1,1,92,0,0.401617," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{35 \, a \sin\left(d x + c\right)^{8} + 40 \, a \sin\left(d x + c\right)^{7} - 140 \, a \sin\left(d x + c\right)^{6} - 168 \, a \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} + 280 \, a \sin\left(d x + c\right)^{3} - 140 \, a \sin\left(d x + c\right)^{2} - 280 \, a \sin\left(d x + c\right)}{280 \, d}"," ",0,"-1/280*(35*a*sin(d*x + c)^8 + 40*a*sin(d*x + c)^7 - 140*a*sin(d*x + c)^6 - 168*a*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 + 280*a*sin(d*x + c)^3 - 140*a*sin(d*x + c)^2 - 280*a*sin(d*x + c))/d","A",0
2,1,63,0,0.626200," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{192 \, a \cos\left(d x + c\right)^{7} + 7 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{1344 \, d}"," ",0,"-1/1344*(192*a*cos(d*x + c)^7 + 7*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a)/d","A",0
3,1,70,0,0.324270," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{5 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} - 15 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3} + 15 \, a \sin\left(d x + c\right)^{2} + 30 \, a \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(5*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 - 15*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3 + 15*a*sin(d*x + c)^2 + 30*a*sin(d*x + c))/d","A",0
4,1,48,0,0.327203," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, a \cos\left(d x + c\right)^{5} - 5 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{160 \, d}"," ",0,"-1/160*(32*a*cos(d*x + c)^5 - 5*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a)/d","A",0
5,1,48,0,0.319633," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 6 \, a \sin\left(d x + c\right)^{2} - 12 \, a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 6*a*sin(d*x + c)^2 - 12*a*sin(d*x + c))/d","A",0
6,1,37,0,0.323558," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, a \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a}{12 \, d}"," ",0,"-1/12*(4*a*cos(d*x + c)^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a)/d","A",0
7,1,20,0,0.354991," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{2 \, a d}"," ",0,"1/2*(a*sin(d*x + c) + a)^2/(a*d)","A",0
8,1,15,0,0.352533," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(d x + c\right) - 1\right)}{d}"," ",0,"-a*log(sin(d*x + c) - 1)/d","A",0
9,1,23,0,0.486751," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \tan\left(d x + c\right) + \frac{a}{\cos\left(d x + c\right)}}{d}"," ",0,"(a*tan(d*x + c) + a/cos(d*x + c))/d","A",0
10,1,42,0,0.327504," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sin\left(d x + c\right) + 1\right) - a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, a}{\sin\left(d x + c\right) - 1}}{4 \, d}"," ",0,"1/4*(a*log(sin(d*x + c) + 1) - a*log(sin(d*x + c) - 1) - 2*a/(sin(d*x + c) - 1))/d","A",0
11,1,35,0,0.378967," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a + \frac{a}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 3*tan(d*x + c))*a + a/cos(d*x + c)^3)/d","A",0
12,1,86,0,0.528108," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, a \sin\left(d x + c\right)^{2} - 3 \, a \sin\left(d x + c\right) - 2 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"1/16*(3*a*log(sin(d*x + c) + 1) - 3*a*log(sin(d*x + c) - 1) - 2*(3*a*sin(d*x + c)^2 - 3*a*sin(d*x + c) - 2*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
13,1,115,0,0.606911," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6144 \, a^{2} \cos\left(d x + c\right)^{7} - 7 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} + 112 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{21504 \, d}"," ",0,"-1/21504*(6144*a^2*cos(d*x + c)^7 - 7*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^2 + 112*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^2)/d","A",0
14,1,95,0,0.491209," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{15 \, a^{2} \sin\left(d x + c\right)^{7} + 35 \, a^{2} \sin\left(d x + c\right)^{6} - 21 \, a^{2} \sin\left(d x + c\right)^{5} - 105 \, a^{2} \sin\left(d x + c\right)^{4} - 35 \, a^{2} \sin\left(d x + c\right)^{3} + 105 \, a^{2} \sin\left(d x + c\right)^{2} + 105 \, a^{2} \sin\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*a^2*sin(d*x + c)^7 + 35*a^2*sin(d*x + c)^6 - 21*a^2*sin(d*x + c)^5 - 105*a^2*sin(d*x + c)^4 - 35*a^2*sin(d*x + c)^3 + 105*a^2*sin(d*x + c)^2 + 105*a^2*sin(d*x + c))/d","A",0
15,1,89,0,0.320748," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{384 \, a^{2} \cos\left(d x + c\right)^{5} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{960 \, d}"," ",0,"-1/960*(384*a^2*cos(d*x + c)^5 - 5*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^2 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2)/d","A",0
16,1,56,0,0.408303," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, a^{2} \sin\left(d x + c\right)^{5} + 5 \, a^{2} \sin\left(d x + c\right)^{4} - 10 \, a^{2} \sin\left(d x + c\right)^{2} - 10 \, a^{2} \sin\left(d x + c\right)}{10 \, d}"," ",0,"-1/10*(2*a^2*sin(d*x + c)^5 + 5*a^2*sin(d*x + c)^4 - 10*a^2*sin(d*x + c)^2 - 10*a^2*sin(d*x + c))/d","A",0
17,1,65,0,0.319536," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{64 \, a^{2} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{96 \, d}"," ",0,"-1/96*(64*a^2*cos(d*x + c)^3 - 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^2 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2)/d","A",0
18,1,20,0,0.341986," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{3 \, a d}"," ",0,"1/3*(a*sin(d*x + c) + a)^3/(a*d)","A",0
19,1,30,0,0.394270," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) + a^{2} \sin\left(d x + c\right)}{d}"," ",0,"-(2*a^2*log(sin(d*x + c) - 1) + a^2*sin(d*x + c))/d","A",0
20,1,47,0,0.666128," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} - a^{2} \tan\left(d x + c\right) - \frac{2 \, a^{2}}{\cos\left(d x + c\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*a^2 - a^2*tan(d*x + c) - 2*a^2/cos(d*x + c))/d","A",0
21,1,18,0,0.323952," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2}}{d {\left(\sin\left(d x + c\right) - 1\right)}}"," ",0,"-a^2/(d*(sin(d*x + c) - 1))","A",0
22,1,52,0,0.604808," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} + \frac{2 \, a^{2}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(a^2*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 + 2*a^2/cos(d*x + c)^3)/d","A",0
23,1,71,0,0.348785," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"1/8*(a^2*log(sin(d*x + c) + 1) - a^2*log(sin(d*x + c) - 1) - 2*(a^2*sin(d*x + c) - 2*a^2)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
24,1,77,0,0.372003," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{2} + {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} a^{2} + \frac{6 \, a^{2}}{\cos\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*((3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^2 + (3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*a^2 + 6*a^2/cos(d*x + c)^5)/d","A",0
25,1,108,0,0.954904," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, a^{2} \sin\left(d x + c\right)^{3} - 6 \, a^{2} \sin\left(d x + c\right)^{2} + a^{2} \sin\left(d x + c\right) + 4 \, a^{2}\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{3} + 2 \, \sin\left(d x + c\right) - 1}}{24 \, d}"," ",0,"1/24*(3*a^2*log(sin(d*x + c) + 1) - 3*a^2*log(sin(d*x + c) - 1) - 2*(3*a^2*sin(d*x + c)^3 - 6*a^2*sin(d*x + c)^2 + a^2*sin(d*x + c) + 4*a^2)/(sin(d*x + c)^4 - 2*sin(d*x + c)^3 + 2*sin(d*x + c) - 1))/d","A",0
26,1,98,0,0.332376," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} a^{2} + 3 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{2} + \frac{30 \, a^{2}}{\cos\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*((15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*a^2 + 3*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^2 + 30*a^2/cos(d*x + c)^7)/d","A",0
27,1,141,0,0.384889," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{27648 \, a^{3} \cos\left(d x + c\right)^{7} - 1024 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{3} - 63 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} + 336 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{64512 \, d}"," ",0,"-1/64512*(27648*a^3*cos(d*x + c)^7 - 1024*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^3 - 63*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^3 + 336*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^3)/d","A",0
28,1,108,0,0.368688," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{21 \, a^{3} \sin\left(d x + c\right)^{8} + 72 \, a^{3} \sin\left(d x + c\right)^{7} + 28 \, a^{3} \sin\left(d x + c\right)^{6} - 168 \, a^{3} \sin\left(d x + c\right)^{5} - 210 \, a^{3} \sin\left(d x + c\right)^{4} + 56 \, a^{3} \sin\left(d x + c\right)^{3} + 252 \, a^{3} \sin\left(d x + c\right)^{2} + 168 \, a^{3} \sin\left(d x + c\right)}{168 \, d}"," ",0,"1/168*(21*a^3*sin(d*x + c)^8 + 72*a^3*sin(d*x + c)^7 + 28*a^3*sin(d*x + c)^6 - 168*a^3*sin(d*x + c)^5 - 210*a^3*sin(d*x + c)^4 + 56*a^3*sin(d*x + c)^3 + 252*a^3*sin(d*x + c)^2 + 168*a^3*sin(d*x + c))/d","A",0
29,1,115,0,0.322240," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1344 \, a^{3} \cos\left(d x + c\right)^{5} - 64 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{3} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 70 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{2240 \, d}"," ",0,"-1/2240*(1344*a^3*cos(d*x + c)^5 - 64*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^3 - 35*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^3 - 70*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3)/d","A",0
30,1,82,0,0.438289," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{5 \, a^{3} \sin\left(d x + c\right)^{6} + 18 \, a^{3} \sin\left(d x + c\right)^{5} + 15 \, a^{3} \sin\left(d x + c\right)^{4} - 20 \, a^{3} \sin\left(d x + c\right)^{3} - 45 \, a^{3} \sin\left(d x + c\right)^{2} - 30 \, a^{3} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(5*a^3*sin(d*x + c)^6 + 18*a^3*sin(d*x + c)^5 + 15*a^3*sin(d*x + c)^4 - 20*a^3*sin(d*x + c)^3 - 45*a^3*sin(d*x + c)^2 - 30*a^3*sin(d*x + c))/d","A",0
31,1,91,0,0.536246," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{480 \, a^{3} \cos\left(d x + c\right)^{3} - 32 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{3} - 45 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{480 \, d}"," ",0,"-1/480*(480*a^3*cos(d*x + c)^3 - 32*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^3 - 45*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^3 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3)/d","A",0
32,1,20,0,0.320390," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{4 \, a d}"," ",0,"1/4*(a*sin(d*x + c) + a)^4/(a*d)","A",0
33,1,43,0,0.387086," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{3} \sin\left(d x + c\right)^{2} + 8 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, a^{3} \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(a^3*sin(d*x + c)^2 + 8*a^3*log(sin(d*x + c) - 1) + 6*a^3*sin(d*x + c))/d","A",0
34,1,68,0,0.414665," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} - a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - a^{3} \tan\left(d x + c\right) - \frac{3 \, a^{3}}{\cos\left(d x + c\right)}}{d}"," ",0,"-(3*(d*x + c - tan(d*x + c))*a^3 - a^3*(1/cos(d*x + c) + cos(d*x + c)) - a^3*tan(d*x + c) - 3*a^3/cos(d*x + c))/d","A",0
35,1,33,0,1.105164," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, a^{3}}{\sin\left(d x + c\right) - 1}}{d}"," ",0,"(a^3*log(sin(d*x + c) - 1) - 2*a^3/(sin(d*x + c) - 1))/d","A",0
36,1,78,0,0.476846," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} - \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{3}}{\cos\left(d x + c\right)^{3}} + \frac{3 \, a^{3}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*a^3*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 - (3*cos(d*x + c)^2 - 1)*a^3/cos(d*x + c)^3 + 3*a^3/cos(d*x + c)^3)/d","B",0
37,1,28,0,0.664318," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3}}{2 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)} d}"," ",0,"1/2*a^3/((sin(d*x + c)^2 - 2*sin(d*x + c) + 1)*d)","A",0
38,1,103,0,0.426806," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{3} + 3 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} a^{3} - \frac{{\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} a^{3}}{\cos\left(d x + c\right)^{5}} + \frac{9 \, a^{3}}{\cos\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*((3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^3 + 3*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*a^3 - (5*cos(d*x + c)^2 - 3)*a^3/cos(d*x + c)^5 + 9*a^3/cos(d*x + c)^5)/d","A",0
39,1,96,0,0.397296," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, a^{3} \sin\left(d x + c\right)^{2} - 9 \, a^{3} \sin\left(d x + c\right) + 10 \, a^{3}\right)}}{\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 1}}{48 \, d}"," ",0,"1/48*(3*a^3*log(sin(d*x + c) + 1) - 3*a^3*log(sin(d*x + c) - 1) - 2*(3*a^3*sin(d*x + c)^2 - 9*a^3*sin(d*x + c) + 10*a^3)/(sin(d*x + c)^3 - 3*sin(d*x + c)^2 + 3*sin(d*x + c) - 1))/d","A",0
40,1,122,0,0.477069," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} a^{3} + {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{3} - \frac{{\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} a^{3}}{\cos\left(d x + c\right)^{7}} + \frac{15 \, a^{3}}{\cos\left(d x + c\right)^{7}}}{35 \, d}"," ",0,"1/35*((15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*a^3 + (5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^3 - (7*cos(d*x + c)^2 - 5)*a^3/cos(d*x + c)^7 + 15*a^3/cos(d*x + c)^7)/d","A",0
41,1,173,0,0.609520," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{33 \, a^{8} \sin\left(d x + c\right)^{13} + 286 \, a^{8} \sin\left(d x + c\right)^{12} + 1014 \, a^{8} \sin\left(d x + c\right)^{11} + 1716 \, a^{8} \sin\left(d x + c\right)^{10} + 715 \, a^{8} \sin\left(d x + c\right)^{9} - 2574 \, a^{8} \sin\left(d x + c\right)^{8} - 5148 \, a^{8} \sin\left(d x + c\right)^{7} - 3432 \, a^{8} \sin\left(d x + c\right)^{6} + 1287 \, a^{8} \sin\left(d x + c\right)^{5} + 4290 \, a^{8} \sin\left(d x + c\right)^{4} + 3718 \, a^{8} \sin\left(d x + c\right)^{3} + 1716 \, a^{8} \sin\left(d x + c\right)^{2} + 429 \, a^{8} \sin\left(d x + c\right)}{429 \, d}"," ",0,"1/429*(33*a^8*sin(d*x + c)^13 + 286*a^8*sin(d*x + c)^12 + 1014*a^8*sin(d*x + c)^11 + 1716*a^8*sin(d*x + c)^10 + 715*a^8*sin(d*x + c)^9 - 2574*a^8*sin(d*x + c)^8 - 5148*a^8*sin(d*x + c)^7 - 3432*a^8*sin(d*x + c)^6 + 1287*a^8*sin(d*x + c)^5 + 4290*a^8*sin(d*x + c)^4 + 3718*a^8*sin(d*x + c)^3 + 1716*a^8*sin(d*x + c)^2 + 429*a^8*sin(d*x + c))/d","B",0
42,1,339,0,0.659715," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{45416448 \, a^{8} \cos\left(d x + c\right)^{5} - 196608 \, {\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} + 5046272 \, {\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} - 45416448 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{8} + 231 \, {\left(384 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 20 \, \sin\left(4 \, d x + 4 \, c\right)^{3} - 840 \, d x - 840 \, c - 15 \, \sin\left(8 \, d x + 8 \, c\right) + 240 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{8} + 77616 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 120 \, d x - 120 \, c - 5 \, \sin\left(8 \, d x + 8 \, c\right) + 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{8} - 4139520 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{8} - 1940400 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{8} - 887040 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{8}}{28385280 \, d}"," ",0,"-1/28385280*(45416448*a^8*cos(d*x + c)^5 - 196608*(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 + 5046272*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^8 - 45416448*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^8 + 231*(384*sin(2*d*x + 2*c)^5 + 20*sin(4*d*x + 4*c)^3 - 840*d*x - 840*c - 15*sin(8*d*x + 8*c) + 240*sin(4*d*x + 4*c))*a^8 + 77616*(32*sin(2*d*x + 2*c)^5 - 120*d*x - 120*c - 5*sin(8*d*x + 8*c) + 40*sin(4*d*x + 4*c))*a^8 - 4139520*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^8 - 1940400*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^8 - 887040*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^8)/d","A",0
43,1,134,0,0.325433," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{5 \, a^{8} \sin\left(d x + c\right)^{11} + 44 \, a^{8} \sin\left(d x + c\right)^{10} + 165 \, a^{8} \sin\left(d x + c\right)^{9} + 330 \, a^{8} \sin\left(d x + c\right)^{8} + 330 \, a^{8} \sin\left(d x + c\right)^{7} - 462 \, a^{8} \sin\left(d x + c\right)^{5} - 660 \, a^{8} \sin\left(d x + c\right)^{4} - 495 \, a^{8} \sin\left(d x + c\right)^{3} - 220 \, a^{8} \sin\left(d x + c\right)^{2} - 55 \, a^{8} \sin\left(d x + c\right)}{55 \, d}"," ",0,"-1/55*(5*a^8*sin(d*x + c)^11 + 44*a^8*sin(d*x + c)^10 + 165*a^8*sin(d*x + c)^9 + 330*a^8*sin(d*x + c)^8 + 330*a^8*sin(d*x + c)^7 - 462*a^8*sin(d*x + c)^5 - 660*a^8*sin(d*x + c)^4 - 495*a^8*sin(d*x + c)^3 - 220*a^8*sin(d*x + c)^2 - 55*a^8*sin(d*x + c))/d","B",0
44,1,319,0,0.377258," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{1720320 \, a^{8} \cos\left(d x + c\right)^{3} - 16384 \, {\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} + 344064 \, {\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} - 2408448 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{8} - 21 \, {\left(96 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 640 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 840 \, d x + 840 \, c - 45 \, \sin\left(8 \, d x + 8 \, c\right) - 120 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{8} + 5880 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 120 \, d x - 120 \, c + 3 \, \sin\left(8 \, d x + 8 \, c\right) + 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{8} + 235200 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{8} - 564480 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{8} - 161280 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{8}}{645120 \, d}"," ",0,"-1/645120*(1720320*a^8*cos(d*x + c)^3 - 16384*(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 + 344064*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*a^8 - 2408448*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^8 - 21*(96*sin(2*d*x + 2*c)^5 - 640*sin(2*d*x + 2*c)^3 + 840*d*x + 840*c - 45*sin(8*d*x + 8*c) - 120*sin(4*d*x + 4*c))*a^8 + 5880*(64*sin(2*d*x + 2*c)^3 - 120*d*x - 120*c + 3*sin(8*d*x + 8*c) + 24*sin(4*d*x + 4*c))*a^8 + 235200*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a^8 - 564480*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^8 - 161280*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^8)/d","A",0
45,1,20,0,0.659961," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{9}}{9 \, a d}"," ",0,"1/9*(a*sin(d*x + c) + a)^9/(a*d)","A",0
46,1,109,0,0.626121," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{15 \, a^{8} \sin\left(d x + c\right)^{7} + 140 \, a^{8} \sin\left(d x + c\right)^{6} + 609 \, a^{8} \sin\left(d x + c\right)^{5} + 1680 \, a^{8} \sin\left(d x + c\right)^{4} + 3465 \, a^{8} \sin\left(d x + c\right)^{3} + 6300 \, a^{8} \sin\left(d x + c\right)^{2} + 13440 \, a^{8} \log\left(\sin\left(d x + c\right) - 1\right) + 13335 \, a^{8} \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(15*a^8*sin(d*x + c)^7 + 140*a^8*sin(d*x + c)^6 + 609*a^8*sin(d*x + c)^5 + 1680*a^8*sin(d*x + c)^4 + 3465*a^8*sin(d*x + c)^3 + 6300*a^8*sin(d*x + c)^2 + 13440*a^8*log(sin(d*x + c) - 1) + 13335*a^8*sin(d*x + c))/d","A",0
47,1,331,0,0.670942," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{384 \, {\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} - 4480 \, {\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} - 5 \, {\left(105 \, d x + 105 \, c - \frac{87 \, \tan\left(d x + c\right)^{5} + 136 \, \tan\left(d x + c\right)^{3} + 57 \, \tan\left(d x + c\right)}{\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 \, \tan\left(d x + c\right)\right)} a^{8} - 840 \, {\left(15 \, d x + 15 \, c - \frac{9 \, \tan\left(d x + c\right)^{3} + 7 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 8 \, \tan\left(d x + c\right)\right)} a^{8} - 8400 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{8} - 6720 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{8} + 13440 \, a^{8} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} + 240 \, a^{8} \tan\left(d x + c\right) + \frac{1920 \, a^{8}}{\cos\left(d x + c\right)}}{240 \, d}"," ",0,"1/240*(384*(cos(d*x + c)^5 - 5*cos(d*x + c)^3 + 5/cos(d*x + c) + 15*cos(d*x + c))*a^8 - 4480*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^8 - 5*(105*d*x + 105*c - (87*tan(d*x + c)^5 + 136*tan(d*x + c)^3 + 57*tan(d*x + c))/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1) - 48*tan(d*x + c))*a^8 - 840*(15*d*x + 15*c - (9*tan(d*x + c)^3 + 7*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 8*tan(d*x + c))*a^8 - 8400*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^8 - 6720*(d*x + c - tan(d*x + c))*a^8 + 13440*a^8*(1/cos(d*x + c) + cos(d*x + c)) + 240*a^8*tan(d*x + c) + 1920*a^8/cos(d*x + c))/d","A",0
