}{\cos\left(d x + c\right)^{5}} - \frac{32 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} b^{3}}{\cos\left(d x + c\right)^{7}}}{1120 \, d}"," ",0,"1/1120*(35*a*b^2*(2*(3*sin(d*x + c)^5 - 8*sin(d*x + c)^3 - 3*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1) - 3*log(sin(d*x + c) + 1) + 3*log(sin(d*x + c) - 1)) - 70*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)) + 672*a^2*b/cos(d*x + c)^5 - 32*(7*cos(d*x + c)^2 - 5)*b^3/cos(d*x + c)^7)/d","A",0
538,1,157,0,0.378805," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{45 \, a b^{2} {\left(\frac{2 \, {\left(\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\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^{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)} + \frac{240 \, a^{2} b}{\cos\left(d x + c\right)^{3}} - \frac{16 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} b^{3}}{\cos\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"1/240*(45*a*b^2*(2*(sin(d*x + c)^3 + sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1) - log(sin(d*x + c) + 1) + 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)) + 240*a^2*b/cos(d*x + c)^3 - 16*(5*cos(d*x + c)^2 - 3)*b^3/cos(d*x + c)^5)/d","A",0
539,1,111,0,0.367290," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{9 \, a b^{2} {\left(\frac{2 \, \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 1} + \log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right)\right)} - 12 \, a^{3} \log\left(\sec\left(d x + c\right) + \tan\left(d x + c\right)\right) - \frac{36 \, a^{2} b}{\cos\left(d x + c\right)} + \frac{4 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} b^{3}}{\cos\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(9*a*b^2*(2*sin(d*x + c)/(sin(d*x + c)^2 - 1) + log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1)) - 12*a^3*log(sec(d*x + c) + tan(d*x + c)) - 36*a^2*b/cos(d*x + c) + 4*(3*cos(d*x + c)^2 - 1)*b^3/cos(d*x + c)^3)/d","A",0
540,1,84,0,0.357250," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, b^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + 3 \, a b^{2} {\left(\log\left(\sin\left(d x + c\right) + 1\right) - \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, \sin\left(d x + c\right)\right)} - 6 \, a^{2} b \cos\left(d x + c\right) + 2 \, a^{3} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*b^3*(1/cos(d*x + c) + cos(d*x + c)) + 3*a*b^2*(log(sin(d*x + c) + 1) - log(sin(d*x + c) - 1) - 2*sin(d*x + c)) - 6*a^2*b*cos(d*x + c) + 2*a^3*sin(d*x + c))/d","A",0
541,1,77,0,0.353123," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 \, a^{2} b \cos\left(d x + c\right)^{3} - 3 \, a b^{2} \sin\left(d x + c\right)^{3} + {\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3} - {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} b^{3}}{3 \, d}"," ",0,"-1/3*(3*a^2*b*cos(d*x + c)^3 - 3*a*b^2*sin(d*x + c)^3 + (sin(d*x + c)^3 - 3*sin(d*x + c))*a^3 - (cos(d*x + c)^3 - 3*cos(d*x + c))*b^3)/d","A",0
542,1,107,0,0.362012," ","integrate(cos(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{9 \, a^{2} b \cos\left(d x + c\right)^{5} - {\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} + 3 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a b^{2} - {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} b^{3}}{15 \, d}"," ",0,"-1/15*(9*a^2*b*cos(d*x + c)^5 - (3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^3 + 3*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a*b^2 - (3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*b^3)/d","A",0
543,1,126,0,0.355144," ","integrate(cos(d*x+c)^7*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{15 \, a^{2} b \cos\left(d x + c\right)^{7} + {\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^{3} - {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a b^{2} - {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} b^{3}}{35 \, d}"," ",0,"-1/35*(15*a^2*b*cos(d*x + c)^7 + (5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^3 - (15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a*b^2 - (5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*b^3)/d","A",0
544,1,108,0,0.339209," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{3 \, b^{3} \tan\left(d x + c\right)^{4} - 4 \, a b^{2} \tan\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b + 2 \, b^{3}\right)} \tan\left(d x + c\right)^{2} - 12 \, {\left(a^{3} + 2 \, a b^{2}\right)} \tan\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{b^{5}}}{12 \, d}"," ",0,"1/12*((3*b^3*tan(d*x + c)^4 - 4*a*b^2*tan(d*x + c)^3 + 6*(a^2*b + 2*b^3)*tan(d*x + c)^2 - 12*(a^3 + 2*a*b^2)*tan(d*x + c))/b^4 + 12*(a^4 + 2*a^2*b^2 + b^4)*log(b*tan(d*x + c) + a)/b^5)/d","A",0
545,1,53,0,0.331003," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{b \tan\left(d x + c\right)^{2} - 2 \, a \tan\left(d x + c\right)}{b^{2}} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{b^{3}}}{2 \, d}"," ",0,"1/2*((b*tan(d*x + c)^2 - 2*a*tan(d*x + c))/b^2 + 2*(a^2 + b^2)*log(b*tan(d*x + c) + a)/b^3)/d","A",0
546,1,18,0,0.337968," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\log\left(b \tan\left(d x + c\right) + a\right)}{b d}"," ",0,"log(b*tan(d*x + c) + a)/(b*d)","A",0
547,1,141,0,0.465798," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{3} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{3} + 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{a \tan\left(d x + c\right) + b}{{\left(a^{2} + b^{2}\right)} \tan\left(d x + c\right)^{2} + a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*b^3*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - b^3*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^3 + 3*a*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + (a*tan(d*x + c) + b)/((a^2 + b^2)*tan(d*x + c)^2 + a^2 + b^2))/d","A",0
548,1,271,0,0.468307," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, b^{5} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{4 \, b^{5} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{4 \, b^{3} \tan\left(d x + c\right)^{2} + {\left(3 \, a^{3} + 7 \, a b^{2}\right)} \tan\left(d x + c\right)^{3} + 2 \, a^{2} b + 6 \, b^{3} + {\left(5 \, a^{3} + 9 \, a b^{2}\right)} \tan\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"1/8*(8*b^5*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 4*b^5*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (4*b^3*tan(d*x + c)^2 + (3*a^3 + 7*a*b^2)*tan(d*x + c)^3 + 2*a^2*b + 6*b^3 + (5*a^3 + 9*a*b^2)*tan(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*tan(d*x + c)^4 + a^4 + 2*a^2*b^2 + b^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*tan(d*x + c)^2))/d","A",0
549,1,361,0,0.451957," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(6 \, a^{2} + 8 \, b^{2} - \frac{3 \, a b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a b \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{12 \, {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)}}{b^{3} - \frac{3 \, b^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, b^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{b^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{4}} + \frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{4}} - \frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}}}{6 \, d}"," ",0,"1/6*(2*(6*a^2 + 8*b^2 - 3*a*b*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a*b*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 12*(a^2 + b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*(a^2 + 2*b^2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/(b^3 - 3*b^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*b^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - b^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 3*(2*a^3 + 3*a*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^4 + 3*(2*a^3 + 3*a*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^4 - 6*(a^4 + 2*a^2*b^2 + b^4)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4))/d","B",0
550,1,163,0,0.436982," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{2}} - \frac{a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{2}} + \frac{\sqrt{a^{2} + b^{2}} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{b^{2}} - \frac{2}{b - \frac{b \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"-(a*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^2 - a*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^2 + sqrt(a^2 + b^2)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/b^2 - 2/(b - b*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","B",0
551,1,80,0,0.432861," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} d}"," ",0,"-log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*d)","A",0
552,1,142,0,0.436214," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{b^{2} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}}{a^{2} + b^{2} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"-(b^2*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(b + a*sin(d*x + c)/(cos(d*x + c) + 1))/(a^2 + b^2 + (a^2 + b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","A",0
553,1,379,0,0.474758," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{3 \, b^{4} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(a^{2} b + 4 \, b^{3} + \frac{6 \, b^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, {\left(a^{3} + 4 \, a b^{2}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}}{3 \, d}"," ",0,"-1/3*(3*b^4*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(a^2*b + 4*b^3 + 6*b^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*(a^3 + 2*a*b^2)*sin(d*x + c)/(cos(d*x + c) + 1) + 2*(a^3 + 4*a*b^2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*(a^2*b + 2*b^3)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*(a^3 + 2*a*b^2)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^4 + 2*a^2*b^2 + b^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6))/d","B",0
554,1,186,0,0.352542," ","integrate(sec(d*x+c)^8/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{10 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}{b^{8} \tan\left(d x + c\right) + a b^{7}} - \frac{2 \, b^{4} \tan\left(d x + c\right)^{5} - 5 \, a b^{3} \tan\left(d x + c\right)^{4} + 10 \, {\left(a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{3} - 10 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \tan\left(d x + c\right)^{2} + 10 \, {\left(5 \, a^{4} + 9 \, a^{2} b^{2} + 3 \, b^{4}\right)} \tan\left(d x + c\right)}{b^{6}} + \frac{60 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{b^{7}}}{10 \, d}"," ",0,"-1/10*(10*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)/(b^8*tan(d*x + c) + a*b^7) - (2*b^4*tan(d*x + c)^5 - 5*a*b^3*tan(d*x + c)^4 + 10*(a^2*b^2 + b^4)*tan(d*x + c)^3 - 10*(2*a^3*b + 3*a*b^3)*tan(d*x + c)^2 + 10*(5*a^4 + 9*a^2*b^2 + 3*b^4)*tan(d*x + c))/b^6 + 60*(a^5 + 2*a^3*b^2 + a*b^4)*log(b*tan(d*x + c) + a)/b^7)/d","A",0
555,1,115,0,0.329839," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}{b^{6} \tan\left(d x + c\right) + a b^{5}} - \frac{b^{2} \tan\left(d x + c\right)^{3} - 3 \, a b \tan\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \tan\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{3} + a b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{b^{5}}}{3 \, d}"," ",0,"-1/3*(3*(a^4 + 2*a^2*b^2 + b^4)/(b^6*tan(d*x + c) + a*b^5) - (b^2*tan(d*x + c)^3 - 3*a*b*tan(d*x + c)^2 + 3*(3*a^2 + 2*b^2)*tan(d*x + c))/b^4 + 12*(a^3 + a*b^2)*log(b*tan(d*x + c) + a)/b^5)/d","A",0
556,1,60,0,0.325766," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{a^{2} + b^{2}}{b^{4} \tan\left(d x + c\right) + a b^{3}} + \frac{2 \, a \log\left(b \tan\left(d x + c\right) + a\right)}{b^{3}} - \frac{\tan\left(d x + c\right)}{b^{2}}}{d}"," ",0,"-((a^2 + b^2)/(b^4*tan(d*x + c) + a*b^3) + 2*a*log(b*tan(d*x + c) + a)/b^3 - tan(d*x + c)/b^2)/d","A",0
557,1,20,0,0.324529," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} b d}"," ",0,"-1/((b*tan(d*x + c) + a)*b*d)","A",0
558,1,282,0,0.437626," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{8 \, a b^{3} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{4 \, a b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{4} + 6 \, a^{2} b^{2} - 3 \, b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, a^{2} b - 2 \, b^{3} + {\left(a^{2} b - 3 \, b^{3}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} \tan\left(d x + c\right)}{a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(8*a*b^3*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 4*a*b^3*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^4 + 6*a^2*b^2 - 3*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (2*a^2*b - 2*b^3 + (a^2*b - 3*b^3)*tan(d*x + c)^2 + (a^3 + a*b^2)*tan(d*x + c))/(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*tan(d*x + c)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*tan(d*x + c)^2 + (a^4*b + 2*a^2*b^3 + b^5)*tan(d*x + c)))/d","A",0
559,1,502,0,0.445374," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{48 \, a b^{5} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{24 \, a b^{5} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{3 \, {\left(a^{6} + 5 \, a^{4} b^{2} + 15 \, a^{2} b^{4} - 5 \, b^{6}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{4 \, a^{4} b + 20 \, a^{2} b^{3} - 8 \, b^{5} + 3 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 5 \, b^{5}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{5} + 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \tan\left(d x + c\right)^{3} + {\left(5 \, a^{4} b + 28 \, a^{2} b^{3} - 25 \, b^{5}\right)} \tan\left(d x + c\right)^{2} + {\left(5 \, a^{5} + 16 \, a^{3} b^{2} + 11 \, a b^{4}\right)} \tan\left(d x + c\right)}{a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{5} + {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)}}{8 \, d}"," ",0,"1/8*(48*a*b^5*log(b*tan(d*x + c) + a)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 24*a*b^5*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3*(a^6 + 5*a^4*b^2 + 15*a^2*b^4 - 5*b^6)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + (4*a^4*b + 20*a^2*b^3 - 8*b^5 + 3*(a^4*b + 4*a^2*b^3 - 5*b^5)*tan(d*x + c)^4 + 3*(a^5 + 4*a^3*b^2 + 3*a*b^4)*tan(d*x + c)^3 + (5*a^4*b + 28*a^2*b^3 - 25*b^5)*tan(d*x + c)^2 + (5*a^5 + 16*a^3*b^2 + 11*a*b^4)*tan(d*x + c))/(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6 + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(d*x + c)^5 + (a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*tan(d*x + c)^4 + 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(d*x + c)^3 + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*tan(d*x + c)^2 + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*tan(d*x + c)))/d","B",0
560,1,827,0,0.633207," ","integrate(sec(d*x+c)^7/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(120 \, a^{5} + 160 \, a^{3} b^{2} + 24 \, a b^{4} + \frac{{\left(180 \, a^{4} b + 245 \, a^{2} b^{3} + 24 \, b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, {\left(48 \, a^{5} + 68 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(300 \, a^{4} b + 385 \, a^{2} b^{3} + 48 \, b^{5}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, {\left(72 \, a^{5} + 100 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{48 \, {\left(15 \, a^{4} b + 20 \, a^{2} b^{3} + 3 \, b^{5}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{30 \, {\left(16 \, a^{5} + 20 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, {\left(60 \, a^{4} b + 85 \, a^{2} b^{3} + 16 \, b^{5}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{30 \, {\left(4 \, a^{5} + 4 \, a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{3 \, {\left(20 \, a^{4} b + 25 \, a^{2} b^{3} + 8 \, b^{5}\right)} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)}}{a^{2} b^{5} + \frac{2 \, a b^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, a^{2} b^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a b^{6} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, a^{2} b^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{12 \, a b^{6} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{10 \, a^{2} b^{5} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{8 \, a b^{6} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{5 \, a^{2} b^{5} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{2 \, a b^{6} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} b^{5} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{120 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}} - \frac{15 \, {\left(8 \, a^{4} + 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{6}} + \frac{15 \, {\left(8 \, a^{4} + 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{6}}}{24 \, d}"," ",0,"-1/24*(2*(120*a^5 + 160*a^3*b^2 + 24*a*b^4 + (180*a^4*b + 245*a^2*b^3 + 24*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 10*(48*a^5 + 68*a^3*b^2 + 15*a*b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(300*a^4*b + 385*a^2*b^3 + 48*b^5)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*(72*a^5 + 100*a^3*b^2 + 15*a*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 48*(15*a^4*b + 20*a^2*b^3 + 3*b^5)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 30*(16*a^5 + 20*a^3*b^2 + 3*a*b^4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*(60*a^4*b + 85*a^2*b^3 + 16*b^5)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 30*(4*a^5 + 4*a^3*b^2 - a*b^4)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 3*(20*a^4*b + 25*a^2*b^3 + 8*b^5)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^2*b^5 + 2*a*b^6*sin(d*x + c)/(cos(d*x + c) + 1) - 5*a^2*b^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a*b^6*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*a^2*b^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 12*a*b^6*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 10*a^2*b^5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 8*a*b^6*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 5*a^2*b^5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 2*a*b^6*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*b^5*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 120*(a^4 + 2*a^2*b^2 + b^4)*a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6) - 15*(8*a^4 + 12*a^2*b^2 + 3*b^4)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^6 + 15*(8*a^4 + 12*a^2*b^2 + 3*b^4)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^6)/d","B",0
561,1,471,0,0.480797," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(6 \, a^{3} + 2 \, a b^{2} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(9 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, {\left(2 \, a^{3} + a b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(3 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(3 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{2} b^{3} + \frac{2 \, a b^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, a^{2} b^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, a b^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{2} b^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, a b^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{2} b^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{6 \, \sqrt{a^{2} + b^{2}} a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{b^{4}} - \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{4}} + \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{4}}}{2 \, d}"," ",0,"-1/2*(2*(6*a^3 + 2*a*b^2 + 6*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (9*a^2*b + 2*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - 6*(2*a^3 + a*b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(3*a^2*b + b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (3*a^2*b + 2*b^3)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^2*b^3 + 2*a*b^4*sin(d*x + c)/(cos(d*x + c) + 1) - 3*a^2*b^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*a*b^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^2*b^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*a*b^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^2*b^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 6*sqrt(a^2 + b^2)*a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/b^4 - 3*(2*a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^4 + 3*(2*a^2 + b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^4)/d","B",0
562,1,212,0,0.454560," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a + \frac{b \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}}{a^{2} b + \frac{2 \, a b^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{a^{2} b \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} - \frac{a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{2}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{2}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{2}}}{d}"," ",0,"-(2*(a + b*sin(d*x + c)/(cos(d*x + c) + 1))/(a^2*b + 2*a*b^2*sin(d*x + c)/(cos(d*x + c) + 1) - a^2*b*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) - a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^2) - log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^2 + log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^2)/d","B",0
563,1,182,0,0.690986," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{a \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(a b + \frac{b^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}}{a^{4} + a^{2} b^{2} + \frac{2 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{4} + a^{2} b^{2}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}}{d}"," ",0,"-(a*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) + 2*(a*b + b^2*sin(d*x + c)/(cos(d*x + c) + 1))/(a^4 + a^2*b^2 + 2*(a^3*b + a*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^4 + a^2*b^2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","B",0
564,1,348,0,0.512421," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, a b^{2} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, a^{3} b - a b^{3} - \frac{3 \, a b^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(a^{4} + 3 \, a^{2} b^{2} - b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{4} - a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + \frac{2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}}{d}"," ",0,"-(3*a*b^2*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(2*a^3*b - a*b^3 - 3*a*b^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (a^4 + 3*a^2*b^2 - b^4)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^4 - a^2*b^2 + b^4)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^6 + 2*a^4*b^2 + a^2*b^4 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - (a^6 + 2*a^4*b^2 + a^2*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4))/d","B",0
565,1,772,0,0.623881," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{15 \, a b^{4} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(2 \, a^{5} b + 14 \, a^{3} b^{3} - 3 \, a b^{5} - \frac{15 \, a b^{5} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{{\left(3 \, a^{6} + 13 \, a^{4} b^{2} + 22 \, a^{2} b^{4} - 3 \, b^{6}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{{\left(4 \, a^{5} b + 28 \, a^{3} b^{3} - 21 \, a b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(a^{6} - 9 \, a^{4} b^{2} - 46 \, a^{2} b^{4} + 9 \, b^{6}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, {\left(2 \, a^{5} b + 6 \, a^{3} b^{3} - 5 \, a b^{5}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(a^{6} + 3 \, a^{4} b^{2} + 38 \, a^{2} b^{4} - 9 \, b^{6}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, {\left(a^{6} + 3 \, a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6} + \frac{2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, {\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{{\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}}}{3 \, d}"," ",0,"-1/3*(15*a*b^4*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2*(2*a^5*b + 14*a^3*b^3 - 3*a*b^5 - 15*a*b^5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + (3*a^6 + 13*a^4*b^2 + 22*a^2*b^4 - 3*b^6)*sin(d*x + c)/(cos(d*x + c) + 1) + (4*a^5*b + 28*a^3*b^3 - 21*a*b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (a^6 - 9*a^4*b^2 - 46*a^2*b^4 + 9*b^6)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*(2*a^5*b + 6*a^3*b^3 - 5*a*b^5)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (a^6 + 3*a^4*b^2 + 38*a^2*b^4 - 9*b^6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*(a^6 + 3*a^4*b^2 - 2*a^2*b^4 + b^6)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(d*x + c)/(cos(d*x + c) + 1) + 2*(a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*(a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - (a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8))/d","B",0