48,1,97,0,0.309943," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{a^{8} \sin\left(d x + c\right)^{5} + 10 \, a^{8} \sin\left(d x + c\right)^{4} + 50 \, a^{8} \sin\left(d x + c\right)^{3} + 180 \, a^{8} \sin\left(d x + c\right)^{2} + 960 \, a^{8} \log\left(\sin\left(d x + c\right) - 1\right) + 645 \, a^{8} \sin\left(d x + c\right) - \frac{320 \, a^{8}}{\sin\left(d x + c\right) - 1}}{5 \, d}"," ",0,"1/5*(a^8*sin(d*x + c)^5 + 10*a^8*sin(d*x + c)^4 + 50*a^8*sin(d*x + c)^3 + 180*a^8*sin(d*x + c)^2 + 960*a^8*log(sin(d*x + c) - 1) + 645*a^8*sin(d*x + c) - 320*a^8/(sin(d*x + c) - 1))/d","A",0
49,1,311,0,0.638628," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{224 \, a^{8} \tan\left(d x + c\right)^{3} + 64 \, {\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} + {\left(8 \, \tan\left(d x + c\right)^{3} + 105 \, d x + 105 \, c - \frac{3 \, {\left(13 \, \tan\left(d x + c\right)^{3} + 11 \, \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 72 \, \tan\left(d x + c\right)\right)} a^{8} + 112 \, {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{8} + 560 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{8} + 8 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{8} - 448 \, 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)} - \frac{448 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{8}}{\cos\left(d x + c\right)^{3}} + \frac{64 \, a^{8}}{\cos\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"1/24*(224*a^8*tan(d*x + c)^3 + 64*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*a^8 + (8*tan(d*x + c)^3 + 105*d*x + 105*c - 3*(13*tan(d*x + c)^3 + 11*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 72*tan(d*x + c))*a^8 + 112*(2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^8 + 560*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^8 + 8*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^8 - 448*a^8*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) - 448*(3*cos(d*x + c)^2 - 1)*a^8/cos(d*x + c)^3 + 64*a^8/cos(d*x + c)^3)/d","A",0
50,1,95,0,0.348463," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{a^{8} \sin\left(d x + c\right)^{3} + 12 \, a^{8} \sin\left(d x + c\right)^{2} + 240 \, a^{8} \log\left(\sin\left(d x + c\right) - 1\right) + 93 \, a^{8} \sin\left(d x + c\right) - \frac{48 \, {\left(5 \, a^{8} \sin\left(d x + c\right) - 4 \, a^{8}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{3 \, d}"," ",0,"-1/3*(a^8*sin(d*x + c)^3 + 12*a^8*sin(d*x + c)^2 + 240*a^8*log(sin(d*x + c) - 1) + 93*a^8*sin(d*x + c) - 48*(5*a^8*sin(d*x + c) - 4*a^8)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
51,1,258,0,0.665120," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{25 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{80 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{10 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{40 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{25 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 8}{a + \frac{5 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{20 \, d}"," ",0,"1/20*((25*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 80*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 10*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 40*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 25*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 8)/(a + 5*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
52,1,47,0,0.312124," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3} - 6 \, \sin\left(d x + c\right)^{2} + 12 \, \sin\left(d x + c\right)}{12 \, a d}"," ",0,"1/12*(3*sin(d*x + c)^4 - 4*sin(d*x + c)^3 - 6*sin(d*x + c)^2 + 12*sin(d*x + c))/(a*d)","A",0
53,1,156,0,0.597466," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{3 \, \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 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 2}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{3 \, d}"," ",0,"1/3*((3*sin(d*x + c)/(cos(d*x + c) + 1) + 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
54,1,25,0,0.329488," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(sin(d*x + c)^2 - 2*sin(d*x + c))/(a*d)","A",0
55,1,52,0,0.595994," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}\right)}}{d}"," ",0,"2*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","B",0
56,1,18,0,0.314424," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\log\left(a \sin\left(d x + c\right) + a\right)}{a d}"," ",0,"log(a*sin(d*x + c) + a)/(a*d)","A",0
57,1,47,0,0.394386," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{2}{a \sin\left(d x + c\right) + a}}{4 \, d}"," ",0,"1/4*(log(sin(d*x + c) + 1)/a - log(sin(d*x + c) - 1)/a - 2/(a*sin(d*x + c) + a))/d","A",0
58,1,129,0,0.610998," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)}}{3 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d}"," ",0,"2/3*(sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d)","B",0
59,1,91,0,0.319650," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 2\right)}}{a \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{16 \, d}"," ",0,"-1/16*(2*(3*sin(d*x + c)^2 + 3*sin(d*x + c) - 2)/(a*sin(d*x + c)^3 + a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 3*log(sin(d*x + c) + 1)/a + 3*log(sin(d*x + c) - 1)/a)/d","A",0
60,1,294,0,0.480237," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{21 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{13 \, \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{5 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 3\right)}}{15 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, 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)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"2/15*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 21*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 13*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 25*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 5*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
61,1,130,0,0.301316," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 15 \, \sin\left(d x + c\right)^{3} - 25 \, \sin\left(d x + c\right)^{2} - 25 \, \sin\left(d x + c\right) + 8\right)}}{a \sin\left(d x + c\right)^{5} + a \sin\left(d x + c\right)^{4} - 2 \, a \sin\left(d x + c\right)^{3} - 2 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{96 \, d}"," ",0,"-1/96*(2*(15*sin(d*x + c)^4 + 15*sin(d*x + c)^3 - 25*sin(d*x + c)^2 - 25*sin(d*x + c) + 8)/(a*sin(d*x + c)^5 + a*sin(d*x + c)^4 - 2*a*sin(d*x + c)^3 - 2*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 15*log(sin(d*x + c) + 1)/a + 15*log(sin(d*x + c) - 1)/a)/d","A",0
62,1,393,0,0.628512," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{135 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{96 \, \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 \, \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 \, \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 \, \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 \, \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}{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 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{120 \, d}"," ",0,"1/120*((135*sin(d*x + c)/(cos(d*x + c) + 1) + 96*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 445*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 960*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 330*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 960*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 330*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 480*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 445*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 480*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 135*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 96)/(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*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
63,1,47,0,0.347348," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{4} + 10 \, \sin\left(d x + c\right)^{2} - 10 \, \sin\left(d x + c\right)}{10 \, a^{2} d}"," ",0,"-1/10*(2*sin(d*x + c)^5 - 5*sin(d*x + c)^4 + 10*sin(d*x + c)^2 - 10*sin(d*x + c))/(a^2*d)","A",0
64,1,267,0,0.725151," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{16 \, \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 \, \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 \, \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}{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 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{12 \, d}"," ",0,"1/12*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 16*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 33*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 48*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 33*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 48*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 9*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 16)/(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*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
65,1,35,0,0.332383," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"1/3*(sin(d*x + c)^3 - 3*sin(d*x + c)^2 + 3*sin(d*x + c))/(a^2*d)","A",0
66,1,140,0,0.488785," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \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}{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 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{d}"," ",0,"-((sin(d*x + c)/(cos(d*x + c) + 1) - 4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 4)/(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*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
67,1,30,0,0.348800," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} - \frac{\sin\left(d x + c\right)}{a^{2}}}{d}"," ",0,"(2*log(sin(d*x + c) + 1)/a^2 - sin(d*x + c)/a^2)/d","A",0
68,1,56,0,0.761615," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{2}{a^{2} + \frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{d}"," ",0,"-2*(2/(a^2 + a^2*sin(d*x + c)/(cos(d*x + c) + 1)) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","A",0
69,1,20,0,0.304361," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{1}{{\left(a \sin\left(d x + c\right) + a\right)} a d}"," ",0,"-1/((a*sin(d*x + c) + a)*a*d)","A",0
70,1,72,0,0.807698," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\sin\left(d x + c\right) + 2\right)}}{a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{8 \, d}"," ",0,"-1/8*(2*(sin(d*x + c) + 2)/(a^2*sin(d*x + c)^2 + 2*a^2*sin(d*x + c) + a^2) - log(sin(d*x + c) + 1)/a^2 + log(sin(d*x + c) - 1)/a^2)/d","A",0
71,1,204,0,0.424219," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{10 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 2\right)}}{5 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, 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)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d}"," ",0,"-2/5*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 10*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 5*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d)","B",0
72,1,108,0,0.367982," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{3} + 6 \, \sin\left(d x + c\right)^{2} + \sin\left(d x + c\right) - 4\right)}}{a^{2} \sin\left(d x + c\right)^{4} + 2 \, a^{2} \sin\left(d x + c\right)^{3} - 2 \, a^{2} \sin\left(d x + c\right) - a^{2}} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{24 \, d}"," ",0,"-1/24*(2*(3*sin(d*x + c)^3 + 6*sin(d*x + c)^2 + sin(d*x + c) - 4)/(a^2*sin(d*x + c)^4 + 2*a^2*sin(d*x + c)^3 - 2*a^2*sin(d*x + c) - a^2) - 3*log(sin(d*x + c) + 1)/a^2 + 3*log(sin(d*x + c) - 1)/a^2)/d","A",0
73,1,396,0,0.778322," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{76 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{28 \, \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)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{56 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{28 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{42 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{21 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 6\right)}}{21 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d}"," ",0,"-2/21*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 76*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 28*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 42*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 56*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 28*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 42*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 21*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 6)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d)","B",0
74,1,167,0,0.372854," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{5} + 30 \, \sin\left(d x + c\right)^{4} - 10 \, \sin\left(d x + c\right)^{3} - 50 \, \sin\left(d x + c\right)^{2} - 17 \, \sin\left(d x + c\right) + 16\right)}}{a^{2} \sin\left(d x + c\right)^{6} + 2 \, a^{2} \sin\left(d x + c\right)^{5} - a^{2} \sin\left(d x + c\right)^{4} - 4 \, a^{2} \sin\left(d x + c\right)^{3} - a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{128 \, d}"," ",0,"-1/128*(2*(15*sin(d*x + c)^5 + 30*sin(d*x + c)^4 - 10*sin(d*x + c)^3 - 50*sin(d*x + c)^2 - 17*sin(d*x + c) + 16)/(a^2*sin(d*x + c)^6 + 2*a^2*sin(d*x + c)^5 - a^2*sin(d*x + c)^4 - 4*a^2*sin(d*x + c)^3 - a^2*sin(d*x + c)^2 + 2*a^2*sin(d*x + c) + a^2) - 15*log(sin(d*x + c) + 1)/a^2 + 15*log(sin(d*x + c) - 1)/a^2)/d","A",0
75,1,310,0,0.773788," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \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 \, \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 \, \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 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 136}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{60 \, d}"," ",0,"1/60*((15*sin(d*x + c)/(cos(d*x + c) + 1) + 320*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 390*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*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 360*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 15*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 136)/(a^3 + 5*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
76,1,45,0,0.448515," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3} + 6 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right)}{4 \, a^{3} d}"," ",0,"-1/4*(sin(d*x + c)^4 - 4*sin(d*x + c)^3 + 6*sin(d*x + c)^2 - 4*sin(d*x + c))/(a^3*d)","B",0
77,1,184,0,0.465805," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{9 \, \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 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 22}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{3 \, d}"," ",0,"-1/3*((9*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*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 22)/(a^3 + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
78,1,41,0,0.308554," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\sin\left(d x + c\right)^{2} - 6 \, \sin\left(d x + c\right)}{a^{3}} + \frac{8 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((sin(d*x + c)^2 - 6*sin(d*x + c))/a^3 + 8*log(sin(d*x + c) + 1)/a^3)/d","A",0
79,1,139,0,0.589445," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 5}{a^{3} + \frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{d}"," ",0,"-2*((sin(d*x + c)/(cos(d*x + c) + 1) + 4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5)/(a^3 + a^3*sin(d*x + c)/(cos(d*x + c) + 1) + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
80,1,37,0,0.367595," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2}{a^{3} \sin\left(d x + c\right) + a^{3}} + \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}}}{d}"," ",0,"-(2/(a^3*sin(d*x + c) + a^3) + log(sin(d*x + c) + 1)/a^3)/d","A",0
81,1,99,0,0.427344," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{3 \, {\left(a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)} d}"," ",0,"-2/3*(3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((a^3 + 3*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)*d)","B",0
82,1,20,0,0.384024," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a d}"," ",0,"-1/2/((a*sin(d*x + c) + a)^2*a*d)","A",0
83,1,98,0,0.501137," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 9 \, \sin\left(d x + c\right) + 10\right)}}{a^{3} \sin\left(d x + c\right)^{3} + 3 \, a^{3} \sin\left(d x + c\right)^{2} + 3 \, a^{3} \sin\left(d x + c\right) + a^{3}} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3}}}{48 \, d}"," ",0,"-1/48*(2*(3*sin(d*x + c)^2 + 9*sin(d*x + c) + 10)/(a^3*sin(d*x + c)^3 + 3*a^3*sin(d*x + c)^2 + 3*a^3*sin(d*x + c) + a^3) - 3*log(sin(d*x + c) + 1)/a^3 + 3*log(sin(d*x + c) - 1)/a^3)/d","A",0
84,1,310,0,0.455353," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{43 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{77 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{105 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{175 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{105 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{35 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 13\right)}}{35 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"-2/35*(43*sin(d*x + c)/(cos(d*x + c) + 1) + 77*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 105*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 175*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 105*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 35*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 13)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 14*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
85,1,146,0,0.326219," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{4} + 45 \, \sin\left(d x + c\right)^{3} + 35 \, \sin\left(d x + c\right)^{2} - 15 \, \sin\left(d x + c\right) - 32\right)}}{a^{3} \sin\left(d x + c\right)^{5} + 3 \, a^{3} \sin\left(d x + c\right)^{4} + 2 \, a^{3} \sin\left(d x + c\right)^{3} - 2 \, a^{3} \sin\left(d x + c\right)^{2} - 3 \, a^{3} \sin\left(d x + c\right) - a^{3}} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3}}}{192 \, d}"," ",0,"-1/192*(2*(15*sin(d*x + c)^4 + 45*sin(d*x + c)^3 + 35*sin(d*x + c)^2 - 15*sin(d*x + c) - 32)/(a^3*sin(d*x + c)^5 + 3*a^3*sin(d*x + c)^4 + 2*a^3*sin(d*x + c)^3 - 2*a^3*sin(d*x + c)^2 - 3*a^3*sin(d*x + c) - a^3) - 15*log(sin(d*x + c) + 1)/a^3 + 15*log(sin(d*x + c) - 1)/a^3)/d","A",0
86,1,482,0,0.444072," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{51 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{39 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{235 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{450 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{306 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{294 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{378 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{63 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{273 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{189 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{63 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + 19\right)}}{63 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"-2/63*(51*sin(d*x + c)/(cos(d*x + c) + 1) + 39*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 235*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 450*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 306*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 294*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 378*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 63*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 273*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 189*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 63*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 19)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
87,1,188,0,0.602931," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{6} + 315 \, \sin\left(d x + c\right)^{5} + 140 \, \sin\left(d x + c\right)^{4} - 420 \, \sin\left(d x + c\right)^{3} - 469 \, \sin\left(d x + c\right)^{2} - 7 \, \sin\left(d x + c\right) + 176\right)}}{a^{3} \sin\left(d x + c\right)^{7} + 3 \, a^{3} \sin\left(d x + c\right)^{6} + a^{3} \sin\left(d x + c\right)^{5} - 5 \, a^{3} \sin\left(d x + c\right)^{4} - 5 \, a^{3} \sin\left(d x + c\right)^{3} + a^{3} \sin\left(d x + c\right)^{2} + 3 \, a^{3} \sin\left(d x + c\right) + a^{3}} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3}}}{1280 \, d}"," ",0,"-1/1280*(2*(105*sin(d*x + c)^6 + 315*sin(d*x + c)^5 + 140*sin(d*x + c)^4 - 420*sin(d*x + c)^3 - 469*sin(d*x + c)^2 - 7*sin(d*x + c) + 176)/(a^3*sin(d*x + c)^7 + 3*a^3*sin(d*x + c)^6 + a^3*sin(d*x + c)^5 - 5*a^3*sin(d*x + c)^4 - 5*a^3*sin(d*x + c)^3 + a^3*sin(d*x + c)^2 + 3*a^3*sin(d*x + c) + a^3) - 105*log(sin(d*x + c) + 1)/a^3 + 105*log(sin(d*x + c) - 1)/a^3)/d","A",0