566,1,200,0,0.493495," ","integrate(sec(d*x+c)^8/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(11 \, a^{6} + 21 \, a^{4} b^{2} + 9 \, a^{2} b^{4} - b^{6} + 12 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)\right)}}{b^{9} \tan\left(d x + c\right)^{2} + 2 \, a b^{8} \tan\left(d x + c\right) + a^{2} b^{7}} + \frac{b^{3} \tan\left(d x + c\right)^{4} - 4 \, a b^{2} \tan\left(d x + c\right)^{3} + 6 \, {\left(2 \, a^{2} b + b^{3}\right)} \tan\left(d x + c\right)^{2} - 4 \, {\left(10 \, a^{3} + 9 \, a b^{2}\right)} \tan\left(d x + c\right)}{b^{6}} + \frac{12 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{b^{7}}}{4 \, d}"," ",0,"1/4*(2*(11*a^6 + 21*a^4*b^2 + 9*a^2*b^4 - b^6 + 12*(a^5*b + 2*a^3*b^3 + a*b^5)*tan(d*x + c))/(b^9*tan(d*x + c)^2 + 2*a*b^8*tan(d*x + c) + a^2*b^7) + (b^3*tan(d*x + c)^4 - 4*a*b^2*tan(d*x + c)^3 + 6*(2*a^2*b + b^3)*tan(d*x + c)^2 - 4*(10*a^3 + 9*a*b^2)*tan(d*x + c))/b^6 + 12*(5*a^4 + 6*a^2*b^2 + b^4)*log(b*tan(d*x + c) + a)/b^7)/d","A",0
567,1,128,0,0.438171," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{7 \, a^{4} + 6 \, a^{2} b^{2} - b^{4} + 8 \, {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)}{b^{7} \tan\left(d x + c\right)^{2} + 2 \, a b^{6} \tan\left(d x + c\right) + a^{2} b^{5}} + \frac{b \tan\left(d x + c\right)^{2} - 6 \, a \tan\left(d x + c\right)}{b^{4}} + \frac{4 \, {\left(3 \, a^{2} + b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{b^{5}}}{2 \, d}"," ",0,"1/2*((7*a^4 + 6*a^2*b^2 - b^4 + 8*(a^3*b + a*b^3)*tan(d*x + c))/(b^7*tan(d*x + c)^2 + 2*a*b^6*tan(d*x + c) + a^2*b^5) + (b*tan(d*x + c)^2 - 6*a*tan(d*x + c))/b^4 + 4*(3*a^2 + b^2)*log(b*tan(d*x + c) + a)/b^5)/d","A",0
568,1,78,0,0.349833," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{4 \, a b \tan\left(d x + c\right) + 3 \, a^{2} - b^{2}}{b^{5} \tan\left(d x + c\right)^{2} + 2 \, a b^{4} \tan\left(d x + c\right) + a^{2} b^{3}} + \frac{2 \, \log\left(b \tan\left(d x + c\right) + a\right)}{b^{3}}}{2 \, d}"," ",0,"1/2*((4*a*b*tan(d*x + c) + 3*a^2 - b^2)/(b^5*tan(d*x + c)^2 + 2*a*b^4*tan(d*x + c) + a^2*b^3) + 2*log(b*tan(d*x + c) + a)/b^3)/d","A",0
569,1,20,0,0.318761," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(b \tan\left(d x + c\right) + a\right)}^{2} b d}"," ",0,"-1/2/((b*tan(d*x + c) + a)^2*b*d)","A",0
570,1,458,0,0.464515," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(a^{5} + 10 \, a^{3} b^{2} - 15 \, a b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{4 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{2 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{3 \, a^{4} b - 10 \, a^{2} b^{3} - b^{5} + {\left(a^{3} b^{2} - 11 \, a b^{4}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{4} b - 6 \, a^{2} b^{3} - b^{5}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{3} b^{2} - 10 \, a b^{4}\right)} \tan\left(d x + c\right)}{a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*((a^5 + 10*a^3*b^2 - 15*a*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 4*(5*a^2*b^3 - b^5)*log(b*tan(d*x + c) + a)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 2*(5*a^2*b^3 - b^5)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + (3*a^4*b - 10*a^2*b^3 - b^5 + (a^3*b^2 - 11*a*b^4)*tan(d*x + c)^3 + 2*(a^4*b - 6*a^2*b^3 - b^5)*tan(d*x + c)^2 + (a^5 + 3*a^3*b^2 - 10*a*b^4)*tan(d*x + c))/(a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*tan(d*x + c)^4 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*tan(d*x + c)^3 + (a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*tan(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*tan(d*x + c)))/d","B",0
571,1,738,0,0.459101," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{7} + 7 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 35 \, a b^{6}\right)} {\left(d x + c\right)}}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{24 \, {\left(7 \, a^{2} b^{5} - b^{7}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{12 \, {\left(7 \, a^{2} b^{5} - b^{7}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{6 \, a^{6} b + 44 \, a^{4} b^{3} - 62 \, a^{2} b^{5} - 4 \, b^{7} + 3 \, {\left(a^{5} b^{2} + 6 \, a^{3} b^{4} - 27 \, a b^{6}\right)} \tan\left(d x + c\right)^{5} + 6 \, {\left(a^{6} b + 6 \, a^{4} b^{3} - 13 \, a^{2} b^{5} - 2 \, b^{7}\right)} \tan\left(d x + c\right)^{4} + {\left(3 \, a^{7} + 23 \, a^{5} b^{2} + 61 \, a^{3} b^{4} - 151 \, a b^{6}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{6} b + 37 \, a^{4} b^{3} - 73 \, a^{2} b^{5} - 9 \, b^{7}\right)} \tan\left(d x + c\right)^{2} + {\left(5 \, a^{7} + 26 \, a^{5} b^{2} + 49 \, a^{3} b^{4} - 68 \, a b^{6}\right)} \tan\left(d x + c\right)}{a^{10} + 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} + 4 \, a^{4} b^{6} + a^{2} b^{8} + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{6} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)^{5} + {\left(a^{10} + 6 \, a^{8} b^{2} + 14 \, a^{6} b^{4} + 16 \, a^{4} b^{6} + 9 \, a^{2} b^{8} + 2 \, b^{10}\right)} \tan\left(d x + c\right)^{4} + 4 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)^{3} + {\left(2 \, a^{10} + 9 \, a^{8} b^{2} + 16 \, a^{6} b^{4} + 14 \, a^{4} b^{6} + 6 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)}}{8 \, d}"," ",0,"1/8*(3*(a^7 + 7*a^5*b^2 + 35*a^3*b^4 - 35*a*b^6)*(d*x + c)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + 24*(7*a^2*b^5 - b^7)*log(b*tan(d*x + c) + a)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - 12*(7*a^2*b^5 - b^7)*log(tan(d*x + c)^2 + 1)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + (6*a^6*b + 44*a^4*b^3 - 62*a^2*b^5 - 4*b^7 + 3*(a^5*b^2 + 6*a^3*b^4 - 27*a*b^6)*tan(d*x + c)^5 + 6*(a^6*b + 6*a^4*b^3 - 13*a^2*b^5 - 2*b^7)*tan(d*x + c)^4 + (3*a^7 + 23*a^5*b^2 + 61*a^3*b^4 - 151*a*b^6)*tan(d*x + c)^3 + 2*(5*a^6*b + 37*a^4*b^3 - 73*a^2*b^5 - 9*b^7)*tan(d*x + c)^2 + (5*a^7 + 26*a^5*b^2 + 49*a^3*b^4 - 68*a*b^6)*tan(d*x + c))/(a^10 + 4*a^8*b^2 + 6*a^6*b^4 + 4*a^4*b^6 + a^2*b^8 + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*tan(d*x + c)^6 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*tan(d*x + c)^5 + (a^10 + 6*a^8*b^2 + 14*a^6*b^4 + 16*a^4*b^6 + 9*a^2*b^8 + 2*b^10)*tan(d*x + c)^4 + 4*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*tan(d*x + c)^3 + (2*a^10 + 9*a^8*b^2 + 16*a^6*b^4 + 14*a^4*b^6 + 6*a^2*b^8 + b^10)*tan(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*tan(d*x + c)))/d","B",0
572,1,902,0,0.747688," ","integrate(sec(d*x+c)^7/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(60 \, a^{6} + 35 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + \frac{{\left(210 \, a^{5} b + 125 \, a^{3} b^{3} - 6 \, a b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(120 \, a^{6} - 10 \, a^{4} b^{2} - 55 \, a^{2} b^{4} + 3 \, b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(330 \, a^{5} b + 205 \, a^{3} b^{3} - 12 \, a b^{5}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, {\left(180 \, a^{6} - 95 \, a^{4} b^{2} - 120 \, a^{2} b^{4} + 9 \, b^{6}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{12 \, {\left(60 \, a^{5} b + 35 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6 \, {\left(40 \, a^{6} - 30 \, a^{4} b^{2} - 35 \, a^{2} b^{4} + 3 \, b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, {\left(50 \, a^{5} b + 25 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3 \, {\left(20 \, a^{6} - 15 \, a^{4} b^{2} - 15 \, a^{2} b^{4} + 2 \, b^{6}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{3 \, {\left(10 \, a^{5} b + 5 \, a^{3} b^{3} - 2 \, a b^{5}\right)} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)}}{a^{4} b^{5} + \frac{4 \, a^{3} b^{6} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, a^{3} b^{6} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{24 \, a^{3} b^{6} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{16 \, a^{3} b^{6} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{4 \, a^{3} b^{6} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{4} b^{5} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{{\left(5 \, a^{4} b^{5} - 4 \, a^{2} b^{7}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, {\left(5 \, a^{4} b^{5} - 6 \, a^{2} b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, {\left(5 \, a^{4} b^{5} - 6 \, a^{2} b^{7}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{{\left(5 \, a^{4} b^{5} - 4 \, a^{2} b^{7}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{15 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{6}} + \frac{15 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{6}} - \frac{15 \, {\left(4 \, a^{4} + 5 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}}}{6 \, d}"," ",0,"1/6*(2*(60*a^6 + 35*a^4*b^2 - 3*a^2*b^4 + (210*a^5*b + 125*a^3*b^3 - 6*a*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(120*a^6 - 10*a^4*b^2 - 55*a^2*b^4 + 3*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(330*a^5*b + 205*a^3*b^3 - 12*a*b^5)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*(180*a^6 - 95*a^4*b^2 - 120*a^2*b^4 + 9*b^6)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 12*(60*a^5*b + 35*a^3*b^3 - 3*a*b^5)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6*(40*a^6 - 30*a^4*b^2 - 35*a^2*b^4 + 3*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*(50*a^5*b + 25*a^3*b^3 - 4*a*b^5)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3*(20*a^6 - 15*a^4*b^2 - 15*a^2*b^4 + 2*b^6)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 3*(10*a^5*b + 5*a^3*b^3 - 2*a*b^5)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^4*b^5 + 4*a^3*b^6*sin(d*x + c)/(cos(d*x + c) + 1) - 16*a^3*b^6*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 24*a^3*b^6*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 16*a^3*b^6*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 4*a^3*b^6*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^4*b^5*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - (5*a^4*b^5 - 4*a^2*b^7)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*(5*a^4*b^5 - 6*a^2*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*(5*a^4*b^5 - 6*a^2*b^7)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + (5*a^4*b^5 - 4*a^2*b^7)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 15*(4*a^3 + 3*a*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^6 + 15*(4*a^3 + 3*a*b^2)*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^6 - 15*(4*a^4 + 5*a^2*b^2 + b^4)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6))/d","B",0
573,1,518,0,0.450439," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(6 \, a^{4} - a^{2} b^{2} + \frac{{\left(21 \, a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(6 \, a^{4} - 9 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(6 \, a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(6 \, a^{4} - 9 \, a^{2} b^{2} + 2 \, b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(3 \, a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{4} b^{3} + \frac{4 \, a^{3} b^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{8 \, a^{3} b^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4 \, a^{3} b^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{4} b^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{{\left(3 \, a^{4} b^{3} - 4 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{{\left(3 \, a^{4} b^{3} - 4 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{6 \, a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}{b^{4}} + \frac{6 \, a \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)}{b^{4}} - \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}}}{2 \, d}"," ",0,"1/2*(2*(6*a^4 - a^2*b^2 + (21*a^3*b - 2*a*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(6*a^4 - 9*a^2*b^2 + b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(6*a^3*b - a*b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (6*a^4 - 9*a^2*b^2 + 2*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (3*a^3*b - 2*a*b^3)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^4*b^3 + 4*a^3*b^4*sin(d*x + c)/(cos(d*x + c) + 1) - 8*a^3*b^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4*a^3*b^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^4*b^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - (3*a^4*b^3 - 4*a^2*b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + (3*a^4*b^3 - 4*a^2*b^5)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 6*a*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1)/b^4 + 6*a*log(sin(d*x + c)/(cos(d*x + c) + 1) - 1)/b^4 - 3*(2*a^2 + b^2)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4))/d","B",0
574,1,326,0,0.448160," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{2} b - \frac{{\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{6} + a^{4} b^{2} + \frac{4 \, {\left(a^{5} b + a^{3} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(a^{6} - a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{5} b + a^{3} b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(a^{6} + a^{4} b^{2}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}}}{2 \, d}"," ",0,"-1/2*(2*(a^2*b - (a^3 - 2*a*b^2)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^2*b - 2*b^3)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (a^3 + 2*a*b^2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^6 + a^4*b^2 + 4*(a^5*b + a^3*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(a^6 - a^4*b^2 - 2*a^2*b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(a^5*b + a^3*b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (a^6 + a^4*b^2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2))/d","B",0
575,1,412,0,0.454366," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(2 \, a^{2} - b^{2}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} + \frac{2 \, {\left(4 \, a^{4} b + a^{2} b^{3} + \frac{{\left(11 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(4 \, a^{4} b - 7 \, a^{2} b^{3} - 2 \, b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4} + \frac{4 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(a^{8} - 3 \, a^{4} b^{4} - 2 \, a^{2} b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}}{2 \, d}"," ",0,"-1/2*((2*a^2 - b^2)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) + 2*(4*a^4*b + a^2*b^3 + (11*a^3*b^2 + 2*a*b^4)*sin(d*x + c)/(cos(d*x + c) + 1) - (4*a^4*b - 7*a^2*b^3 - 2*b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (5*a^3*b^2 + 2*a*b^4)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^8 + 2*a^6*b^2 + a^4*b^4 + 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(a^8 - 3*a^4*b^4 - 2*a^2*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (a^8 + 2*a^6*b^2 + a^4*b^4)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4))/d","B",0
576,1,658,0,0.468578," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(4 \, a^{2} b^{2} - b^{4}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(6 \, a^{6} b - 10 \, a^{4} b^{3} - a^{2} b^{5} + \frac{{\left(2 \, a^{7} + 18 \, a^{5} b^{2} - 31 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(2 \, a^{6} b - 2 \, a^{4} b^{3} + 12 \, a^{2} b^{5} + b^{7}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, {\left(2 \, a^{7} + 2 \, a^{5} b^{2} + 15 \, a^{3} b^{4}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{{\left(2 \, a^{6} b - 30 \, a^{4} b^{3} + 15 \, a^{2} b^{5} + 2 \, b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 9 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}\right)}}{a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6} + \frac{4 \, {\left(a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{10} - a^{8} b^{2} - 9 \, a^{6} b^{4} - 11 \, a^{4} b^{6} - 4 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(a^{10} - a^{8} b^{2} - 9 \, a^{6} b^{4} - 11 \, a^{4} b^{6} - 4 \, a^{2} b^{8}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, {\left(a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{{\left(a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}}{2 \, d}"," ",0,"-1/2*(3*(4*a^2*b^2 - b^4)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 2*(6*a^6*b - 10*a^4*b^3 - a^2*b^5 + (2*a^7 + 18*a^5*b^2 - 31*a^3*b^4 - 2*a*b^6)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(2*a^6*b - 2*a^4*b^3 + 12*a^2*b^5 + b^7)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*(2*a^7 + 2*a^5*b^2 + 15*a^3*b^4)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - (2*a^6*b - 30*a^4*b^3 + 15*a^2*b^5 + 2*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (2*a^7 - 6*a^5*b^2 + 9*a^3*b^4 + 2*a*b^6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/(a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6 + 4*(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^10 - a^8*b^2 - 9*a^6*b^4 - 11*a^4*b^6 - 4*a^2*b^8)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (a^10 - a^8*b^2 - 9*a^6*b^4 - 11*a^4*b^6 - 4*a^2*b^8)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + (a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6))/d","B",0
577,1,1229,0,0.542027," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{15 \, {\left(6 \, a^{2} b^{4} - b^{6}\right)} \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(6 \, a^{8} b + 64 \, a^{6} b^{3} - 50 \, a^{4} b^{5} - 3 \, a^{2} b^{7} + \frac{{\left(6 \, a^{9} + 48 \, a^{7} b^{2} + 202 \, a^{5} b^{4} - 161 \, a^{3} b^{6} - 6 \, a b^{8}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, {\left(6 \, a^{8} b + 56 \, a^{6} b^{3} - 14 \, a^{4} b^{5} - 67 \, a^{2} b^{7} - 3 \, b^{9}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(2 \, a^{9} - 4 \, a^{7} b^{2} - 86 \, a^{5} b^{4} + 133 \, a^{3} b^{6} + 3 \, a b^{8}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, {\left(8 \, a^{8} b + 28 \, a^{6} b^{3} + 188 \, a^{4} b^{5} - 156 \, a^{2} b^{7} - 9 \, b^{9}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, {\left(2 \, a^{9} + 4 \, a^{7} b^{2} + 62 \, a^{5} b^{4} - 255 \, a^{3} b^{6}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2 \, {\left(14 \, a^{8} b + 56 \, a^{6} b^{3} - 246 \, a^{4} b^{5} + 141 \, a^{2} b^{7} + 9 \, b^{9}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{4 \, {\left(2 \, a^{9} + 8 \, a^{7} b^{2} + 42 \, a^{5} b^{4} + 33 \, a^{3} b^{6} - 3 \, a b^{8}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, {\left(2 \, a^{8} b + 8 \, a^{6} b^{3} - 78 \, a^{4} b^{5} + 23 \, a^{2} b^{7} + 2 \, b^{9}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{3 \, {\left(2 \, a^{9} + 8 \, a^{7} b^{2} - 18 \, a^{5} b^{4} + 13 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)}}{a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8} + \frac{4 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{{\left(a^{12} + 8 \, a^{10} b^{2} + 22 \, a^{8} b^{4} + 28 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 4 \, a^{2} b^{10}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2 \, {\left(a^{12} - 2 \, a^{10} b^{2} - 18 \, a^{8} b^{4} - 32 \, a^{6} b^{6} - 23 \, a^{4} b^{8} - 6 \, a^{2} b^{10}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, {\left(a^{12} - 2 \, a^{10} b^{2} - 18 \, a^{8} b^{4} - 32 \, a^{6} b^{6} - 23 \, a^{4} b^{8} - 6 \, a^{2} b^{10}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{8 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{{\left(a^{12} + 8 \, a^{10} b^{2} + 22 \, a^{8} b^{4} + 28 \, a^{6} b^{6} + 17 \, a^{4} b^{8} + 4 \, a^{2} b^{10}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, {\left(a^{11} b + 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} + 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{{\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}}}{6 \, d}"," ",0,"-1/6*(15*(6*a^2*b^4 - b^6)*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*sqrt(a^2 + b^2)) - 2*(6*a^8*b + 64*a^6*b^3 - 50*a^4*b^5 - 3*a^2*b^7 + (6*a^9 + 48*a^7*b^2 + 202*a^5*b^4 - 161*a^3*b^6 - 6*a*b^8)*sin(d*x + c)/(cos(d*x + c) + 1) + 2*(6*a^8*b + 56*a^6*b^3 - 14*a^4*b^5 - 67*a^2*b^7 - 3*b^9)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(2*a^9 - 4*a^7*b^2 - 86*a^5*b^4 + 133*a^3*b^6 + 3*a*b^8)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*(8*a^8*b + 28*a^6*b^3 + 188*a^4*b^5 - 156*a^2*b^7 - 9*b^9)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*(2*a^9 + 4*a^7*b^2 + 62*a^5*b^4 - 255*a^3*b^6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2*(14*a^8*b + 56*a^6*b^3 - 246*a^4*b^5 + 141*a^2*b^7 + 9*b^9)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 4*(2*a^9 + 8*a^7*b^2 + 42*a^5*b^4 + 33*a^3*b^6 - 3*a*b^8)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*(2*a^8*b + 8*a^6*b^3 - 78*a^4*b^5 + 23*a^2*b^7 + 2*b^9)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 3*(2*a^9 + 8*a^7*b^2 - 18*a^5*b^4 + 13*a^3*b^6 + 2*a*b^8)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/(a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8 + 4*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*sin(d*x + c)/(cos(d*x + c) + 1) + (a^12 + 8*a^10*b^2 + 22*a^8*b^4 + 28*a^6*b^6 + 17*a^4*b^8 + 4*a^2*b^10)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2*(a^12 - 2*a^10*b^2 - 18*a^8*b^4 - 32*a^6*b^6 - 23*a^4*b^8 - 6*a^2*b^10)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*(a^12 - 2*a^10*b^2 - 18*a^8*b^4 - 32*a^6*b^6 - 23*a^4*b^8 - 6*a^2*b^10)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 8*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + (a^12 + 8*a^10*b^2 + 22*a^8*b^4 + 28*a^6*b^6 + 17*a^4*b^8 + 4*a^2*b^10)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*(a^11*b + 4*a^9*b^3 + 6*a^7*b^5 + 4*a^5*b^7 + a^3*b^9)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + (a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10))/d","B",0
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579,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a), x)","F",0
580,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a), x)","F",0
581,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a), x)","F",0
582,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{b \tan\left(f x + e\right) + a}{\sqrt{d \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/sqrt(d*sec(f*x + e)), x)","F",0
583,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(3/2), x)","F",0
584,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(5/2), x)","F",0
585,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(7/2), x)","F",0
586,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a)^2, x)","F",0
587,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a)^2, x)","F",0
588,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)^2, x)","F",0
589,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\sqrt{d \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/sqrt(d*sec(f*x + e)), x)","F",0
590,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(3/2), x)","F",0
591,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(5/2), x)","F",0
592,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(7/2), x)","F",0
593,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(9/2), x)","F",0
594,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\int \sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)^3, x)","F",0
597,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\sqrt{d \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/sqrt(d*sec(f*x + e)), x)","F",0
598,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/(d*sec(f*x + e))^(3/2), x)","F",0
599,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/(d*sec(f*x + e))^(5/2), x)","F",0
600,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(7/2)/(b*tan(f*x + e) + a), x)","F",0