88,1,295,0,0.641071," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{8 \, {\left(\frac{133 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{294 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{490 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{175 \, \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}} + 19\right)}}{a^{8} + \frac{7 \, a^{8} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{21 \, a^{8} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{35 \, a^{8} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{35 \, a^{8} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{21 \, a^{8} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{7 \, a^{8} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{8} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} + \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{8}}\right)}}{105 \, d}"," ",0,"2/105*(8*(133*sin(d*x + c)/(cos(d*x + c) + 1) + 294*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 490*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 175*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 105*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 19)/(a^8 + 7*a^8*sin(d*x + c)/(cos(d*x + c) + 1) + 21*a^8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 35*a^8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 35*a^8*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 21*a^8*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 7*a^8*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^8*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) + 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^8)/d","B",0
89,1,74,0,0.323987," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{\sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)}{{\left(a^{8} \sin\left(d x + c\right)^{4} + 4 \, a^{8} \sin\left(d x + c\right)^{3} + 6 \, a^{8} \sin\left(d x + c\right)^{2} + 4 \, a^{8} \sin\left(d x + c\right) + a^{8}\right)} d}"," ",0,"(sin(d*x + c)^3 + sin(d*x + c))/((a^8*sin(d*x + c)^4 + 4*a^8*sin(d*x + c)^3 + 6*a^8*sin(d*x + c)^2 + 4*a^8*sin(d*x + c) + a^8)*d)","B",0
90,1,375,0,0.387704," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{225 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{189 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{693 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{483 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{63 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 8\right)}}{63 \, {\left(a^{8} + \frac{9 \, a^{8} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{36 \, a^{8} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{84 \, a^{8} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{126 \, a^{8} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{126 \, a^{8} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{84 \, a^{8} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{36 \, a^{8} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9 \, a^{8} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{8} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}\right)} d}"," ",0,"-2/63*(9*sin(d*x + c)/(cos(d*x + c) + 1) + 225*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 189*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 693*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 315*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 483*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 63*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 63*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 8)/((a^8 + 9*a^8*sin(d*x + c)/(cos(d*x + c) + 1) + 36*a^8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 84*a^8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 126*a^8*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 126*a^8*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 84*a^8*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 36*a^8*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9*a^8*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^8*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)*d)","B",0
91,1,93,0,0.315287," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{5 \, \sin\left(d x + c\right)^{2} - 5 \, \sin\left(d x + c\right) + 2}{15 \, {\left(a^{8} \sin\left(d x + c\right)^{5} + 5 \, a^{8} \sin\left(d x + c\right)^{4} + 10 \, a^{8} \sin\left(d x + c\right)^{3} + 10 \, a^{8} \sin\left(d x + c\right)^{2} + 5 \, a^{8} \sin\left(d x + c\right) + a^{8}\right)} d}"," ",0,"-1/15*(5*sin(d*x + c)^2 - 5*sin(d*x + c) + 2)/((a^8*sin(d*x + c)^5 + 5*a^8*sin(d*x + c)^4 + 10*a^8*sin(d*x + c)^3 + 10*a^8*sin(d*x + c)^2 + 5*a^8*sin(d*x + c) + a^8)*d)","A",0
92,1,461,0,0.424617," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{517 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4895 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{11220 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{27060 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{32802 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{37422 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{23100 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{13860 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{3465 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{1155 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 152\right)}}{1155 \, {\left(a^{8} + \frac{11 \, a^{8} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{55 \, a^{8} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{165 \, a^{8} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{330 \, a^{8} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{462 \, a^{8} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{462 \, a^{8} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{330 \, a^{8} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{165 \, a^{8} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{55 \, a^{8} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{11 \, a^{8} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{8} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}\right)} d}"," ",0,"-2/1155*(517*sin(d*x + c)/(cos(d*x + c) + 1) + 4895*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 11220*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 27060*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 32802*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 37422*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 23100*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 13860*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 3465*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 1155*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 152)/((a^8 + 11*a^8*sin(d*x + c)/(cos(d*x + c) + 1) + 55*a^8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 165*a^8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 330*a^8*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 462*a^8*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 462*a^8*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 330*a^8*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 165*a^8*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 55*a^8*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 11*a^8*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^8*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)*d)","B",0
93,1,96,0,0.319840," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{3 \, \sin\left(d x + c\right) - 2}{15 \, {\left(a^{8} \sin\left(d x + c\right)^{6} + 6 \, a^{8} \sin\left(d x + c\right)^{5} + 15 \, a^{8} \sin\left(d x + c\right)^{4} + 20 \, a^{8} \sin\left(d x + c\right)^{3} + 15 \, a^{8} \sin\left(d x + c\right)^{2} + 6 \, a^{8} \sin\left(d x + c\right) + a^{8}\right)} d}"," ",0,"1/15*(3*sin(d*x + c) - 2)/((a^8*sin(d*x + c)^6 + 6*a^8*sin(d*x + c)^5 + 15*a^8*sin(d*x + c)^4 + 20*a^8*sin(d*x + c)^3 + 15*a^8*sin(d*x + c)^2 + 6*a^8*sin(d*x + c) + a^8)*d)","B",0
94,1,547,0,0.520819," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{7111 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{51675 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{171457 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{451165 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{785070 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1076790 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1051050 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{810810 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{435435 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{183183 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{45045 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{9009 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + 1240\right)}}{9009 \, {\left(a^{8} + \frac{13 \, a^{8} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{78 \, a^{8} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{286 \, a^{8} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{715 \, a^{8} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1287 \, a^{8} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1716 \, a^{8} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1716 \, a^{8} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{1287 \, a^{8} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{715 \, a^{8} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{286 \, a^{8} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{78 \, a^{8} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{13 \, a^{8} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{a^{8} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}\right)} d}"," ",0,"-2/9009*(7111*sin(d*x + c)/(cos(d*x + c) + 1) + 51675*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 171457*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 451165*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 785070*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1076790*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1051050*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 810810*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 435435*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 183183*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 45045*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 9009*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 1240)/((a^8 + 13*a^8*sin(d*x + c)/(cos(d*x + c) + 1) + 78*a^8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 286*a^8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 715*a^8*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1287*a^8*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1716*a^8*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1716*a^8*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 1287*a^8*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 715*a^8*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 286*a^8*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 78*a^8*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 13*a^8*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + a^8*sin(d*x + c)^13/(cos(d*x + c) + 1)^13)*d)","B",0
95,1,20,0,0.307589," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{1}{7 \, {\left(a \sin\left(d x + c\right) + a\right)}^{7} a d}"," ",0,"-1/7/((a*sin(d*x + c) + a)^7*a*d)","A",0
96,1,213,0,0.323124," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{7} + 840 \, \sin\left(d x + c\right)^{6} + 2975 \, \sin\left(d x + c\right)^{5} + 6160 \, \sin\left(d x + c\right)^{4} + 8351 \, \sin\left(d x + c\right)^{3} + 8008 \, \sin\left(d x + c\right)^{2} + 5993 \, \sin\left(d x + c\right) + 4096\right)}}{a^{8} \sin\left(d x + c\right)^{8} + 8 \, a^{8} \sin\left(d x + c\right)^{7} + 28 \, a^{8} \sin\left(d x + c\right)^{6} + 56 \, a^{8} \sin\left(d x + c\right)^{5} + 70 \, a^{8} \sin\left(d x + c\right)^{4} + 56 \, a^{8} \sin\left(d x + c\right)^{3} + 28 \, a^{8} \sin\left(d x + c\right)^{2} + 8 \, a^{8} \sin\left(d x + c\right) + a^{8}} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{8}} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{8}}}{53760 \, d}"," ",0,"-1/53760*(2*(105*sin(d*x + c)^7 + 840*sin(d*x + c)^6 + 2975*sin(d*x + c)^5 + 6160*sin(d*x + c)^4 + 8351*sin(d*x + c)^3 + 8008*sin(d*x + c)^2 + 5993*sin(d*x + c) + 4096)/(a^8*sin(d*x + c)^8 + 8*a^8*sin(d*x + c)^7 + 28*a^8*sin(d*x + c)^6 + 56*a^8*sin(d*x + c)^5 + 70*a^8*sin(d*x + c)^4 + 56*a^8*sin(d*x + c)^3 + 28*a^8*sin(d*x + c)^2 + 8*a^8*sin(d*x + c) + a^8) - 105*log(sin(d*x + c) + 1)/a^8 + 105*log(sin(d*x + c) - 1)/a^8)/d","A",0
97,1,740,0,0.596215," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{18181 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{128384 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{545224 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1667360 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3612364 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5742464 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{6271096 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3928496 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{850850 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{5289856 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{7137416 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{5989984 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{3607604 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{1555840 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{486200 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{97240 \, \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{12155 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} + 1896\right)}}{12155 \, {\left(a^{8} + \frac{16 \, a^{8} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{119 \, a^{8} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{544 \, a^{8} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1700 \, a^{8} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3808 \, a^{8} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{6188 \, a^{8} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{7072 \, a^{8} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{4862 \, a^{8} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4862 \, a^{8} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{7072 \, a^{8} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{6188 \, a^{8} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{3808 \, a^{8} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{1700 \, a^{8} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{544 \, a^{8} \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{119 \, a^{8} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{16 \, a^{8} \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{a^{8} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}}\right)} d}"," ",0,"-2/12155*(18181*sin(d*x + c)/(cos(d*x + c) + 1) + 128384*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 545224*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1667360*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3612364*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5742464*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 6271096*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3928496*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 850850*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 5289856*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 7137416*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 5989984*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 3607604*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 1555840*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 486200*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 97240*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 12155*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 + 1896)/((a^8 + 16*a^8*sin(d*x + c)/(cos(d*x + c) + 1) + 119*a^8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 544*a^8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1700*a^8*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3808*a^8*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 6188*a^8*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 7072*a^8*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 4862*a^8*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4862*a^8*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 7072*a^8*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 6188*a^8*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 3808*a^8*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 1700*a^8*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 544*a^8*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 119*a^8*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 16*a^8*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - a^8*sin(d*x + c)^18/(cos(d*x + c) + 1)^18)*d)","B",0
98,1,248,0,0.537456," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(315 \, \sin\left(d x + c\right)^{9} + 2520 \, \sin\left(d x + c\right)^{8} + 8610 \, \sin\left(d x + c\right)^{7} + 15960 \, \sin\left(d x + c\right)^{6} + 16128 \, \sin\left(d x + c\right)^{5} + 5544 \, \sin\left(d x + c\right)^{4} - 7074 \, \sin\left(d x + c\right)^{3} - 11736 \, \sin\left(d x + c\right)^{2} - 9019 \, \sin\left(d x + c\right) - 5120\right)}}{a^{8} \sin\left(d x + c\right)^{10} + 8 \, a^{8} \sin\left(d x + c\right)^{9} + 27 \, a^{8} \sin\left(d x + c\right)^{8} + 48 \, a^{8} \sin\left(d x + c\right)^{7} + 42 \, a^{8} \sin\left(d x + c\right)^{6} - 42 \, a^{8} \sin\left(d x + c\right)^{4} - 48 \, a^{8} \sin\left(d x + c\right)^{3} - 27 \, a^{8} \sin\left(d x + c\right)^{2} - 8 \, a^{8} \sin\left(d x + c\right) - a^{8}} - \frac{315 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{8}} + \frac{315 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{8}}}{64512 \, d}"," ",0,"-1/64512*(2*(315*sin(d*x + c)^9 + 2520*sin(d*x + c)^8 + 8610*sin(d*x + c)^7 + 15960*sin(d*x + c)^6 + 16128*sin(d*x + c)^5 + 5544*sin(d*x + c)^4 - 7074*sin(d*x + c)^3 - 11736*sin(d*x + c)^2 - 9019*sin(d*x + c) - 5120)/(a^8*sin(d*x + c)^10 + 8*a^8*sin(d*x + c)^9 + 27*a^8*sin(d*x + c)^8 + 48*a^8*sin(d*x + c)^7 + 42*a^8*sin(d*x + c)^6 - 42*a^8*sin(d*x + c)^4 - 48*a^8*sin(d*x + c)^3 - 27*a^8*sin(d*x + c)^2 - 8*a^8*sin(d*x + c) - a^8) - 315*log(sin(d*x + c) + 1)/a^8 + 315*log(sin(d*x + c) - 1)/a^8)/d","A",0