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605,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)/(b*tan(f*x + e) + a), x)","F",0
606,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sec\left(f x + e\right)}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))/(b*tan(f*x + e) + a), x)","F",0
607,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)), x)","F",0
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612,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d \sec\left(f x + e\right)}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))/(b*tan(f*x + e) + a)^2, x)","F",0
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615,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a)^2), x)","F",0
616,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a)^2), x)","F",0
617,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)*(b*tan(f*x + e) + a), x)","F",0
625,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a), x)","F",0
626,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(1/3), x)","F",0
627,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x, algorithm=""maxima"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(5/3), x)","F",0
628,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)*(b*tan(f*x + e) + a)^2, x)","F",0
629,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a)^2, x)","F",0
630,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(1/3), x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(5/3), x)","F",0
632,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)/(b*tan(f*x + e) + a), x)","F",0
633,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)/(b*tan(f*x + e) + a), x)","F",0
634,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a)), x)","F",0
635,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(b \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/3)*(b*tan(f*x + e) + a)), x)","F",0
636,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)/(b*tan(f*x + e) + a)^2, x)","F",0
638,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a)^2), x)","F",0
639,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/3)*(b*tan(f*x + e) + a)^2), x)","F",0
640,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{3} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3*(d*sec(f*x + e))^m, x)","F",0
641,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*(d*sec(f*x + e))^m, x)","F",0
642,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)*(d*sec(f*x + e))^m, x)","F",0
643,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{m}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^m/(b*tan(f*x + e) + a), x)","F",0
644,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{m}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^m/(b*tan(f*x + e) + a)^2, x)","F",0
645,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^n,x, algorithm=""maxima"")","\int \left(d \sec\left(f x + e\right)\right)^{m} {\left(b \tan\left(f x + e\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^m*(b*tan(f*x + e) + a)^n, x)","F",0
646,1,286,0,0.339580," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}} + \frac{2 \, {\left({\left(n^{2} + 3 \, n + 2\right)} b^{3} \tan\left(d x + c\right)^{3} + {\left(n^{2} + n\right)} a b^{2} \tan\left(d x + c\right)^{2} - 2 \, a^{2} b n \tan\left(d x + c\right) + 2 \, a^{3}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}}{{\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} b^{3}} + \frac{{\left({\left(n^{4} + 10 \, n^{3} + 35 \, n^{2} + 50 \, n + 24\right)} b^{5} \tan\left(d x + c\right)^{5} + {\left(n^{4} + 6 \, n^{3} + 11 \, n^{2} + 6 \, n\right)} a b^{4} \tan\left(d x + c\right)^{4} - 4 \, {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} a^{2} b^{3} \tan\left(d x + c\right)^{3} + 12 \, {\left(n^{2} + n\right)} a^{3} b^{2} \tan\left(d x + c\right)^{2} - 24 \, a^{4} b n \tan\left(d x + c\right) + 24 \, a^{5}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}}{{\left(n^{5} + 15 \, n^{4} + 85 \, n^{3} + 225 \, n^{2} + 274 \, n + 120\right)} b^{5}}}{d}"," ",0,"((b*tan(d*x + c) + a)^(n + 1)/(b*(n + 1)) + 2*((n^2 + 3*n + 2)*b^3*tan(d*x + c)^3 + (n^2 + n)*a*b^2*tan(d*x + c)^2 - 2*a^2*b*n*tan(d*x + c) + 2*a^3)*(b*tan(d*x + c) + a)^n/((n^3 + 6*n^2 + 11*n + 6)*b^3) + ((n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*b^5*tan(d*x + c)^5 + (n^4 + 6*n^3 + 11*n^2 + 6*n)*a*b^4*tan(d*x + c)^4 - 4*(n^3 + 3*n^2 + 2*n)*a^2*b^3*tan(d*x + c)^3 + 12*(n^2 + n)*a^3*b^2*tan(d*x + c)^2 - 24*a^4*b*n*tan(d*x + c) + 24*a^5)*(b*tan(d*x + c) + a)^n/((n^5 + 15*n^4 + 85*n^3 + 225*n^2 + 274*n + 120)*b^5))/d","A",0
647,1,116,0,0.388487," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}} + \frac{{\left({\left(n^{2} + 3 \, n + 2\right)} b^{3} \tan\left(d x + c\right)^{3} + {\left(n^{2} + n\right)} a b^{2} \tan\left(d x + c\right)^{2} - 2 \, a^{2} b n \tan\left(d x + c\right) + 2 \, a^{3}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}}{{\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} b^{3}}}{d}"," ",0,"((b*tan(d*x + c) + a)^(n + 1)/(b*(n + 1)) + ((n^2 + 3*n + 2)*b^3*tan(d*x + c)^3 + (n^2 + n)*a*b^2*tan(d*x + c)^2 - 2*a^2*b*n*tan(d*x + c) + 2*a^3)*(b*tan(d*x + c) + a)^n/((n^3 + 6*n^2 + 11*n + 6)*b^3))/d","A",0
648,1,26,0,0.446622," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n + 1}}{b d {\left(n + 1\right)}}"," ",0,"(b*tan(d*x + c) + a)^(n + 1)/(b*d*(n + 1))","A",0
649,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cos(d*x + c)^2, x)","F",0
650,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cos(d*x + c)^4, x)","F",0
651,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sec(d*x + c)^3, x)","F",0
652,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sec(d*x + c), x)","F",0
653,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cos(d*x + c), x)","F",0
654,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cos(d*x + c)^3, x)","F",0
655,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(I*a*tan(d*x + c) + a), x)","F",0
656,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(I*a*tan(d*x + c) + a), x)","F",0
657,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a), x)","F",0
658,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(I*a*tan(d*x + c) + a), x)","F",0
659,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
660,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(3/2), x)","F",0
661,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(5/2), x)","F",0
662,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(7/2), x)","F",0
663,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
664,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
665,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
666,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
667,-2,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
668,-2,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
669,-2,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
670,-2,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
671,-2,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
672,-2,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
673,1,202,0,0.654318," ","integrate((e*cos(d*x+c))^(7/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(7 i \, e^{3} \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 i \, e^{3} \cos\left(\frac{7}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) - 35 i \, e^{3} \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 105 i \, e^{3} \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 7 \, e^{3} \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, e^{3} \sin\left(\frac{7}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 35 \, e^{3} \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 105 \, e^{3} \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{140 \, d}"," ",0,"1/140*(7*I*e^3*cos(5/2*d*x + 5/2*c) - 5*I*e^3*cos(7/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) - 35*I*e^3*cos(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 105*I*e^3*cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 7*e^3*sin(5/2*d*x + 5/2*c) + 5*e^3*sin(7/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 35*e^3*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 105*e^3*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*sqrt(a)*sqrt(e)/d","A",0
674,1,148,0,0.823741," ","integrate((e*cos(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(5 i \, e^{2} \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 i \, e^{2} \cos\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 30 i \, e^{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 5 \, e^{2} \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, e^{2} \sin\left(\frac{5}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 30 \, e^{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{30 \, d}"," ",0,"1/30*(5*I*e^2*cos(3/2*d*x + 3/2*c) - 3*I*e^2*cos(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 30*I*e^2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 5*e^2*sin(3/2*d*x + 3/2*c) + 3*e^2*sin(5/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 30*e^2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))*sqrt(a)*sqrt(e)/d","A",0
675,1,59,0,0.845481," ","integrate((e*cos(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(-i \, e \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 i \, e \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + e \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, e \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a} \sqrt{e}}{3 \, d}"," ",0,"1/3*(-I*e*cos(3/2*d*x + 3/2*c) + 3*I*e*cos(1/2*d*x + 1/2*c) + e*sin(3/2*d*x + 3/2*c) + 3*e*sin(1/2*d*x + 1/2*c))*sqrt(a)*sqrt(e)/d","A",0
676,1,76,0,0.786078," ","integrate((e*cos(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, \sqrt{a} \sqrt{e} \sqrt{-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}{d \sqrt{-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}"," ",0,"-2*I*sqrt(a)*sqrt(e)*sqrt(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(d*sqrt(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
677,1,1400,0,0.876032," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(-2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - 2 \, \sqrt{2} \arctan\left(\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + 2 \, \sqrt{2} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + i \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - i \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - \sqrt{2} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right)\right)} \sqrt{a}}{4 \, d \sqrt{e}}"," ",0,"1/4*(-2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - 2*sqrt(2)*arctan2(sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + 2*sqrt(2)*arctan2(-sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), -sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + I*sqrt(2)*log(2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - I*sqrt(2)*log(-2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + sqrt(2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - sqrt(2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + sqrt(2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - sqrt(2)*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2))*sqrt(a)/(d*sqrt(e))","B",0