99,1,866,0,0.627624," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{19787 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{136032 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{540806 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1483064 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2552175 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2356608 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1108536 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{6930288 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{10934842 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{7793344 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{1058148 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{9204208 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{9985222 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{4837248 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{1108536 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{3527160 \, \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{2985489 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{1478048 \, \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} - \frac{495482 \, \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} - \frac{100776 \, \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} - \frac{12597 \, \sin\left(d x + c\right)^{21}}{{\left(\cos\left(d x + c\right) + 1\right)}^{21}} + 2024\right)}}{12597 \, {\left(a^{8} + \frac{16 \, a^{8} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{117 \, a^{8} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{512 \, a^{8} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1463 \, a^{8} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2736 \, a^{8} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2907 \, a^{8} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{5814 \, a^{8} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{10336 \, a^{8} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{8398 \, a^{8} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{8398 \, a^{8} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{10336 \, a^{8} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{5814 \, a^{8} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{2907 \, a^{8} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{2736 \, a^{8} \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{1463 \, a^{8} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} - \frac{512 \, a^{8} \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} - \frac{117 \, a^{8} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} - \frac{16 \, a^{8} \sin\left(d x + c\right)^{21}}{{\left(\cos\left(d x + c\right) + 1\right)}^{21}} - \frac{a^{8} \sin\left(d x + c\right)^{22}}{{\left(\cos\left(d x + c\right) + 1\right)}^{22}}\right)} d}"," ",0,"-2/12597*(19787*sin(d*x + c)/(cos(d*x + c) + 1) + 136032*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 540806*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1483064*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2552175*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2356608*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 1108536*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 6930288*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 10934842*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 7793344*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1058148*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 9204208*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 9985222*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 4837248*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 1108536*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 3527160*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 2985489*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 1478048*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 - 495482*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 - 100776*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 - 12597*sin(d*x + c)^21/(cos(d*x + c) + 1)^21 + 2024)/((a^8 + 16*a^8*sin(d*x + c)/(cos(d*x + c) + 1) + 117*a^8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 512*a^8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1463*a^8*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2736*a^8*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2907*a^8*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 5814*a^8*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 10336*a^8*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 8398*a^8*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 8398*a^8*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 10336*a^8*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 5814*a^8*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 2907*a^8*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 2736*a^8*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 1463*a^8*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 - 512*a^8*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 - 117*a^8*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 - 16*a^8*sin(d*x + c)^21/(cos(d*x + c) + 1)^21 - a^8*sin(d*x + c)^22/(cos(d*x + c) + 1)^22)*d)","B",0
100,1,305,0,0.977644," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3465 \, \sin\left(d x + c\right)^{11} + 27720 \, \sin\left(d x + c\right)^{10} + 91245 \, \sin\left(d x + c\right)^{9} + 147840 \, \sin\left(d x + c\right)^{8} + 82698 \, \sin\left(d x + c\right)^{7} - 114576 \, \sin\left(d x + c\right)^{6} - 255222 \, \sin\left(d x + c\right)^{5} - 190080 \, \sin\left(d x + c\right)^{4} - 21395 \, \sin\left(d x + c\right)^{3} + 72776 \, \sin\left(d x + c\right)^{2} + 66953 \, \sin\left(d x + c\right) + 34816\right)}}{a^{8} \sin\left(d x + c\right)^{12} + 8 \, a^{8} \sin\left(d x + c\right)^{11} + 26 \, a^{8} \sin\left(d x + c\right)^{10} + 40 \, a^{8} \sin\left(d x + c\right)^{9} + 15 \, a^{8} \sin\left(d x + c\right)^{8} - 48 \, a^{8} \sin\left(d x + c\right)^{7} - 84 \, a^{8} \sin\left(d x + c\right)^{6} - 48 \, a^{8} \sin\left(d x + c\right)^{5} + 15 \, a^{8} \sin\left(d x + c\right)^{4} + 40 \, a^{8} \sin\left(d x + c\right)^{3} + 26 \, a^{8} \sin\left(d x + c\right)^{2} + 8 \, a^{8} \sin\left(d x + c\right) + a^{8}} - \frac{3465 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{8}} + \frac{3465 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{8}}}{430080 \, d}"," ",0,"-1/430080*(2*(3465*sin(d*x + c)^11 + 27720*sin(d*x + c)^10 + 91245*sin(d*x + c)^9 + 147840*sin(d*x + c)^8 + 82698*sin(d*x + c)^7 - 114576*sin(d*x + c)^6 - 255222*sin(d*x + c)^5 - 190080*sin(d*x + c)^4 - 21395*sin(d*x + c)^3 + 72776*sin(d*x + c)^2 + 66953*sin(d*x + c) + 34816)/(a^8*sin(d*x + c)^12 + 8*a^8*sin(d*x + c)^11 + 26*a^8*sin(d*x + c)^10 + 40*a^8*sin(d*x + c)^9 + 15*a^8*sin(d*x + c)^8 - 48*a^8*sin(d*x + c)^7 - 84*a^8*sin(d*x + c)^6 - 48*a^8*sin(d*x + c)^5 + 15*a^8*sin(d*x + c)^4 + 40*a^8*sin(d*x + c)^3 + 26*a^8*sin(d*x + c)^2 + 8*a^8*sin(d*x + c) + a^8) - 3465*log(sin(d*x + c) + 1)/a^8 + 3465*log(sin(d*x + c) - 1)/a^8)/d","A",0
101,1,72,0,0.375584," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(429 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{15}{2}} - 2970 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} a + 7020 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{2} - 5720 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{3}\right)}}{6435 \, a^{7} d}"," ",0,"-2/6435*(429*(a*sin(d*x + c) + a)^(15/2) - 2970*(a*sin(d*x + c) + a)^(13/2)*a + 7020*(a*sin(d*x + c) + a)^(11/2)*a^2 - 5720*(a*sin(d*x + c) + a)^(9/2)*a^3)/(a^7*d)","A",0
102,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^6, x)","F",0
103,1,55,0,0.304796," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(63 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 308 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 396 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2}\right)}}{693 \, a^{5} d}"," ",0,"2/693*(63*(a*sin(d*x + c) + a)^(11/2) - 308*(a*sin(d*x + c) + a)^(9/2)*a + 396*(a*sin(d*x + c) + a)^(7/2)*a^2)/(a^5*d)","A",0
104,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4, x)","F",0
105,1,38,0,0.440346," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(5 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 14 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a\right)}}{35 \, a^{3} d}"," ",0,"-2/35*(5*(a*sin(d*x + c) + a)^(7/2) - 14*(a*sin(d*x + c) + a)^(5/2)*a)/(a^3*d)","A",0
106,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
107,1,20,0,0.667052," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{3 \, a d}"," ",0,"2/3*(a*sin(d*x + c) + a)^(3/2)/(a*d)","A",0
108,1,58,0,0.937841," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right)}{2 \, d}"," ",0,"-1/2*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a)))/d","A",0
109,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
110,1,117,0,0.599562," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{3 \, \sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(3 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{2} - 4 \, a^{3}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 2 \, \sqrt{a \sin\left(d x + c\right) + a} a}}{16 \, a d}"," ",0,"-1/16*(3*sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(3*(a*sin(d*x + c) + a)*a^2 - 4*a^3)/((a*sin(d*x + c) + a)^(3/2) - 2*sqrt(a*sin(d*x + c) + a)*a))/(a*d)","A",0
111,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
112,1,168,0,1.006160," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{105 \, \sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(105 \, {\left(a \sin\left(d x + c\right) + a\right)}^{3} a^{2} - 350 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a^{3} + 224 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{4} + 64 \, a^{5}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2}}}{768 \, a d}"," ",0,"-1/768*(105*sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(105*(a*sin(d*x + c) + a)^3*a^2 - 350*(a*sin(d*x + c) + a)^2*a^3 + 224*(a*sin(d*x + c) + a)*a^4 + 64*a^5)/((a*sin(d*x + c) + a)^(7/2) - 4*(a*sin(d*x + c) + a)^(5/2)*a + 4*(a*sin(d*x + c) + a)^(3/2)*a^2))/(a*d)","A",0
113,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*sec(d*x + c)^6, x)","F",0
114,1,72,0,0.331384," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(715 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{17}{2}} - 4862 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{15}{2}} a + 11220 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} a^{2} - 8840 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{3}\right)}}{12155 \, a^{7} d}"," ",0,"-2/12155*(715*(a*sin(d*x + c) + a)^(17/2) - 4862*(a*sin(d*x + c) + a)^(15/2)*a + 11220*(a*sin(d*x + c) + a)^(13/2)*a^2 - 8840*(a*sin(d*x + c) + a)^(11/2)*a^3)/(a^7*d)","A",0
115,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^6, x)","F",0
116,1,55,0,0.320952," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(99 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 468 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} a + 572 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{2}\right)}}{1287 \, a^{5} d}"," ",0,"2/1287*(99*(a*sin(d*x + c) + a)^(13/2) - 468*(a*sin(d*x + c) + a)^(11/2)*a + 572*(a*sin(d*x + c) + a)^(9/2)*a^2)/(a^5*d)","A",0
117,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
118,1,38,0,0.316173," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(7 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 18 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a\right)}}{63 \, a^{3} d}"," ",0,"-2/63*(7*(a*sin(d*x + c) + a)^(9/2) - 18*(a*sin(d*x + c) + a)^(7/2)*a)/(a^3*d)","A",0
119,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
120,1,20,0,1.512074," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{5 \, a d}"," ",0,"2/5*(a*sin(d*x + c) + a)^(5/2)/(a*d)","A",0
121,1,80,0,0.928884," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + 2 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}}{a d}"," ",0,"-(sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 2*sqrt(a*sin(d*x + c) + a)*a^2)/(a*d)","A",0
122,1,98,0,2.506576," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{\frac{3}{2}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{\frac{3}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)}}{d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)} {\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*(a^(3/2) + 2*a^(3/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^(3/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) - 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(3/2))","B",0
123,1,94,0,1.407308," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, \sqrt{a \sin\left(d x + c\right) + a} a^{3}}{a \sin\left(d x + c\right) - a}}{8 \, a d}"," ",0,"-1/8*(sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*sqrt(a*sin(d*x + c) + a)*a^3/(a*sin(d*x + c) - a))/(a*d)","A",0
124,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,1,151,0,0.608188," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{15 \, \sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(15 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a^{3} - 50 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{4} + 32 \, a^{5}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 4 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}}}{128 \, a d}"," ",0,"-1/128*(15*sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(15*(a*sin(d*x + c) + a)^2*a^3 - 50*(a*sin(d*x + c) + a)*a^4 + 32*a^5)/((a*sin(d*x + c) + a)^(5/2) - 4*(a*sin(d*x + c) + a)^(3/2)*a + 4*sqrt(a*sin(d*x + c) + a)*a^2))/(a*d)","A",0
126,-1,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,1,55,0,0.519613," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(143 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{15}{2}} - 660 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} a + 780 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} a^{2}\right)}}{2145 \, a^{5} d}"," ",0,"2/2145*(143*(a*sin(d*x + c) + a)^(15/2) - 660*(a*sin(d*x + c) + a)^(13/2)*a + 780*(a*sin(d*x + c) + a)^(11/2)*a^2)/(a^5*d)","A",0
128,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
129,1,38,0,0.474183," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(9 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 22 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a\right)}}{99 \, a^{3} d}"," ",0,"-2/99*(9*(a*sin(d*x + c) + a)^(11/2) - 22*(a*sin(d*x + c) + a)^(9/2)*a)/(a^3*d)","A",0
130,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
131,1,20,0,0.564775," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}{7 \, a d}"," ",0,"2/7*(a*sin(d*x + c) + a)^(7/2)/(a*d)","A",0
132,1,97,0,0.518995," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} + 6 \, \sqrt{a \sin\left(d x + c\right) + a} a^{3}\right)}}{3 \, a d}"," ",0,"-2/3*(3*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + (a*sin(d*x + c) + a)^(3/2)*a^2 + 6*sqrt(a*sin(d*x + c) + a)*a^3)/(a*d)","A",0
133,1,191,0,1.074569," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, 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 \, 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 \, 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 \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)}}{d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)} {\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*(3*a^(5/2) - 2*a^(5/2)*sin(d*x + c)/(cos(d*x + c) + 1) + 9*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*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*a^(5/2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) - 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(5/2))","B",0
134,1,94,0,0.532342," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) - \frac{4 \, \sqrt{a \sin\left(d x + c\right) + a} a^{4}}{a \sin\left(d x + c\right) - a}}{4 \, a d}"," ",0,"1/4*(sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) - 4*sqrt(a*sin(d*x + c) + a)*a^4/(a*sin(d*x + c) - a))/(a*d)","A",0
135,1,184,0,0.518054," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{\frac{5}{2}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{\frac{5}{2}} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)}}{3 \, d {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \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}} - 1\right)} {\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,"-2/3*(a^(5/2) + 4*a^(5/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^(5/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^(5/2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^(5/2)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)/(d*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(5/2))","B",0
136,1,134,0,0.420536," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{3 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{4} - 10 \, \sqrt{a \sin\left(d x + c\right) + a} a^{5}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} - 4 \, {\left(a \sin\left(d x + c\right) + a\right)} a + 4 \, a^{2}}}{64 \, a d}"," ",0,"-1/64*(3*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(3*(a*sin(d*x + c) + a)^(3/2)*a^4 - 10*sqrt(a*sin(d*x + c) + a)*a^5)/((a*sin(d*x + c) + a)^2 - 4*(a*sin(d*x + c) + a)*a + 4*a^2))/(a*d)","A",0
137,-1,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,1,185,0,0.729699," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{105 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(105 \, {\left(a \sin\left(d x + c\right) + a\right)}^{3} a^{4} - 560 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a^{5} + 924 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{6} - 384 \, a^{7}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 12 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} - 8 \, \sqrt{a \sin\left(d x + c\right) + a} a^{3}}}{1536 \, a d}"," ",0,"-1/1536*(105*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(105*(a*sin(d*x + c) + a)^3*a^4 - 560*(a*sin(d*x + c) + a)^2*a^5 + 924*(a*sin(d*x + c) + a)*a^6 - 384*a^7)/((a*sin(d*x + c) + a)^(7/2) - 6*(a*sin(d*x + c) + a)^(5/2)*a + 12*(a*sin(d*x + c) + a)^(3/2)*a^2 - 8*sqrt(a*sin(d*x + c) + a)*a^3))/(a*d)","A",0
139,1,72,0,0.836895," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(1615 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{21}{2}} - 10710 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{19}{2}} a + 23940 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{17}{2}} a^{2} - 18088 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{15}{2}} a^{3}\right)}}{33915 \, a^{7} d}"," ",0,"-2/33915*(1615*(a*sin(d*x + c) + a)^(21/2) - 10710*(a*sin(d*x + c) + a)^(19/2)*a + 23940*(a*sin(d*x + c) + a)^(17/2)*a^2 - 18088*(a*sin(d*x + c) + a)^(15/2)*a^3)/(a^7*d)","A",0
140,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(7/2)*cos(d*x + c)^6, x)","F",0
141,1,55,0,0.324099," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(195 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{17}{2}} - 884 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{15}{2}} a + 1020 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} a^{2}\right)}}{3315 \, a^{5} d}"," ",0,"2/3315*(195*(a*sin(d*x + c) + a)^(17/2) - 884*(a*sin(d*x + c) + a)^(15/2)*a + 1020*(a*sin(d*x + c) + a)^(13/2)*a^2)/(a^5*d)","A",0
142,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(7/2)*cos(d*x + c)^4, x)","F",0
143,1,38,0,0.403281," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(11 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 26 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} a\right)}}{143 \, a^{3} d}"," ",0,"-2/143*(11*(a*sin(d*x + c) + a)^(13/2) - 26*(a*sin(d*x + c) + a)^(11/2)*a)/(a^3*d)","A",0
144,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(7/2)*cos(d*x + c)^2, x)","F",0
145,1,20,0,0.516850," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}}}{9 \, a d}"," ",0,"2/9*(a*sin(d*x + c) + a)^(9/2)/(a*d)","A",0
146,1,115,0,0.811519," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(30 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + 3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} + 10 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 60 \, \sqrt{a \sin\left(d x + c\right) + a} a^{4}\right)}}{15 \, a d}"," ",0,"-2/15*(30*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 3*(a*sin(d*x + c) + a)^(5/2)*a^2 + 10*(a*sin(d*x + c) + a)^(3/2)*a^3 + 60*sqrt(a*sin(d*x + c) + a)*a^4)/(a*d)","A",0
147,1,237,0,0.546737," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(23 \, 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 \, 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 \, 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 \, 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 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)}}{3 \, d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}"," ",0,"-2/3*(23*a^(7/2) - 20*a^(7/2)*sin(d*x + c)/(cos(d*x + c) + 1) + 88*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*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*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*a^(7/2)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) - 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(7/2))","B",0
148,1,112,0,0.482279," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a} a^{4} - \frac{4 \, \sqrt{a \sin\left(d x + c\right) + a} a^{5}}{a \sin\left(d x + c\right) - a}}{2 \, a d}"," ",0,"1/2*(3*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*sqrt(a*sin(d*x + c) + a)*a^4 - 4*sqrt(a*sin(d*x + c) + a)*a^5/(a*sin(d*x + c) - a))/(a*d)","A",0
149,1,320,0,0.598342," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(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 \, 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 \, 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 \, 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 \, 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{a^{\frac{7}{2}} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)}}{3 \, d {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \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}} - 1\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}"," ",0,"2/3*(a^(7/2) - 6*a^(7/2)*sin(d*x + c)/(cos(d*x + c) + 1) + 5*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*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*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*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 + a^(7/2)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)/(d*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(7/2))","B",0
150,1,132,0,0.425806," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{\sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left({\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{5} + 2 \, \sqrt{a \sin\left(d x + c\right) + a} a^{6}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2} - 4 \, {\left(a \sin\left(d x + c\right) + a\right)} a + 4 \, a^{2}}}{32 \, a d}"," ",0,"1/32*(sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*((a*sin(d*x + c) + a)^(3/2)*a^5 + 2*sqrt(a*sin(d*x + c) + a)*a^6)/((a*sin(d*x + c) + a)^2 - 4*(a*sin(d*x + c) + a)*a + 4*a^2))/(a*d)","A",0
151,1,270,0,0.532714," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{\frac{7}{2}} + \frac{6 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a^{\frac{7}{2}} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, 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)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{\frac{7}{2}} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)}}{5 \, d {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 1\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}"," ",0,"-2/5*(a^(7/2) + 6*a^(7/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^(7/2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a^(7/2)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^(7/2)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a^(7/2)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^(7/2)*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)/(d*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^(7/2))","B",0
152,1,168,0,0.464332," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{15 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(15 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{5} - 80 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{6} + 132 \, \sqrt{a \sin\left(d x + c\right) + a} a^{7}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3} - 6 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a + 12 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{2} - 8 \, a^{3}}}{768 \, a d}"," ",0,"-1/768*(15*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(15*(a*sin(d*x + c) + a)^(5/2)*a^5 - 80*(a*sin(d*x + c) + a)^(3/2)*a^6 + 132*sqrt(a*sin(d*x + c) + a)*a^7)/((a*sin(d*x + c) + a)^3 - 6*(a*sin(d*x + c) + a)^2*a + 12*(a*sin(d*x + c) + a)*a^2 - 8*a^3))/(a*d)","A",0
153,-1,0,0,0.000000," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,1,219,0,0.451322," ","integrate(sec(d*x+c)^9*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","-\frac{315 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(315 \, {\left(a \sin\left(d x + c\right) + a\right)}^{4} a^{5} - 2310 \, {\left(a \sin\left(d x + c\right) + a\right)}^{3} a^{6} + 6132 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a^{7} - 6696 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{8} + 2048 \, a^{9}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 8 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 24 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 32 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 16 \, \sqrt{a \sin\left(d x + c\right) + a} a^{4}}}{8192 \, a d}"," ",0,"-1/8192*(315*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(315*(a*sin(d*x + c) + a)^4*a^5 - 2310*(a*sin(d*x + c) + a)^3*a^6 + 6132*(a*sin(d*x + c) + a)^2*a^7 - 6696*(a*sin(d*x + c) + a)*a^8 + 2048*a^9)/((a*sin(d*x + c) + a)^(9/2) - 8*(a*sin(d*x + c) + a)^(7/2)*a + 24*(a*sin(d*x + c) + a)^(5/2)*a^2 - 32*(a*sin(d*x + c) + a)^(3/2)*a^3 + 16*sqrt(a*sin(d*x + c) + a)*a^4))/(a*d)","A",0
155,-1,0,0,0.000000," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,1,281,0,0.408630," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15015 \, \sqrt{a \sin\left(d x + c\right) + a} - \frac{3003 \, {\left(3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}\right)}}{a^{2}} + \frac{143 \, {\left(35 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 180 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 378 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{a \sin\left(d x + c\right) + a} a^{4}\right)}}{a^{4}} - \frac{5 \, {\left(231 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 1638 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} a + 5005 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{2} - 8580 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{3} + 9009 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{4} - 6006 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{5} + 3003 \, \sqrt{a \sin\left(d x + c\right) + a} a^{6}\right)}}{a^{6}}\right)}}{15015 \, a d}"," ",0,"2/15015*(15015*sqrt(a*sin(d*x + c) + a) - 3003*(3*(a*sin(d*x + c) + a)^(5/2) - 10*(a*sin(d*x + c) + a)^(3/2)*a + 15*sqrt(a*sin(d*x + c) + a)*a^2)/a^2 + 143*(35*(a*sin(d*x + c) + a)^(9/2) - 180*(a*sin(d*x + c) + a)^(7/2)*a + 378*(a*sin(d*x + c) + a)^(5/2)*a^2 - 420*(a*sin(d*x + c) + a)^(3/2)*a^3 + 315*sqrt(a*sin(d*x + c) + a)*a^4)/a^4 - 5*(231*(a*sin(d*x + c) + a)^(13/2) - 1638*(a*sin(d*x + c) + a)^(11/2)*a + 5005*(a*sin(d*x + c) + a)^(9/2)*a^2 - 8580*(a*sin(d*x + c) + a)^(7/2)*a^3 + 9009*(a*sin(d*x + c) + a)^(5/2)*a^4 - 6006*(a*sin(d*x + c) + a)^(3/2)*a^5 + 3003*sqrt(a*sin(d*x + c) + a)*a^6)/a^6)/(a*d)","B",0
157,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{6}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/sqrt(a*sin(d*x + c) + a), x)","F",0
158,1,160,0,0.716878," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(315 \, \sqrt{a \sin\left(d x + c\right) + a} - \frac{42 \, {\left(3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}\right)}}{a^{2}} + \frac{35 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 180 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 378 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{a \sin\left(d x + c\right) + a} a^{4}}{a^{4}}\right)}}{315 \, a d}"," ",0,"2/315*(315*sqrt(a*sin(d*x + c) + a) - 42*(3*(a*sin(d*x + c) + a)^(5/2) - 10*(a*sin(d*x + c) + a)^(3/2)*a + 15*sqrt(a*sin(d*x + c) + a)*a^2)/a^2 + (35*(a*sin(d*x + c) + a)^(9/2) - 180*(a*sin(d*x + c) + a)^(7/2)*a + 378*(a*sin(d*x + c) + a)^(5/2)*a^2 - 420*(a*sin(d*x + c) + a)^(3/2)*a^3 + 315*sqrt(a*sin(d*x + c) + a)*a^4)/a^4)/(a*d)","B",0
159,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/sqrt(a*sin(d*x + c) + a), x)","F",0
160,1,75,0,0.531210," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, \sqrt{a \sin\left(d x + c\right) + a} - \frac{3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}}{a^{2}}\right)}}{15 \, a d}"," ",0,"2/15*(15*sqrt(a*sin(d*x + c) + a) - (3*(a*sin(d*x + c) + a)^(5/2) - 10*(a*sin(d*x + c) + a)^(3/2)*a + 15*sqrt(a*sin(d*x + c) + a)*a^2)/a^2)/(a*d)","A",0
161,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
162,1,20,0,0.551488," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a}}{a d}"," ",0,"2*sqrt(a*sin(d*x + c) + a)/(a*d)","A",0
163,1,78,0,1.246722," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, a}{\sqrt{a \sin\left(d x + c\right) + a}}}{4 \, a d}"," ",0,"-1/4*(sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*a/sqrt(a*sin(d*x + c) + a))/(a*d)","A",0
164,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
165,1,132,0,0.744922," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{15 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(15 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a - 20 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{2} - 8 \, a^{3}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a}}{96 \, a d}"," ",0,"-1/96*(15*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(15*(a*sin(d*x + c) + a)^2*a - 20*(a*sin(d*x + c) + a)*a^2 - 8*a^3)/((a*sin(d*x + c) + a)^(5/2) - 2*(a*sin(d*x + c) + a)^(3/2)*a))/(a*d)","A",0
166,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(a*sin(d*x + c) + a), x)","F",0
167,1,183,0,0.814440," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{315 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(315 \, {\left(a \sin\left(d x + c\right) + a\right)}^{4} a - 1050 \, {\left(a \sin\left(d x + c\right) + a\right)}^{3} a^{2} + 672 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a^{3} + 192 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{4} + 128 \, a^{5}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2}}}{2560 \, a d}"," ",0,"-1/2560*(315*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a))) + 4*(315*(a*sin(d*x + c) + a)^4*a - 1050*(a*sin(d*x + c) + a)^3*a^2 + 672*(a*sin(d*x + c) + a)^2*a^3 + 192*(a*sin(d*x + c) + a)*a^4 + 128*a^5)/((a*sin(d*x + c) + a)^(9/2) - 4*(a*sin(d*x + c) + a)^(7/2)*a + 4*(a*sin(d*x + c) + a)^(5/2)*a^2))/(a*d)","A",0
168,0,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{6}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^6/sqrt(a*sin(d*x + c) + a), x)","F",0
169,1,72,0,0.310095," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(105 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 770 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 1980 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2} - 1848 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{3}\right)}}{1155 \, a^{7} d}"," ",0,"-2/1155*(105*(a*sin(d*x + c) + a)^(11/2) - 770*(a*sin(d*x + c) + a)^(9/2)*a + 1980*(a*sin(d*x + c) + a)^(7/2)*a^2 - 1848*(a*sin(d*x + c) + a)^(5/2)*a^3)/(a^7*d)","A",0
170,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{6}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(a*sin(d*x + c) + a)^(3/2), x)","F",0
171,1,55,0,0.411087," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 84 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 140 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2}\right)}}{105 \, a^{5} d}"," ",0,"2/105*(15*(a*sin(d*x + c) + a)^(7/2) - 84*(a*sin(d*x + c) + a)^(5/2)*a + 140*(a*sin(d*x + c) + a)^(3/2)*a^2)/(a^5*d)","A",0
172,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(a*sin(d*x + c) + a)^(3/2), x)","F",0
173,1,36,0,0.376263," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 6 \, \sqrt{a \sin\left(d x + c\right) + a} a\right)}}{3 \, a^{3} d}"," ",0,"-2/3*((a*sin(d*x + c) + a)^(3/2) - 6*sqrt(a*sin(d*x + c) + a)*a)/(a^3*d)","A",0
174,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(a*sin(d*x + c) + a)^(3/2), x)","F",0
175,1,20,0,0.459420," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2}{\sqrt{a \sin\left(d x + c\right) + a} a d}"," ",0,"-2/(sqrt(a*sin(d*x + c) + a)*a*d)","A",0
176,1,91,0,0.708651," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(3 \, a \sin\left(d x + c\right) + 5 \, a\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}}{24 \, a d}"," ",0,"-1/24*(3*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a)))/sqrt(a) + 4*(3*a*sin(d*x + c) + 5*a)/(a*sin(d*x + c) + a)^(3/2))/(a*d)","A",0
177,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(a*sin(d*x + c) + a)^(3/2), x)","F",0
178,1,146,0,0.751369," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{105 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(105 \, {\left(a \sin\left(d x + c\right) + a\right)}^{3} - 140 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a - 56 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{2} - 48 \, a^{3}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a}}{960 \, a d}"," ",0,"-1/960*(105*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a)))/sqrt(a) + 4*(105*(a*sin(d*x + c) + a)^3 - 140*(a*sin(d*x + c) + a)^2*a - 56*(a*sin(d*x + c) + a)*a^2 - 48*a^3)/((a*sin(d*x + c) + a)^(7/2) - 2*(a*sin(d*x + c) + a)^(5/2)*a))/(a*d)","A",0
179,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,1,197,0,0.462630," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{3465 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(3465 \, {\left(a \sin\left(d x + c\right) + a\right)}^{5} - 11550 \, {\left(a \sin\left(d x + c\right) + a\right)}^{4} a + 7392 \, {\left(a \sin\left(d x + c\right) + a\right)}^{3} a^{2} + 2112 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a^{3} + 1408 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{4} + 1280 \, a^{5}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 4 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2}}}{35840 \, a d}"," ",0,"-1/35840*(3465*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a)))/sqrt(a) + 4*(3465*(a*sin(d*x + c) + a)^5 - 11550*(a*sin(d*x + c) + a)^4*a + 7392*(a*sin(d*x + c) + a)^3*a^2 + 2112*(a*sin(d*x + c) + a)^2*a^3 + 1408*(a*sin(d*x + c) + a)*a^4 + 1280*a^5)/((a*sin(d*x + c) + a)^(11/2) - 4*(a*sin(d*x + c) + a)^(9/2)*a + 4*(a*sin(d*x + c) + a)^(7/2)*a^2))/(a*d)","A",0
181,-1,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,0,0,0,0.000000," ","integrate(cos(d*x+c)^10/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{10}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^10/(a*sin(d*x + c) + a)^(5/2), x)","F",0
183,1,89,0,0.665723," ","integrate(cos(d*x+c)^9/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(1155 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 10920 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} a + 40040 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{2} - 68640 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{3} + 48048 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{4}\right)}}{15015 \, a^{9} d}"," ",0,"2/15015*(1155*(a*sin(d*x + c) + a)^(13/2) - 10920*(a*sin(d*x + c) + a)^(11/2)*a + 40040*(a*sin(d*x + c) + a)^(9/2)*a^2 - 68640*(a*sin(d*x + c) + a)^(7/2)*a^3 + 48048*(a*sin(d*x + c) + a)^(5/2)*a^4)/(a^9*d)","A",0
184,0,0,0,0.000000," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{8}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^8/(a*sin(d*x + c) + a)^(5/2), x)","F",0
185,1,72,0,1.311456," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(35 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 270 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 756 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 840 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3}\right)}}{315 \, a^{7} d}"," ",0,"-2/315*(35*(a*sin(d*x + c) + a)^(9/2) - 270*(a*sin(d*x + c) + a)^(7/2)*a + 756*(a*sin(d*x + c) + a)^(5/2)*a^2 - 840*(a*sin(d*x + c) + a)^(3/2)*a^3)/(a^7*d)","A",0
186,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{6}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(a*sin(d*x + c) + a)^(5/2), x)","F",0
187,1,55,0,0.325322," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 20 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 60 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}\right)}}{15 \, a^{5} d}"," ",0,"2/15*(3*(a*sin(d*x + c) + a)^(5/2) - 20*(a*sin(d*x + c) + a)^(3/2)*a + 60*sqrt(a*sin(d*x + c) + a)*a^2)/(a^5*d)","A",0
188,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(a*sin(d*x + c) + a)^(5/2), x)","F",0
189,1,42,0,1.155726," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\sqrt{a \sin\left(d x + c\right) + a}}{a^{2}} + \frac{2}{\sqrt{a \sin\left(d x + c\right) + a} a}\right)}}{a d}"," ",0,"-2*(sqrt(a*sin(d*x + c) + a)/a^2 + 2/(sqrt(a*sin(d*x + c) + a)*a))/(a*d)","A",0
190,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(a*sin(d*x + c) + a)^(5/2), x)","F",0
191,1,20,0,0.614383," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2}{3 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a d}"," ",0,"-2/3/((a*sin(d*x + c) + a)^(3/2)*a*d)","A",0
192,1,114,0,1.432636," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right)}{a^{\frac{3}{2}}} + \frac{4 \, {\left(15 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} + 10 \, {\left(a \sin\left(d x + c\right) + a\right)} a + 12 \, a^{2}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a}}{240 \, a d}"," ",0,"-1/240*(15*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a)))/a^(3/2) + 4*(15*(a*sin(d*x + c) + a)^2 + 10*(a*sin(d*x + c) + a)*a + 12*a^2)/((a*sin(d*x + c) + a)^(5/2)*a))/(a*d)","A",0
193,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(a*sin(d*x + c) + a)^(5/2), x)","F",0
194,1,167,0,1.225602," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(315 \, {\left(a \sin\left(d x + c\right) + a\right)}^{4} - 420 \, {\left(a \sin\left(d x + c\right) + a\right)}^{3} a - 168 \, {\left(a \sin\left(d x + c\right) + a\right)}^{2} a^{2} - 144 \, {\left(a \sin\left(d x + c\right) + a\right)} a^{3} - 160 \, a^{4}\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a - 2 \, {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2}} + \frac{315 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{a \sin\left(d x + c\right) + a}}\right)}{a^{\frac{3}{2}}}}{4480 \, a d}"," ",0,"-1/4480*(4*(315*(a*sin(d*x + c) + a)^4 - 420*(a*sin(d*x + c) + a)^3*a - 168*(a*sin(d*x + c) + a)^2*a^2 - 144*(a*sin(d*x + c) + a)*a^3 - 160*a^4)/((a*sin(d*x + c) + a)^(9/2)*a - 2*(a*sin(d*x + c) + a)^(7/2)*a^2) + 315*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(a*sin(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(a*sin(d*x + c) + a)))/a^(3/2))/(a*d)","A",0
195,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a), x)","F",0
197,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a), x)","F",0
198,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a), x)","F",0
199,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a), x)","F",0
200,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(d x + c\right) + a}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
201,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)/(e*cos(d*x + c))^(3/2), x)","F",0
202,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)/(e*cos(d*x + c))^(5/2), x)","F",0
203,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{a \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)/(e*cos(d*x + c))^(7/2), x)","F",0
204,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a)^2, x)","F",0
205,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^2, x)","F",0
206,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^2, x)","F",0
207,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^2, x)","F",0
208,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/sqrt(e*cos(d*x + c)), x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(3/2), x)","F",0
210,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(5/2), x)","F",0
211,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(7/2), x)","F",0
212,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(9/2), x)","F",0
213,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(11/2), x)","F",0
214,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a)^3, x)","F",0
215,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^3, x)","F",0
216,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^3, x)","F",0
217,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^3, x)","F",0
218,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/sqrt(e*cos(d*x + c)), x)","F",0
219,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(3/2), x)","F",0
220,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(5/2), x)","F",0
221,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(7/2), x)","F",0
222,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(9/2), x)","F",0
223,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(11/2), x)","F",0
224,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^4, x)","F",0
225,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^4, x)","F",0
226,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/sqrt(e*cos(d*x + c)), x)","F",0
227,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(3/2), x)","F",0
228,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(5/2), x)","F",0
229,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(7/2), x)","F",0
230,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(9/2), x)","F",0
231,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(11/2), x)","F",0
232,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(13/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(13/2), x)","F",0
233,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(11/2)/(a*sin(d*x + c) + a), x)","F",0
234,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(9/2)/(a*sin(d*x + c) + a), x)","F",0
235,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(a*sin(d*x + c) + a), x)","F",0
236,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(a*sin(d*x + c) + a), x)","F",0
237,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(a*sin(d*x + c) + a), x)","F",0
238,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)), x)","F",0
240,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)), x)","F",0
241,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)), x)","F",0
242,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(a*sin(d*x + c) + a)), x)","F",0
243,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(11/2)/(a*sin(d*x + c) + a)^2, x)","F",0
244,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(9/2)/(a*sin(d*x + c) + a)^2, x)","F",0
245,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(a*sin(d*x + c) + a)^2, x)","F",0
246,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(a*sin(d*x + c) + a)^2, x)","F",0
247,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(a*sin(d*x + c) + a)^2, x)","F",0
248,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a)^2, x)","F",0
249,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^2), x)","F",0