678,1,1834,0,1.402429," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(16 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 16 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 16 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 16 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(16 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 16 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 16 i \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(-16 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 16 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 16 i \, \sqrt{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + 8 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - 8 \, {\left(\sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + \sqrt{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(8 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 8 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-8 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 8 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(8 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 8 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 8 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-8 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 8 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - 128 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 128 i \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{{\left(-64 i \, e^{2} \cos\left(2 \, d x + 2 \, c\right) + 64 \, e^{2} \sin\left(2 \, d x + 2 \, c\right) - 64 i \, e^{2}\right)} d}"," ",0,"-(16*(sqrt(2)*cos(2*d*x + 2*c) + I*sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 16*(sqrt(2)*cos(2*d*x + 2*c) + I*sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 16*(sqrt(2)*cos(2*d*x + 2*c) + I*sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + 16*(sqrt(2)*cos(2*d*x + 2*c) + I*sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (16*I*sqrt(2)*cos(2*d*x + 2*c) - 16*sqrt(2)*sin(2*d*x + 2*c) + 16*I*sqrt(2))*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) + (-16*I*sqrt(2)*cos(2*d*x + 2*c) + 16*sqrt(2)*sin(2*d*x + 2*c) - 16*I*sqrt(2))*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) + 8*(sqrt(2)*cos(2*d*x + 2*c) + I*sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - 8*(sqrt(2)*cos(2*d*x + 2*c) + I*sqrt(2)*sin(2*d*x + 2*c) + sqrt(2))*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (8*I*sqrt(2)*cos(2*d*x + 2*c) - 8*sqrt(2)*sin(2*d*x + 2*c) + 8*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-8*I*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*sin(2*d*x + 2*c) - 8*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (8*I*sqrt(2)*cos(2*d*x + 2*c) - 8*sqrt(2)*sin(2*d*x + 2*c) + 8*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-8*I*sqrt(2)*cos(2*d*x + 2*c) + 8*sqrt(2)*sin(2*d*x + 2*c) - 8*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - 128*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 128*I*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)*sqrt(e)/((-64*I*e^2*cos(2*d*x + 2*c) + 64*e^2*sin(2*d*x + 2*c) - 64*I*e^2)*d)","B",0
679,1,2265,0,1.267535," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(192 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(192 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(192 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(192 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(192 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 192 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 384 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(-192 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 384 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 192 i \, \sqrt{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(96 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 192 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 96 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 192 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 96 \, \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(96 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 192 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 96 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 192 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 96 \, \sqrt{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(-96 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 192 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 96 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 192 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 96 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(96 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 192 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 96 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 192 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 96 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(-96 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 192 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 96 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 192 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 96 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) - {\left(96 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 192 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 96 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 192 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 96 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 1536 \, \cos\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 512 \, \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1536 i \, \sin\left(\frac{7}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 512 i \, \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{{\left(-1024 i \, e^{3} \cos\left(4 \, d x + 4 \, c\right) - 2048 i \, e^{3} \cos\left(2 \, d x + 2 \, c\right) + 1024 \, e^{3} \sin\left(4 \, d x + 4 \, c\right) + 2048 \, e^{3} \sin\left(2 \, d x + 2 \, c\right) - 1024 i \, e^{3}\right)} d}"," ",0,"-((192*sqrt(2)*cos(4*d*x + 4*c) + 384*sqrt(2)*cos(2*d*x + 2*c) + 192*I*sqrt(2)*sin(4*d*x + 4*c) + 384*I*sqrt(2)*sin(2*d*x + 2*c) + 192*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (192*sqrt(2)*cos(4*d*x + 4*c) + 384*sqrt(2)*cos(2*d*x + 2*c) + 192*I*sqrt(2)*sin(4*d*x + 4*c) + 384*I*sqrt(2)*sin(2*d*x + 2*c) + 192*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (192*sqrt(2)*cos(4*d*x + 4*c) + 384*sqrt(2)*cos(2*d*x + 2*c) + 192*I*sqrt(2)*sin(4*d*x + 4*c) + 384*I*sqrt(2)*sin(2*d*x + 2*c) + 192*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (192*sqrt(2)*cos(4*d*x + 4*c) + 384*sqrt(2)*cos(2*d*x + 2*c) + 192*I*sqrt(2)*sin(4*d*x + 4*c) + 384*I*sqrt(2)*sin(2*d*x + 2*c) + 192*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (192*I*sqrt(2)*cos(4*d*x + 4*c) + 384*I*sqrt(2)*cos(2*d*x + 2*c) - 192*sqrt(2)*sin(4*d*x + 4*c) - 384*sqrt(2)*sin(2*d*x + 2*c) + 192*I*sqrt(2))*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) - (-192*I*sqrt(2)*cos(4*d*x + 4*c) - 384*I*sqrt(2)*cos(2*d*x + 2*c) + 192*sqrt(2)*sin(4*d*x + 4*c) + 384*sqrt(2)*sin(2*d*x + 2*c) - 192*I*sqrt(2))*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) - (96*sqrt(2)*cos(4*d*x + 4*c) + 192*sqrt(2)*cos(2*d*x + 2*c) + 96*I*sqrt(2)*sin(4*d*x + 4*c) + 192*I*sqrt(2)*sin(2*d*x + 2*c) + 96*sqrt(2))*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (96*sqrt(2)*cos(4*d*x + 4*c) + 192*sqrt(2)*cos(2*d*x + 2*c) + 96*I*sqrt(2)*sin(4*d*x + 4*c) + 192*I*sqrt(2)*sin(2*d*x + 2*c) + 96*sqrt(2))*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (-96*I*sqrt(2)*cos(4*d*x + 4*c) - 192*I*sqrt(2)*cos(2*d*x + 2*c) + 96*sqrt(2)*sin(4*d*x + 4*c) + 192*sqrt(2)*sin(2*d*x + 2*c) - 96*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (96*I*sqrt(2)*cos(4*d*x + 4*c) + 192*I*sqrt(2)*cos(2*d*x + 2*c) - 96*sqrt(2)*sin(4*d*x + 4*c) - 192*sqrt(2)*sin(2*d*x + 2*c) + 96*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (-96*I*sqrt(2)*cos(4*d*x + 4*c) - 192*I*sqrt(2)*cos(2*d*x + 2*c) + 96*sqrt(2)*sin(4*d*x + 4*c) + 192*sqrt(2)*sin(2*d*x + 2*c) - 96*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) - (96*I*sqrt(2)*cos(4*d*x + 4*c) + 192*I*sqrt(2)*cos(2*d*x + 2*c) - 96*sqrt(2)*sin(4*d*x + 4*c) - 192*sqrt(2)*sin(2*d*x + 2*c) + 96*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 1536*cos(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 512*cos(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1536*I*sin(7/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 512*I*sin(3/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)*sqrt(e)/((-1024*I*e^3*cos(4*d*x + 4*c) - 2048*I*e^3*cos(2*d*x + 2*c) + 1024*e^3*sin(4*d*x + 4*c) + 2048*e^3*sin(2*d*x + 2*c) - 1024*I*e^3)*d)","B",0
680,1,2671,0,1.447452," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{{\left({\left(5760 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 17280 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 17280 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 5760 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 17280 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 17280 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 5760 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(5760 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 17280 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 17280 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 5760 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 17280 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 17280 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 5760 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(5760 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 17280 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 17280 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 5760 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 17280 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 17280 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 5760 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(5760 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 17280 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 17280 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 5760 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 17280 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 17280 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 5760 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(5760 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 17280 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 17280 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 5760 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) - 17280 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 17280 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 5760 i \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(-5760 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 17280 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 17280 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 5760 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 17280 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 17280 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 5760 i \, \sqrt{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2880 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 8640 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 8640 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2880 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 8640 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 8640 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2880 \, \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(2880 \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 8640 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 8640 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2880 i \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 8640 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 8640 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2880 \, \sqrt{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(2880 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 8640 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 8640 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 2880 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) - 8640 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 8640 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2880 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-2880 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 