250,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^2), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^2), x)","F",0
252,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{15}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(15/2)/(a*sin(d*x + c) + a)^3, x)","F",0
254,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{13}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(13/2)/(a*sin(d*x + c) + a)^3, x)","F",0
255,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(11/2)/(a*sin(d*x + c) + a)^3, x)","F",0
256,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(9/2)/(a*sin(d*x + c) + a)^3, x)","F",0
257,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(a*sin(d*x + c) + a)^3, x)","F",0
258,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(a*sin(d*x + c) + a)^3, x)","F",0
259,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(a*sin(d*x + c) + a)^3, x)","F",0
260,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a)^3, x)","F",0
261,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^3), x)","F",0
262,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{15}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(15/2)/(a*sin(d*x + c) + a)^4, x)","F",0
264,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{13}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(13/2)/(a*sin(d*x + c) + a)^4, x)","F",0
265,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(11/2)/(a*sin(d*x + c) + a)^4, x)","F",0
266,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(9/2)/(a*sin(d*x + c) + a)^4, x)","F",0
267,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(a*sin(d*x + c) + a)^4, x)","F",0
268,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(a*sin(d*x + c) + a)^4, x)","F",0
269,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(a*sin(d*x + c) + a)^4, x)","F",0
270,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a)^4, x)","F",0
271,-1,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*sqrt(a*sin(d*x + c) + a), x)","F",0
274,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a), x)","F",0
275,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
276,1,131,0,0.964678," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{a} \sqrt{e} - \frac{\sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{{\left(e^{2} + \frac{e^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}}"," ",0,"2*(sqrt(a)*sqrt(e) - sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((e^2 + e^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2))","B",0
277,1,206,0,0.969923," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{a} \sqrt{e} - \frac{4 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{\sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{3 \, {\left(e^{3} + \frac{2 \, e^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{e^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}"," ",0,"-2/3*(sqrt(a)*sqrt(e) - 4*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 4*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((e^3 + 2*e^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + e^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2))","B",0
278,1,282,0,0.983175," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(7 \, \sqrt{a} \sqrt{e} + \frac{8 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{25 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{8 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{15 \, {\left(e^{4} + \frac{3 \, e^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, e^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{e^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} 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{7}{2}}}"," ",0,"2/15*(7*sqrt(a)*sqrt(e) + 8*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 25*sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 8*sqrt(a)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((e^4 + 3*e^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*e^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + e^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2))","B",0
279,1,357,0,0.983341," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(9 \, \sqrt{a} \sqrt{e} - \frac{44 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{14 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{84 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{84 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{14 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{44 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{9 \, \sqrt{a} \sqrt{e} \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)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{35 \, {\left(e^{5} + \frac{4 \, e^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, e^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, e^{5} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{e^{5} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} 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{9}{2}}}"," ",0,"-2/35*(9*sqrt(a)*sqrt(e) - 44*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 14*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 84*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 84*sqrt(a)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 14*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 44*sqrt(a)*sqrt(e)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 9*sqrt(a)*sqrt(e)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((e^5 + 4*e^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*e^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*e^5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + e^5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2))","B",0
280,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^(3/2), x)","F",0
281,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^(3/2), x)","F",0
282,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^(3/2), x)","F",0
283,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)/sqrt(e*cos(d*x + c)), x)","F",0
284,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)/(e*cos(d*x + c))^(3/2), x)","F",0
285,1,131,0,1.745008," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{\frac{3}{2}} \sqrt{e} - \frac{a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{3 \, {\left(e^{3} + \frac{e^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}"," ",0,"2/3*(a^(3/2)*sqrt(e) - a^(3/2)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((e^3 + e^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2))","B",0
286,1,207,0,0.967530," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, a^{\frac{3}{2}} \sqrt{e} - \frac{4 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{5 \, {\left(e^{4} + \frac{2 \, e^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{e^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}"," ",0,"2/5*(3*a^(3/2)*sqrt(e) - 4*a^(3/2)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^(3/2)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3*a^(3/2)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((e^4 + 2*e^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + e^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2))","B",0
287,1,281,0,1.129383," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{\frac{3}{2}} \sqrt{e} - \frac{24 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{33 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{33 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{24 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{21 \, {\left(e^{5} + \frac{3 \, e^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, e^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{e^{5} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}}}"," ",0,"-2/21*(a^(3/2)*sqrt(e) - 24*a^(3/2)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 33*a^(3/2)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 33*a^(3/2)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 24*a^(3/2)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^(3/2)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((e^5 + 3*e^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*e^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + e^5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2))","B",0
288,1,357,0,1.014178," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(11/2),x, algorithm=""maxima"")","\frac{2 \, {\left(19 \, a^{\frac{3}{2}} \sqrt{e} - \frac{12 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{58 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{116 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{116 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{58 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{12 \, a^{\frac{3}{2}} \sqrt{e} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{19 \, a^{\frac{3}{2}} \sqrt{e} \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)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{45 \, {\left(e^{6} + \frac{4 \, e^{6} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, e^{6} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, e^{6} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{e^{6} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} 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{11}{2}}}"," ",0,"2/45*(19*a^(3/2)*sqrt(e) - 12*a^(3/2)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 58*a^(3/2)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 116*a^(3/2)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 116*a^(3/2)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 58*a^(3/2)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 12*a^(3/2)*sqrt(e)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 19*a^(3/2)*sqrt(e)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((e^6 + 4*e^6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*e^6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*e^6*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + e^6*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2))","B",0
289,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^(5/2), x)","F",0
290,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^(5/2), x)","F",0
291,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)/sqrt(e*cos(d*x + c)), x)","F",0
292,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)/(e*cos(d*x + c))^(3/2), x)","F",0
293,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)/(e*cos(d*x + c))^(5/2), x)","F",0
294,1,131,0,1.150579," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{\frac{5}{2}} \sqrt{e} - \frac{a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\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)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{5 \, {\left(e^{4} + \frac{e^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}"," ",0,"2/5*(a^(5/2)*sqrt(e) - a^(5/2)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((e^4 + e^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2))","B",0
295,1,207,0,1.001610," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{\frac{5}{2}} \sqrt{e} - \frac{4 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 \, a^{\frac{5}{2}} \sqrt{e} \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} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{21 \, {\left(e^{5} + \frac{2 \, e^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{e^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}}}"," ",0,"2/21*(5*a^(5/2)*sqrt(e) - 4*a^(5/2)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^(5/2)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5*a^(5/2)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((e^5 + 2*e^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + e^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2))","B",0
296,1,282,0,1.008998," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(11/2),x, algorithm=""maxima"")","\frac{2 \, {\left(17 \, a^{\frac{5}{2}} \sqrt{e} - \frac{40 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{49 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{49 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{40 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{17 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{45 \, {\left(e^{6} + \frac{3 \, e^{6} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, e^{6} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{e^{6} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}}}"," ",0,"2/45*(17*a^(5/2)*sqrt(e) - 40*a^(5/2)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 49*a^(5/2)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 49*a^(5/2)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 40*a^(5/2)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 17*a^(5/2)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((e^6 + 3*e^6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*e^6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + e^6*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + 1)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2))","B",0
297,1,357,0,1.125135," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(13/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, a^{\frac{5}{2}} \sqrt{e} + \frac{52 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{150 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{180 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{180 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{150 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{52 \, a^{\frac{5}{2}} \sqrt{e} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{5 \, a^{\frac{5}{2}} \sqrt{e} \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)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{77 \, {\left(e^{7} + \frac{4 \, e^{7} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, e^{7} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, e^{7} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{e^{7} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}}}"," ",0,"2/77*(5*a^(5/2)*sqrt(e) + 52*a^(5/2)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 150*a^(5/2)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 180*a^(5/2)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 180*a^(5/2)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 150*a^(5/2)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 52*a^(5/2)*sqrt(e)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 5*a^(5/2)*sqrt(e)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((e^7 + 4*e^7*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*e^7*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*e^7*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + e^7*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2))","B",0
298,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/sqrt(a*sin(d*x + c) + a), x)","F",0
299,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/sqrt(a*sin(d*x + c) + a), x)","F",0
300,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/sqrt(a*sin(d*x + c) + a), x)","F",0
301,1,130,0,0.808112," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{a} \sqrt{e} - \frac{\sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{{\left(a e + \frac{a e \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}}"," ",0,"-2*(sqrt(a)*sqrt(e) - sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((a*e + a*e*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*sqrt(-sin(d*x + c)/(cos(d*x + c) + 1) + 1))","B",0
302,1,210,0,1.032686," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{a} \sqrt{e} + \frac{4 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{\sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{3 \, {\left(a e^{2} + \frac{2 \, a e^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a e^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} 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{3}{2}}}"," ",0,"2/3*(sqrt(a)*sqrt(e) + 4*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((a*e^2 + 2*a*e^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*e^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2))","B",0
303,1,287,0,1.021403," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(7 \, \sqrt{a} \sqrt{e} - \frac{8 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{25 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{8 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{15 \, {\left(a e^{3} + \frac{3 \, a e^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a e^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a e^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} 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{5}{2}}}"," ",0,"-2/15*(7*sqrt(a)*sqrt(e) - 8*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 25*sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 8*sqrt(a)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((a*e^3 + 3*a*e^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*e^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*e^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2))","B",0
304,1,363,0,0.869562," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(9 \, \sqrt{a} \sqrt{e} + \frac{44 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{14 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{84 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{84 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{14 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{44 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{9 \, \sqrt{a} \sqrt{e} \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)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{35 \, {\left(a e^{4} + \frac{4 \, a e^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a e^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a e^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a e^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}"," ",0,"2/35*(9*sqrt(a)*sqrt(e) + 44*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 14*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 84*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 84*sqrt(a)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 14*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 44*sqrt(a)*sqrt(e)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 9*sqrt(a)*sqrt(e)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((a*e^4 + 4*a*e^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*e^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*e^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*e^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2))","B",0
305,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
306,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
307,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
308,1,131,0,0.832592," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{a} \sqrt{e} - \frac{\sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{3 \, {\left(a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}"," ",0,"-2/3*(sqrt(a)*sqrt(e) - sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*sqrt(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2))","B",0
309,1,211,0,1.094733," ","integrate(1/(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, \sqrt{a} \sqrt{e} + \frac{4 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{5 \, {\left(a^{2} e + \frac{2 \, a^{2} e \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} e \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}}"," ",0,"-2/5*(3*sqrt(a)*sqrt(e) + 4*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3*sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((a^2*e + 2*a^2*e*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*e*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2)*sqrt(-sin(d*x + c)/(cos(d*x + c) + 1) + 1))","B",0
310,1,294,0,0.893661," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{a} \sqrt{e} + \frac{24 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{33 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{33 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{24 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{\sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{21 \, {\left(a^{2} e^{2} + \frac{3 \, a^{2} e^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} e^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} e^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}}"," ",0,"2/21*(sqrt(a)*sqrt(e) + 24*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 33*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 33*sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 24*sqrt(a)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((a^2*e^2 + 3*a^2*e^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*e^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*e^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2))","B",0
311,1,373,0,0.575009," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(19 \, \sqrt{a} \sqrt{e} + \frac{12 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{58 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{116 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{116 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{58 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{12 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{19 \, \sqrt{a} \sqrt{e} \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)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{45 \, {\left(a^{2} e^{3} + \frac{4 \, a^{2} e^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{2} e^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{2} e^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} e^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}"," ",0,"-2/45*(19*sqrt(a)*sqrt(e) + 12*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 58*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 116*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 116*sqrt(a)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 58*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 12*sqrt(a)*sqrt(e)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 19*sqrt(a)*sqrt(e)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((a^2*e^3 + 4*a^2*e^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^2*e^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^2*e^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*e^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2))","B",0
312,1,451,0,1.035690," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(37 \, \sqrt{a} \sqrt{e} + \frac{496 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{559 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{544 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1526 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1526 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{544 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{559 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{496 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{37 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{385 \, {\left(a^{2} e^{4} + \frac{5 \, a^{2} e^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{2} e^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{2} e^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{2} e^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{2} e^{4} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}"," ",0,"2/385*(37*sqrt(a)*sqrt(e) + 496*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 559*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 544*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1526*sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1526*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 544*sqrt(a)*sqrt(e)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 559*sqrt(a)*sqrt(e)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 496*sqrt(a)*sqrt(e)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 37*sqrt(a)*sqrt(e)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((a^2*e^4 + 5*a^2*e^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^2*e^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^2*e^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^2*e^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^2*e^4*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2))","B",0
313,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(9/2)/(a*sin(d*x + c) + a)^(5/2), x)","F",0
314,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(a*sin(d*x + c) + a)^(5/2), x)","F",0
315,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(a*sin(d*x + c) + a)^(5/2), x)","F",0
316,1,131,0,0.955195," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{a} e^{\frac{3}{2}} - \frac{\sqrt{a} e^{\frac{3}{2}} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\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)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{5 \, {\left(a^{3} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{7}{2}}}"," ",0,"-2/5*(sqrt(a)*e^(3/2) - sqrt(a)*e^(3/2)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((a^3 + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(7/2))","B",0
317,1,207,0,0.697500," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(5 \, \sqrt{a} \sqrt{e} + \frac{4 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 \, \sqrt{a} \sqrt{e} \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} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{2}}{21 \, {\left(a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{9}{2}}}"," ",0,"-2/21*(5*sqrt(a)*sqrt(e) + 4*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5*sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*sqrt(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^2/((a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(9/2))","B",0
318,1,287,0,0.527762," ","integrate(1/(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(17 \, \sqrt{a} \sqrt{e} + \frac{40 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{49 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{49 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{40 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{17 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{3}}{45 \, {\left(a^{3} e + \frac{3 \, a^{3} e \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} e \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} e \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{11}{2}} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}}"," ",0,"-2/45*(17*sqrt(a)*sqrt(e) + 40*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 49*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 49*sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 40*sqrt(a)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 17*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^3/((a^3*e + 3*a^3*e*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*e*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*e*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(11/2)*sqrt(-sin(d*x + c)/(cos(d*x + c) + 1) + 1))","B",0
319,1,373,0,0.540313," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(5 \, \sqrt{a} \sqrt{e} - \frac{52 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{150 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{180 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{180 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{150 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{52 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{5 \, \sqrt{a} \sqrt{e} \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)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{4}}{77 \, {\left(a^{3} e^{2} + \frac{4 \, a^{3} e^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{3} e^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{3} e^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} e^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{13}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{3}{2}}}"," ",0,"-2/77*(5*sqrt(a)*sqrt(e) - 52*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) - 150*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 180*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 180*sqrt(a)*sqrt(e)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 150*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 52*sqrt(a)*sqrt(e)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 5*sqrt(a)*sqrt(e)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^4/((a^3*e^2 + 4*a^3*e^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^3*e^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^3*e^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*e^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(13/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(3/2))","B",0
320,1,451,0,0.791696," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(197 \, \sqrt{a} \sqrt{e} + \frac{400 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{15 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1760 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2230 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2230 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1760 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{15 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{400 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{197 \, \sqrt{a} \sqrt{e} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} {\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}^{5}}{585 \, {\left(a^{3} e^{3} + \frac{5 \, a^{3} e^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} e^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{3} e^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{3} e^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{3} e^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{15}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}^{\frac{5}{2}}}"," ",0,"-2/585*(197*sqrt(a)*sqrt(e) + 400*sqrt(a)*sqrt(e)*sin(d*x + c)/(cos(d*x + c) + 1) + 15*sqrt(a)*sqrt(e)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1760*sqrt(a)*sqrt(e)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2230*sqrt(a)*sqrt(e)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2230*sqrt(a)*sqrt(e)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1760*sqrt(a)*sqrt(e)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 15*sqrt(a)*sqrt(e)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 400*sqrt(a)*sqrt(e)*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 197*sqrt(a)*sqrt(e)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)^5/((a^3*e^3 + 5*a^3*e^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*e^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^3*e^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^3*e^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^3*e^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d*(sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(15/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + 1)^(5/2))","B",0
321,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{3}}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/3)/sqrt(a*sin(d*x + c) + a), x)","F",0
322,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{3}}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/3)/sqrt(a*sin(d*x + c) + a), x)","F",0
323,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(2/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{2}{3}}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(2/3)/sqrt(a*sin(d*x + c) + a), x)","F",0
324,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{1}{3}}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(1/3)/sqrt(a*sin(d*x + c) + a), x)","F",0
325,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(1/3)*sqrt(a*sin(d*x + c) + a)), x)","F",0
326,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(4/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{4}{3}} \sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(4/3)*sqrt(a*sin(d*x + c) + a)), x)","F",0
327,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{8} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^8*(e*cos(d*x + c))^p, x)","F",0
328,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{3} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3*(e*cos(d*x + c))^p, x)","F",0
329,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{2} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2*(e*cos(d*x + c))^p, x)","F",0
330,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
331,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a), x)","F",0
332,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^2, x)","F",0
333,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^3, x)","F",0
334,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^8,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{8}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^8, x)","F",0
335,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(7/2)*(e*cos(d*x + c))^p, x)","F",0
336,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(5/2)*(e*cos(d*x + c))^p, x)","F",0
337,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*(e*cos(d*x + c))^p, x)","F",0
338,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
339,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/sqrt(a*sin(d*x + c) + a), x)","F",0
340,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(a*sin(d*x + c) + a)^(5/2), x)","F",0
342,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{p} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p*(a*sin(d*x + c) + a)^m, x)","F",0
343,1,520,0,0.709543," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","-\frac{\frac{{\left({\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} a^{m} \sin\left(d x + c\right)^{7} + {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} a^{m} \sin\left(d x + c\right)^{6} - 6 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} a^{m} \sin\left(d x + c\right)^{5} + 30 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(d x + c\right)^{4} - 120 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(d x + c\right)^{3} + 360 \, {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} - 720 \, a^{m} m \sin\left(d x + c\right) + 720 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040} - \frac{3 \, {\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} a^{m} \sin\left(d x + c\right)^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(d x + c\right)^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(d x + c\right)^{3} + 12 \, {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} - 24 \, a^{m} m \sin\left(d x + c\right) + 24 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120} + \frac{3 \, {\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(d x + c\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} - 2 \, a^{m} m \sin\left(d x + c\right) + 2 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} - \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m + 1}}{a {\left(m + 1\right)}}}{d}"," ",0,"-(((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*a^m*sin(d*x + c)^7 + (m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*a^m*sin(d*x + c)^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*a^m*sin(d*x + c)^5 + 30*(m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(d*x + c)^4 - 120*(m^3 + 3*m^2 + 2*m)*a^m*sin(d*x + c)^3 + 360*(m^2 + m)*a^m*sin(d*x + c)^2 - 720*a^m*m*sin(d*x + c) + 720*a^m)*(sin(d*x + c) + 1)^m/(m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040) - 3*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*a^m*sin(d*x + c)^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(d*x + c)^4 - 4*(m^3 + 3*m^2 + 2*m)*a^m*sin(d*x + c)^3 + 12*(m^2 + m)*a^m*sin(d*x + c)^2 - 24*a^m*m*sin(d*x + c) + 24*a^m)*(sin(d*x + c) + 1)^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120) + 3*((m^2 + 3*m + 2)*a^m*sin(d*x + c)^3 + (m^2 + m)*a^m*sin(d*x + c)^2 - 2*a^m*m*sin(d*x + c) + 2*a^m)*(sin(d*x + c) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) - (a*sin(d*x + c) + a)^(m + 1)/(a*(m + 1)))/d","B",0
344,1,266,0,0.815572," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{\frac{{\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} a^{m} \sin\left(d x + c\right)^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(d x + c\right)^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(d x + c\right)^{3} + 12 \, {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} - 24 \, a^{m} m \sin\left(d x + c\right) + 24 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120} - \frac{2 \, {\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(d x + c\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} - 2 \, a^{m} m \sin\left(d x + c\right) + 2 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} + \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m + 1}}{a {\left(m + 1\right)}}}{d}"," ",0,"(((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*a^m*sin(d*x + c)^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(d*x + c)^4 - 4*(m^3 + 3*m^2 + 2*m)*a^m*sin(d*x + c)^3 + 12*(m^2 + m)*a^m*sin(d*x + c)^2 - 24*a^m*m*sin(d*x + c) + 24*a^m)*(sin(d*x + c) + 1)^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120) - 2*((m^2 + 3*m + 2)*a^m*sin(d*x + c)^3 + (m^2 + m)*a^m*sin(d*x + c)^2 - 2*a^m*m*sin(d*x + c) + 2*a^m)*(sin(d*x + c) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) + (a*sin(d*x + c) + a)^(m + 1)/(a*(m + 1)))/d","B",0
345,1,111,0,0.933870," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","-\frac{\frac{{\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(d x + c\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} - 2 \, a^{m} m \sin\left(d x + c\right) + 2 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} - \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m + 1}}{a {\left(m + 1\right)}}}{d}"," ",0,"-(((m^2 + 3*m + 2)*a^m*sin(d*x + c)^3 + (m^2 + m)*a^m*sin(d*x + c)^2 - 2*a^m*m*sin(d*x + c) + 2*a^m)*(sin(d*x + c) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) - (a*sin(d*x + c) + a)^(m + 1)/(a*(m + 1)))/d","B",0
346,1,26,0,0.540520," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m + 1}}{a d {\left(m + 1\right)}}"," ",0,"(a*sin(d*x + c) + a)^(m + 1)/(a*d*(m + 1))","A",0
347,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c), x)","F",0
348,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c)^3, x)","F",0
349,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c)^5, x)","F",0
350,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)^4, x)","F",0
351,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)^2, x)","F",0
352,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c)^2, x)","F",0
353,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sec(d*x + c)^4, x)","F",0
354,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(a*sin(d*x + c) + a)^m, x)","F",0
355,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(a*sin(d*x + c) + a)^m, x)","F",0
356,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^m, x)","F",0
357,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/sqrt(e*cos(d*x + c)), x)","F",0
358,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(3/2), x)","F",0
359,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(5/2), x)","F",0
360,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-4-m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 4} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 4)*(a*sin(d*x + c) + a)^m, x)","F",0
361,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 3} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 3)*(a*sin(d*x + c) + a)^m, x)","F",0
362,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 2)*(a*sin(d*x + c) + a)^m, x)","F",0
363,1,65,0,0.459074," ","integrate((e*cos(d*x+c))^(-1-m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{a^{m} e^{-m - 1} e^{\left(m \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right) - m \log\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)\right)}}{d m}"," ",0,"a^m*e^(-m - 1)*e^(m*log(sin(d*x + c)/(cos(d*x + c) + 1) + 1) - m*log(-sin(d*x + c)/(cos(d*x + c) + 1) + 1))/(d*m)","A",0
364,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^m),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{m}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^m, x)","F",0
365,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1-m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m + 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m + 1)*(a*sin(d*x + c) + a)^m, x)","F",0
366,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(2-m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m + 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m + 2)*(a*sin(d*x + c) + a)^m, x)","F",0