8640 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 8640 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2880 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 8640 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 8640 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 2880 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(2880 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) + 8640 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 8640 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 2880 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) - 8640 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 8640 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 2880 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-2880 i \, \sqrt{2} \cos\left(6 \, d x + 6 \, c\right) - 8640 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 8640 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 2880 \, \sqrt{2} \sin\left(6 \, d x + 6 \, c\right) + 8640 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 8640 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 2880 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 15360 \, \cos\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 129024 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 46080 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 15360 i \, \sin\left(\frac{9}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 129024 i \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 46080 i \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{{\left(-36864 i \, e^{4} \cos\left(6 \, d x + 6 \, c\right) - 110592 i \, e^{4} \cos\left(4 \, d x + 4 \, c\right) - 110592 i \, e^{4} \cos\left(2 \, d x + 2 \, c\right) + 36864 \, e^{4} \sin\left(6 \, d x + 6 \, c\right) + 110592 \, e^{4} \sin\left(4 \, d x + 4 \, c\right) + 110592 \, e^{4} \sin\left(2 \, d x + 2 \, c\right) - 36864 i \, e^{4}\right)} d}"," ",0,"-((5760*sqrt(2)*cos(6*d*x + 6*c) + 17280*sqrt(2)*cos(4*d*x + 4*c) + 17280*sqrt(2)*cos(2*d*x + 2*c) + 5760*I*sqrt(2)*sin(6*d*x + 6*c) + 17280*I*sqrt(2)*sin(4*d*x + 4*c) + 17280*I*sqrt(2)*sin(2*d*x + 2*c) + 5760*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (5760*sqrt(2)*cos(6*d*x + 6*c) + 17280*sqrt(2)*cos(4*d*x + 4*c) + 17280*sqrt(2)*cos(2*d*x + 2*c) + 5760*I*sqrt(2)*sin(6*d*x + 6*c) + 17280*I*sqrt(2)*sin(4*d*x + 4*c) + 17280*I*sqrt(2)*sin(2*d*x + 2*c) + 5760*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (5760*sqrt(2)*cos(6*d*x + 6*c) + 17280*sqrt(2)*cos(4*d*x + 4*c) + 17280*sqrt(2)*cos(2*d*x + 2*c) + 5760*I*sqrt(2)*sin(6*d*x + 6*c) + 17280*I*sqrt(2)*sin(4*d*x + 4*c) + 17280*I*sqrt(2)*sin(2*d*x + 2*c) + 5760*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (5760*sqrt(2)*cos(6*d*x + 6*c) + 17280*sqrt(2)*cos(4*d*x + 4*c) + 17280*sqrt(2)*cos(2*d*x + 2*c) + 5760*I*sqrt(2)*sin(6*d*x + 6*c) + 17280*I*sqrt(2)*sin(4*d*x + 4*c) + 17280*I*sqrt(2)*sin(2*d*x + 2*c) + 5760*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (5760*I*sqrt(2)*cos(6*d*x + 6*c) + 17280*I*sqrt(2)*cos(4*d*x + 4*c) + 17280*I*sqrt(2)*cos(2*d*x + 2*c) - 5760*sqrt(2)*sin(6*d*x + 6*c) - 17280*sqrt(2)*sin(4*d*x + 4*c) - 17280*sqrt(2)*sin(2*d*x + 2*c) + 5760*I*sqrt(2))*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) + (-5760*I*sqrt(2)*cos(6*d*x + 6*c) - 17280*I*sqrt(2)*cos(4*d*x + 4*c) - 17280*I*sqrt(2)*cos(2*d*x + 2*c) + 5760*sqrt(2)*sin(6*d*x + 6*c) + 17280*sqrt(2)*sin(4*d*x + 4*c) + 17280*sqrt(2)*sin(2*d*x + 2*c) - 5760*I*sqrt(2))*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) + (2880*sqrt(2)*cos(6*d*x + 6*c) + 8640*sqrt(2)*cos(4*d*x + 4*c) + 8640*sqrt(2)*cos(2*d*x + 2*c) + 2880*I*sqrt(2)*sin(6*d*x + 6*c) + 8640*I*sqrt(2)*sin(4*d*x + 4*c) + 8640*I*sqrt(2)*sin(2*d*x + 2*c) + 2880*sqrt(2))*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (2880*sqrt(2)*cos(6*d*x + 6*c) + 8640*sqrt(2)*cos(4*d*x + 4*c) + 8640*sqrt(2)*cos(2*d*x + 2*c) + 2880*I*sqrt(2)*sin(6*d*x + 6*c) + 8640*I*sqrt(2)*sin(4*d*x + 4*c) + 8640*I*sqrt(2)*sin(2*d*x + 2*c) + 2880*sqrt(2))*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (2880*I*sqrt(2)*cos(6*d*x + 6*c) + 8640*I*sqrt(2)*cos(4*d*x + 4*c) + 8640*I*sqrt(2)*cos(2*d*x + 2*c) - 2880*sqrt(2)*sin(6*d*x + 6*c) - 8640*sqrt(2)*sin(4*d*x + 4*c) - 8640*sqrt(2)*sin(2*d*x + 2*c) + 2880*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-2880*I*sqrt(2)*cos(6*d*x + 6*c) - 8640*I*sqrt(2)*cos(4*d*x + 4*c) - 8640*I*sqrt(2)*cos(2*d*x + 2*c) + 2880*sqrt(2)*sin(6*d*x + 6*c) + 8640*sqrt(2)*sin(4*d*x + 4*c) + 8640*sqrt(2)*sin(2*d*x + 2*c) - 2880*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (2880*I*sqrt(2)*cos(6*d*x + 6*c) + 8640*I*sqrt(2)*cos(4*d*x + 4*c) + 8640*I*sqrt(2)*cos(2*d*x + 2*c) - 2880*sqrt(2)*sin(6*d*x + 6*c) - 8640*sqrt(2)*sin(4*d*x + 4*c) - 8640*sqrt(2)*sin(2*d*x + 2*c) + 2880*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-2880*I*sqrt(2)*cos(6*d*x + 6*c) - 8640*I*sqrt(2)*cos(4*d*x + 4*c) - 8640*I*sqrt(2)*cos(2*d*x + 2*c) + 2880*sqrt(2)*sin(6*d*x + 6*c) + 8640*sqrt(2)*sin(4*d*x + 4*c) + 8640*sqrt(2)*sin(2*d*x + 2*c) - 2880*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 15360*cos(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 129024*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 46080*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 15360*I*sin(9/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 129024*I*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 46080*I*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)*sqrt(e)/((-36864*I*e^4*cos(6*d*x + 6*c) - 110592*I*e^4*cos(4*d*x + 4*c) - 110592*I*e^4*cos(2*d*x + 2*c) + 36864*e^4*sin(6*d*x + 6*c) + 110592*e^4*sin(4*d*x + 4*c) + 110592*e^4*sin(2*d*x + 2*c) - 36864*I*e^4)*d)","B",0
681,1,202,0,1.417957," ","integrate((e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(5 i \, e^{2} \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) - 7 i \, e^{2} \cos\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 i \, e^{2} \cos\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) - 105 i \, e^{2} \cos\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 5 \, e^{2} \sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right) + 7 \, e^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 35 \, e^{2} \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right) + 105 \, e^{2} \sin\left(\frac{1}{7} \, \arctan\left(\sin\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right), \cos\left(\frac{7}{2} \, d x + \frac{7}{2} \, c\right)\right)\right)\right)} \sqrt{e}}{140 \, \sqrt{a} d}"," ",0,"1/140*(5*I*e^2*cos(7/2*d*x + 7/2*c) - 7*I*e^2*cos(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*I*e^2*cos(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) - 105*I*e^2*cos(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 5*e^2*sin(7/2*d*x + 7/2*c) + 7*e^2*sin(5/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 35*e^2*sin(3/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))) + 105*e^2*sin(1/7*arctan2(sin(7/2*d*x + 7/2*c), cos(7/2*d*x + 7/2*c))))*sqrt(e)/(sqrt(a)*d)","A",0
682,1,136,0,1.193672," ","integrate((e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(3 i \, e \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) - 5 i \, e \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 i \, e \cos\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 3 \, e \sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right) + 5 \, e \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right) + 30 \, e \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right), \cos\left(\frac{5}{2} \, d x + \frac{5}{2} \, c\right)\right)\right)\right)} \sqrt{e}}{30 \, \sqrt{a} d}"," ",0,"1/30*(3*I*e*cos(5/2*d*x + 5/2*c) - 5*I*e*cos(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*I*e*cos(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 3*e*sin(5/2*d*x + 5/2*c) + 5*e*sin(3/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))) + 30*e*sin(1/5*arctan2(sin(5/2*d*x + 5/2*c), cos(5/2*d*x + 5/2*c))))*sqrt(e)/(sqrt(a)*d)","A",0
683,1,80,0,0.993879," ","integrate((e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{e} {\left(i \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - 3 i \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 3 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)\right)}}{3 \, \sqrt{a} d}"," ",0,"1/3*sqrt(e)*(I*cos(3/2*d*x + 3/2*c) - 3*I*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(3/2*d*x + 3/2*c) + 3*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))))/(sqrt(a)*d)","A",0
684,1,76,0,0.648293," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 i \, \sqrt{-\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}{\sqrt{a} d \sqrt{e} \sqrt{-\frac{2 i \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}}"," ",0,"2*I*sqrt(-sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(sqrt(a)*d*sqrt(e)*sqrt(-2*I*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1))","B",0
685,1,714,0,1.484143," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 2 i \, \sqrt{2} \arctan\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1, -\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 2 \, \sqrt{2} \arctan\left(\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) + 2 \, \sqrt{2} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \sin\left(d x + c\right), -\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \cos\left(d x + c\right) + 1\right) + i \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - i \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\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) + \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 \, \sqrt{a} d e^{\frac{3}{2}}}"," ",0,"-1/4*(2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) + 2*I*sqrt(2)*arctan2(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1, -sqrt(2)*sin(1/2*d*x + 1/2*c) + 1) - 2*sqrt(2)*arctan2(sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) + 2*sqrt(2)*arctan2(-sqrt(2)*sin(1/2*d*x + 1/2*c) + sin(d*x + c), -sqrt(2)*cos(1/2*d*x + 1/2*c) + cos(d*x + c) + 1) + I*sqrt(2)*log(2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) + 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) + 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 + 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) - I*sqrt(2)*log(-2*sqrt(2)*sin(d*x + c)*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*cos(1/2*d*x + 1/2*c) - 1)*cos(d*x + c) + cos(d*x + c)^2 + 2*cos(1/2*d*x + 1/2*c)^2 + sin(d*x + c)^2 + 2*sin(1/2*d*x + 1/2*c)^2 - 2*sqrt(2)*cos(1/2*d*x + 1/2*c) + 1) - 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))/(sqrt(a)*d*e^(3/2))","A",0
686,1,2168,0,0.849479," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(16 \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + {\left(16 \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(16 i \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 16 \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 i \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(-16 i \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 16 \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 16 i \, \sqrt{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(8 \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 i \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) + {\left(8 \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 i \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, \sqrt{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 1\right) - {\left(-8 i \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - {\left(8 i \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - {\left(-8 i \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) - {\left(8 i \, \sqrt{2} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 8 \, \sqrt{2} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 8 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 2\right) + 128 \, \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + 128 i \, \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)} \sqrt{a} \sqrt{e}}{{\left(-64 i \, a e^{3} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) + 64 \, a e^{3} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right), \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right)\right)\right) - 64 i \, a e^{3}\right)} d}"," ",0,"-((16*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2))*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (16*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2))*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (16*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2))*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (16*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2))*arctan2(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1, -sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (16*I*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 16*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*I*sqrt(2))*arctan2(sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (-16*I*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 16*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 16*I*sqrt(2))*arctan2(-sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))), -sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (8*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*I*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*sqrt(2))*log(2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) + (8*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*I*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*sqrt(2))*log(-2*sqrt(2)*sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*(sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 1)*cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + cos(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + sin(2/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 1) - (-8*I*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*I*sqrt(2))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - (8*I*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*I*sqrt(2))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - (-8*I*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*I*sqrt(2))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) - (8*I*sqrt(2)*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 8*sqrt(2)*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 8*I*sqrt(2))*log(2*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 + 2*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c)))^2 - 2*sqrt(2)*cos(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 2*sqrt(2)*sin(1/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 2) + 128*cos(3/2*d*x + 3/2*c) + 128*I*sin(3/2*d*x + 3/2*c))*sqrt(a)*sqrt(e)/((-64*I*a*e^3*cos(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) + 64*a*e^3*sin(4/3*arctan2(sin(3/2*d*x + 3/2*c), cos(3/2*d*x + 3/2*c))) - 64*I*a*e^3)*d)","B",0
687,1,2264,0,1.545867," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(192 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(192 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(192 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(192 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1, -\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(192 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 384 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 192 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 384 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 192 i \, \sqrt{2}\right)} \arctan\left(\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(-192 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 384 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 192 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 384 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 192 i \, \sqrt{2}\right)} \arctan\left(-\sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right), -\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(96 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 192 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 96 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 192 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 96 \, \sqrt{2}\right)} \log\left(2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) - {\left(96 \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 192 \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 96 i \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 192 i \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 96 \, \sqrt{2}\right)} \log\left(-2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1\right)} \cos\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(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + \sin\left(\frac{1}{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}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 1\right) + {\left(96 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 192 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 96 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 192 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 96 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-96 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 192 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 96 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 192 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 96 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(96 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) + 192 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) - 96 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) - 192 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) + 96 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + {\left(-96 i \, \sqrt{2} \cos\left(4 \, d x + 4 \, c\right) - 192 i \, \sqrt{2} \cos\left(2 \, d x + 2 \, c\right) + 96 \, \sqrt{2} \sin\left(4 \, d x + 4 \, c\right) + 192 \, \sqrt{2} \sin\left(2 \, d x + 2 \, c\right) - 96 i \, \sqrt{2}\right)} \log\left(2 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)^{2} - 2 \, \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 2\right) + 512 \, \cos\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1536 \, \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) + 512 i \, \sin\left(\frac{5}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right) - 1536 i \, \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right)\right)\right)\right)} \sqrt{a} \sqrt{e}}{{\left(-1024 i \, a e^{4} \cos\left(4 \, d x + 4 \, c\right) - 2048 i \, a e^{4} \cos\left(2 \, d x + 2 \, c\right) + 1024 \, a e^{4} \sin\left(4 \, d x + 4 \, c\right) + 2048 \, a e^{4} \sin\left(2 \, d x + 2 \, c\right) - 1024 i \, a e^{4}\right)} d}"," ",0,"-((192*sqrt(2)*cos(4*d*x + 4*c) + 384*sqrt(2)*cos(2*d*x + 2*c) + 192*I*sqrt(2)*sin(4*d*x + 4*c) + 384*I*sqrt(2)*sin(2*d*x + 2*c) + 192*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (192*sqrt(2)*cos(4*d*x + 4*c) + 384*sqrt(2)*cos(2*d*x + 2*c) + 192*I*sqrt(2)*sin(4*d*x + 4*c) + 384*I*sqrt(2)*sin(2*d*x + 2*c) + 192*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (192*sqrt(2)*cos(4*d*x + 4*c) + 384*sqrt(2)*cos(2*d*x + 2*c) + 192*I*sqrt(2)*sin(4*d*x + 4*c) + 384*I*sqrt(2)*sin(2*d*x + 2*c) + 192*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (192*sqrt(2)*cos(4*d*x + 4*c) + 384*sqrt(2)*cos(2*d*x + 2*c) + 192*I*sqrt(2)*sin(4*d*x + 4*c) + 384*I*sqrt(2)*sin(2*d*x + 2*c) + 192*sqrt(2))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1, -sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (192*I*sqrt(2)*cos(4*d*x + 4*c) + 384*I*sqrt(2)*cos(2*d*x + 2*c) - 192*sqrt(2)*sin(4*d*x + 4*c) - 384*sqrt(2)*sin(2*d*x + 2*c) + 192*I*sqrt(2))*arctan2(sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), sqrt(2)*cos(1/4*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) + (-192*I*sqrt(2)*cos(4*d*x + 4*c) - 384*I*sqrt(2)*cos(2*d*x + 2*c) + 192*sqrt(2)*sin(4*d*x + 4*c) + 384*sqrt(2)*sin(2*d*x + 2*c) - 192*I*sqrt(2))*arctan2(-sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))), -sqrt(2)*cos(1/4*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) + (96*sqrt(2)*cos(4*d*x + 4*c) + 192*sqrt(2)*cos(2*d*x + 2*c) + 96*I*sqrt(2)*sin(4*d*x + 4*c) + 192*I*sqrt(2)*sin(2*d*x + 2*c) + 96*sqrt(2))*log(2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) - (96*sqrt(2)*cos(4*d*x + 4*c) + 192*sqrt(2)*cos(2*d*x + 2*c) + 96*I*sqrt(2)*sin(4*d*x + 4*c) + 192*I*sqrt(2)*sin(2*d*x + 2*c) + 96*sqrt(2))*log(-2*sqrt(2)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*(sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1)*cos(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)))^2 + 2*cos(1/4*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(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 1) + (96*I*sqrt(2)*cos(4*d*x + 4*c) + 192*I*sqrt(2)*cos(2*d*x + 2*c) - 96*sqrt(2)*sin(4*d*x + 4*c) - 192*sqrt(2)*sin(2*d*x + 2*c) + 96*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-96*I*sqrt(2)*cos(4*d*x + 4*c) - 192*I*sqrt(2)*cos(2*d*x + 2*c) + 96*sqrt(2)*sin(4*d*x + 4*c) + 192*sqrt(2)*sin(2*d*x + 2*c) - 96*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (96*I*sqrt(2)*cos(4*d*x + 4*c) + 192*I*sqrt(2)*cos(2*d*x + 2*c) - 96*sqrt(2)*sin(4*d*x + 4*c) - 192*sqrt(2)*sin(2*d*x + 2*c) + 96*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + (-96*I*sqrt(2)*cos(4*d*x + 4*c) - 192*I*sqrt(2)*cos(2*d*x + 2*c) + 96*sqrt(2)*sin(4*d*x + 4*c) + 192*sqrt(2)*sin(2*d*x + 2*c) - 96*I*sqrt(2))*log(2*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 + 2*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c)))^2 - 2*sqrt(2)*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 2*sqrt(2)*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 2) + 512*cos(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1536*cos(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) + 512*I*sin(5/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))) - 1536*I*sin(1/4*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c))))*sqrt(a)*sqrt(e)/((-1024*I*a*e^4*cos(4*d*x + 4*c) - 2048*I*a*e^4*cos(2*d*x + 2*c) + 1024*a*e^4*sin(4*d*x + 4*c) + 2048*a*e^4*sin(2*d*x + 2*c) - 1024*I*a*e^4)*d)","B",0
688,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{m} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^m*(I*a*tan(d*x + c) + a)^n, x)","F",0
689,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \left(e \cos\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2*(e*cos(d*x + c))^m, x)","F",0
690,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)} \left(e \cos\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)*(e*cos(d*x + c))^m, x)","F",0
691,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
692,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
693,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*(e*cos(d*x + c))^m, x)","F",0
694,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{m}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^m/sqrt(I*a*tan(d*x + c) + a), x)","F",0
695,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{3} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3*(d*cos(f*x + e))^m, x)","F",0
696,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*(d*cos(f*x + e))^m, x)","F",0
697,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)*(d*cos(f*x + e))^m, x)","F",0
698,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{m}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^m/(b*tan(f*x + e) + a), x)","F",0
699,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{m}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^m/(b*tan(f*x + e) + a)^2, x)","F",0
700,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^n,x, algorithm=""maxima"")","\int \left(d \cos\left(f x + e\right)\right)^{m} {\left(b \tan\left(f x + e\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^m*(b*tan(f*x + e) + a)^n, x)","F",0