367,1,624,0,1.386332," ","integrate((e*cos(d*x+c))^(5-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left({\left(m^{2} - 11 \, m + 32\right)} a^{m} e^{5} - \frac{2 \, {\left(m^{2} - 15 \, m + 60\right)} a^{m} e^{5} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(3 \, m^{2} - m - 160\right)} a^{m} e^{5} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, {\left(m^{2} - 7 \, m - 20\right)} a^{m} e^{5} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, {\left(m^{2} + 5 \, m + 160\right)} a^{m} e^{5} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, {\left(3 \, m^{2} - 13 \, m + 116\right)} a^{m} e^{5} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, {\left(m^{2} + 5 \, m + 160\right)} a^{m} e^{5} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, {\left(m^{2} - 7 \, m - 20\right)} a^{m} e^{5} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{{\left(3 \, m^{2} - m - 160\right)} a^{m} e^{5} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, {\left(m^{2} - 15 \, m + 60\right)} a^{m} e^{5} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{{\left(m^{2} - 11 \, m + 32\right)} a^{m} e^{5} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} e^{\left(-2 \, m \log\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right) + m \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left({\left(m^{3} - 12 \, m^{2} + 47 \, m - 60\right)} e^{2 \, m} + \frac{5 \, {\left(m^{3} - 12 \, m^{2} + 47 \, m - 60\right)} e^{2 \, m} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, {\left(m^{3} - 12 \, m^{2} + 47 \, m - 60\right)} e^{2 \, m} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, {\left(m^{3} - 12 \, m^{2} + 47 \, m - 60\right)} e^{2 \, m} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, {\left(m^{3} - 12 \, m^{2} + 47 \, m - 60\right)} e^{2 \, m} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{{\left(m^{3} - 12 \, m^{2} + 47 \, m - 60\right)} e^{2 \, m} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d}"," ",0,"((m^2 - 11*m + 32)*a^m*e^5 - 2*(m^2 - 15*m + 60)*a^m*e^5*sin(d*x + c)/(cos(d*x + c) + 1) - (3*m^2 - m - 160)*a^m*e^5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*(m^2 - 7*m - 20)*a^m*e^5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*(m^2 + 5*m + 160)*a^m*e^5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*(3*m^2 - 13*m + 116)*a^m*e^5*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*(m^2 + 5*m + 160)*a^m*e^5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*(m^2 - 7*m - 20)*a^m*e^5*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - (3*m^2 - m - 160)*a^m*e^5*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*(m^2 - 15*m + 60)*a^m*e^5*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + (m^2 - 11*m + 32)*a^m*e^5*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*e^(-2*m*log(-sin(d*x + c)/(cos(d*x + c) + 1) + 1) + m*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1))/(((m^3 - 12*m^2 + 47*m - 60)*e^(2*m) + 5*(m^3 - 12*m^2 + 47*m - 60)*e^(2*m)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*(m^3 - 12*m^2 + 47*m - 60)*e^(2*m)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*(m^3 - 12*m^2 + 47*m - 60)*e^(2*m)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*(m^3 - 12*m^2 + 47*m - 60)*e^(2*m)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + (m^3 - 12*m^2 + 47*m - 60)*e^(2*m)*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d)","B",0
368,1,351,0,1.380730," ","integrate((e*cos(d*x+c))^(3-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left(a^{m} e^{3} {\left(m - 4\right)} - \frac{2 \, a^{m} e^{3} {\left(m - 6\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{a^{m} e^{3} {\left(m + 12\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a^{m} e^{3} {\left(m + 2\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a^{m} e^{3} {\left(m + 12\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, a^{m} e^{3} {\left(m - 6\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{m} e^{3} {\left(m - 4\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} e^{\left(-2 \, m \log\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right) + m \log\left(\frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left({\left(m^{2} - 5 \, m + 6\right)} e^{2 \, m} + \frac{3 \, {\left(m^{2} - 5 \, m + 6\right)} e^{2 \, m} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, {\left(m^{2} - 5 \, m + 6\right)} e^{2 \, m} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{{\left(m^{2} - 5 \, m + 6\right)} e^{2 \, m} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d}"," ",0,"(a^m*e^3*(m - 4) - 2*a^m*e^3*(m - 6)*sin(d*x + c)/(cos(d*x + c) + 1) - a^m*e^3*(m + 12)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a^m*e^3*(m + 2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a^m*e^3*(m + 12)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*a^m*e^3*(m - 6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^m*e^3*(m - 4)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*e^(-2*m*log(-sin(d*x + c)/(cos(d*x + c) + 1) + 1) + m*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1))/(((m^2 - 5*m + 6)*e^(2*m) + 3*(m^2 - 5*m + 6)*e^(2*m)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*(m^2 - 5*m + 6)*e^(2*m)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + (m^2 - 5*m + 6)*e^(2*m)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d)","B",0
369,1,144,0,0.953555," ","integrate((e*cos(d*x+c))^(1-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left(a^{m} e - \frac{2 \, a^{m} e \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a^{m} e \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} e^{\left(-2 \, m \log\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right) + m \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 \, m} {\left(m - 1\right)} + \frac{e^{2 \, m} {\left(m - 1\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)} d}"," ",0,"(a^m*e - 2*a^m*e*sin(d*x + c)/(cos(d*x + c) + 1) + a^m*e*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*e^(-2*m*log(-sin(d*x + c)/(cos(d*x + c) + 1) + 1) + m*log(sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1))/((e^(2*m)*(m - 1) + e^(2*m)*(m - 1)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)*d)","B",0
370,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-1-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m - 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m - 1)*(a*sin(d*x + c) + a)^m, x)","F",0
371,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-3-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m - 3} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m - 3)*(a*sin(d*x + c) + a)^m, x)","F",0
372,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(4-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 4} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m + 4)*(a*sin(d*x + c) + a)^m, x)","F",0
373,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(2-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m + 2)*(a*sin(d*x + c) + a)^m, x)","F",0
374,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^(2*m)),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{2 \, m}}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(2*m), x)","F",0
375,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-2-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-2 \, m - 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-2*m - 2)*(a*sin(d*x + c) + a)^m, x)","F",0
376,1,70,0,0.339489," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{5 \, b \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} - 15 \, b \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3} + 15 \, b \sin\left(d x + c\right)^{2} + 30 \, a \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(5*b*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 - 15*b*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3 + 15*b*sin(d*x + c)^2 + 30*a*sin(d*x + c))/d","A",0
377,1,48,0,0.315778," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, b \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 6 \, b \sin\left(d x + c\right)^{2} - 12 \, a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*b*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 6*b*sin(d*x + c)^2 - 12*a*sin(d*x + c))/d","A",0
378,1,20,0,0.354232," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{2 \, b d}"," ",0,"1/2*(b*sin(d*x + c) + a)^2/(b*d)","A",0
379,1,35,0,0.356490," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(a - b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a + b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{2 \, d}"," ",0,"1/2*((a - b)*log(sin(d*x + c) + 1) - (a + b)*log(sin(d*x + c) - 1))/d","A",0
380,1,53,0,0.324153," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sin\left(d x + c\right) + 1\right) - a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(a \sin\left(d x + c\right) + b\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*(a*log(sin(d*x + c) + 1) - a*log(sin(d*x + c) - 1) - 2*(a*sin(d*x + c) + b)/(sin(d*x + c)^2 - 1))/d","A",0
381,1,78,0,0.328058," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, a \sin\left(d x + c\right)^{3} - 5 \, a \sin\left(d x + c\right) - 2 \, b\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*(3*a*log(sin(d*x + c) + 1) - 3*a*log(sin(d*x + c) - 1) - 2*(3*a*sin(d*x + c)^3 - 5*a*sin(d*x + c) - 2*b)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
382,1,48,0,0.370944," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, b \cos\left(d x + c\right)^{5} - 5 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{160 \, d}"," ",0,"-1/160*(32*b*cos(d*x + c)^5 - 5*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a)/d","A",0
383,1,37,0,0.332545," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, b \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a}{12 \, d}"," ",0,"-1/12*(4*b*cos(d*x + c)^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a)/d","A",0
384,1,23,0,0.330967," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \tan\left(d x + c\right) + \frac{b}{\cos\left(d x + c\right)}}{d}"," ",0,"(a*tan(d*x + c) + b/cos(d*x + c))/d","A",0
385,1,35,0,0.328753," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a + \frac{b}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 3*tan(d*x + c))*a + b/cos(d*x + c)^3)/d","A",0
386,1,48,0,0.329424," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a + \frac{3 \, b}{\cos\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*((3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a + 3*b/cos(d*x + c)^5)/d","A",0
387,1,106,0,0.320787," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{15 \, b^{2} \sin\left(d x + c\right)^{7} + 35 \, a b \sin\left(d x + c\right)^{6} - 105 \, a b \sin\left(d x + c\right)^{4} + 21 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{5} + 105 \, a b \sin\left(d x + c\right)^{2} - 35 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{3} + 105 \, a^{2} \sin\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*b^2*sin(d*x + c)^7 + 35*a*b*sin(d*x + c)^6 - 105*a*b*sin(d*x + c)^4 + 21*(a^2 - 2*b^2)*sin(d*x + c)^5 + 105*a*b*sin(d*x + c)^2 - 35*(2*a^2 - b^2)*sin(d*x + c)^3 + 105*a^2*sin(d*x + c))/d","A",0
388,1,73,0,0.321051," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, b^{2} \sin\left(d x + c\right)^{5} + 15 \, a b \sin\left(d x + c\right)^{4} - 30 \, a b \sin\left(d x + c\right)^{2} + 10 \, {\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{3} - 30 \, a^{2} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(6*b^2*sin(d*x + c)^5 + 15*a*b*sin(d*x + c)^4 - 30*a*b*sin(d*x + c)^2 + 10*(a^2 - b^2)*sin(d*x + c)^3 - 30*a^2*sin(d*x + c))/d","A",0
389,1,20,0,0.329937," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{3 \, b d}"," ",0,"1/3*(b*sin(d*x + c) + a)^3/(b*d)","A",0
390,1,60,0,0.329031," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, b^{2} \sin\left(d x + c\right) - {\left(a^{2} - 2 \, a b + b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{2 \, d}"," ",0,"-1/2*(2*b^2*sin(d*x + c) - (a^2 - 2*a*b + b^2)*log(sin(d*x + c) + 1) + (a^2 + 2*a*b + b^2)*log(sin(d*x + c) - 1))/d","A",0
391,1,78,0,0.324876," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(2 \, a b + {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((a^2 - b^2)*log(sin(d*x + c) + 1) - (a^2 - b^2)*log(sin(d*x + c) - 1) - 2*(2*a*b + (a^2 + b^2)*sin(d*x + c))/(sin(d*x + c)^2 - 1))/d","A",0
392,1,115,0,0.320110," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left({\left(3 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{3} - 4 \, a b - {\left(5 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*((3*a^2 - b^2)*log(sin(d*x + c) + 1) - (3*a^2 - b^2)*log(sin(d*x + c) - 1) - 2*((3*a^2 - b^2)*sin(d*x + c)^3 - 4*a*b - (5*a^2 + b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
393,1,114,0,0.328237," ","integrate(cos(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6144 \, a b \cos\left(d x + c\right)^{7} + 112 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 7 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{21504 \, d}"," ",0,"-1/21504*(6144*a*b*cos(d*x + c)^7 + 112*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^2 - 7*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*b^2)/d","A",0
394,1,88,0,0.316864," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{384 \, a b \cos\left(d x + c\right)^{5} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{960 \, d}"," ",0,"-1/960*(384*a*b*cos(d*x + c)^5 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2 - 5*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*b^2)/d","A",0
395,1,64,0,0.333608," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{64 \, a b \cos\left(d x + c\right)^{3} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{96 \, d}"," ",0,"-1/96*(64*a*b*cos(d*x + c)^3 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2 - 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*b^2)/d","A",0
396,1,46,0,0.479609," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} b^{2} - a^{2} \tan\left(d x + c\right) - \frac{2 \, a b}{\cos\left(d x + c\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*b^2 - a^2*tan(d*x + c) - 2*a*b/cos(d*x + c))/d","A",0
397,1,51,0,0.329794," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} + \frac{2 \, a b}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(b^2*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 + 2*a*b/cos(d*x + c)^3)/d","A",0
398,1,76,0,0.372185," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{2} + {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} b^{2} + \frac{6 \, a b}{\cos\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*((3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^2 + (3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*b^2 + 6*a*b/cos(d*x + c)^5)/d","A",0
399,1,97,0,0.322208," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{2} + {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} b^{2} + \frac{30 \, a b}{\cos\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*(3*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^2 + (15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*b^2 + 30*a*b/cos(d*x + c)^7)/d","A",0
400,1,144,0,0.335961," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{105 \, b^{3} \sin\left(d x + c\right)^{8} + 360 \, a b^{2} \sin\left(d x + c\right)^{7} + 140 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)^{6} + 168 \, {\left(a^{3} - 6 \, a b^{2}\right)} \sin\left(d x + c\right)^{5} + 1260 \, a^{2} b \sin\left(d x + c\right)^{2} - 210 \, {\left(6 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{4} + 840 \, a^{3} \sin\left(d x + c\right) - 280 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(d x + c\right)^{3}}{840 \, d}"," ",0,"1/840*(105*b^3*sin(d*x + c)^8 + 360*a*b^2*sin(d*x + c)^7 + 140*(3*a^2*b - 2*b^3)*sin(d*x + c)^6 + 168*(a^3 - 6*a*b^2)*sin(d*x + c)^5 + 1260*a^2*b*sin(d*x + c)^2 - 210*(6*a^2*b - b^3)*sin(d*x + c)^4 + 840*a^3*sin(d*x + c) - 280*(2*a^3 - 3*a*b^2)*sin(d*x + c)^3)/d","A",0
401,1,100,0,0.321985," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{10 \, b^{3} \sin\left(d x + c\right)^{6} + 36 \, a b^{2} \sin\left(d x + c\right)^{5} - 90 \, a^{2} b \sin\left(d x + c\right)^{2} + 15 \, {\left(3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{4} - 60 \, a^{3} \sin\left(d x + c\right) + 20 \, {\left(a^{3} - 3 \, a b^{2}\right)} \sin\left(d x + c\right)^{3}}{60 \, d}"," ",0,"-1/60*(10*b^3*sin(d*x + c)^6 + 36*a*b^2*sin(d*x + c)^5 - 90*a^2*b*sin(d*x + c)^2 + 15*(3*a^2*b - b^3)*sin(d*x + c)^4 - 60*a^3*sin(d*x + c) + 20*(a^3 - 3*a*b^2)*sin(d*x + c)^3)/d","A",0
402,1,20,0,0.314443," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{4 \, b d}"," ",0,"1/4*(b*sin(d*x + c) + a)^4/(b*d)","A",0
403,1,91,0,0.329707," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{b^{3} \sin\left(d x + c\right)^{2} + 6 \, a b^{2} \sin\left(d x + c\right) - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{2 \, d}"," ",0,"-1/2*(b^3*sin(d*x + c)^2 + 6*a*b^2*sin(d*x + c) - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*log(sin(d*x + c) + 1) + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*log(sin(d*x + c) - 1))/d","A",0
404,1,98,0,0.330602," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(a^{3} - 3 \, a b^{2} + 2 \, b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, a^{2} b + b^{3} + {\left(a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((a^3 - 3*a*b^2 + 2*b^3)*log(sin(d*x + c) + 1) - (a^3 - 3*a*b^2 - 2*b^3)*log(sin(d*x + c) - 1) - 2*(3*a^2*b + b^3 + (a^3 + 3*a*b^2)*sin(d*x + c))/(sin(d*x + c)^2 - 1))/d","A",0
405,1,136,0,0.324321," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, {\left(a^{3} - a b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{3} - a b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + \frac{2 \, {\left(4 \, b^{3} \sin\left(d x + c\right)^{2} - 3 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{3} + 6 \, a^{2} b - 2 \, b^{3} + {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*(3*(a^3 - a*b^2)*log(sin(d*x + c) + 1) - 3*(a^3 - a*b^2)*log(sin(d*x + c) - 1) + 2*(4*b^3*sin(d*x + c)^2 - 3*(a^3 - a*b^2)*sin(d*x + c)^3 + 6*a^2*b - 2*b^3 + (5*a^3 + 3*a*b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
406,1,117,0,0.416407," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1344 \, a^{2} b \cos\left(d x + c\right)^{5} - 70 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{2} - 64 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} b^{3}}{2240 \, d}"," ",0,"-1/2240*(1344*a^2*b*cos(d*x + c)^5 - 70*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 - 35*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a*b^2 - 64*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*b^3)/d","A",0
407,1,93,0,1.016639," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{480 \, a^{2} b \cos\left(d x + c\right)^{3} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 45 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{2} - 32 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} b^{3}}{480 \, d}"," ",0,"-1/480*(480*a^2*b*cos(d*x + c)^3 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 - 45*(4*d*x + 4*c - sin(4*d*x + 4*c))*a*b^2 - 32*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*b^3)/d","A",0
408,1,70,0,0.512709," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a b^{2} - b^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - a^{3} \tan\left(d x + c\right) - \frac{3 \, a^{2} b}{\cos\left(d x + c\right)}}{d}"," ",0,"-(3*(d*x + c - tan(d*x + c))*a*b^2 - b^3*(1/cos(d*x + c) + cos(d*x + c)) - a^3*tan(d*x + c) - 3*a^2*b/cos(d*x + c))/d","A",0
409,1,80,0,0.332763," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, a b^{2} \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} - \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} b^{3}}{\cos\left(d x + c\right)^{3}} + \frac{3 \, a^{2} b}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*a*b^2*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 - (3*cos(d*x + c)^2 - 1)*b^3/cos(d*x + c)^3 + 3*a^2*b/cos(d*x + c)^3)/d","A",0
410,1,105,0,0.334780," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{3} + 3 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} a b^{2} - \frac{{\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} b^{3}}{\cos\left(d x + c\right)^{5}} + \frac{9 \, a^{2} b}{\cos\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*((3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^3 + 3*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*a*b^2 - (5*cos(d*x + c)^2 - 3)*b^3/cos(d*x + c)^5 + 9*a^2*b/cos(d*x + c)^5)/d","A",0
411,1,124,0,0.334920," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{3} + {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} a b^{2} - \frac{{\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} b^{3}}{\cos\left(d x + c\right)^{7}} + \frac{15 \, a^{2} b}{\cos\left(d x + c\right)^{7}}}{35 \, d}"," ",0,"1/35*((5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^3 + (15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*a*b^2 - (7*cos(d*x + c)^2 - 5)*b^3/cos(d*x + c)^7 + 15*a^2*b/cos(d*x + c)^7)/d","A",0
412,1,145,0,0.337285," ","integrate(sec(d*x+c)^10*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(35 \, \tan\left(d x + c\right)^{9} + 180 \, \tan\left(d x + c\right)^{7} + 378 \, \tan\left(d x + c\right)^{5} + 420 \, \tan\left(d x + c\right)^{3} + 315 \, \tan\left(d x + c\right)\right)} a^{3} + 3 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} a b^{2} - \frac{5 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 7\right)} b^{3}}{\cos\left(d x + c\right)^{9}} + \frac{105 \, a^{2} b}{\cos\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"1/315*((35*tan(d*x + c)^9 + 180*tan(d*x + c)^7 + 378*tan(d*x + c)^5 + 420*tan(d*x + c)^3 + 315*tan(d*x + c))*a^3 + 3*(35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*a*b^2 - 5*(9*cos(d*x + c)^2 - 7)*b^3/cos(d*x + c)^9 + 105*a^2*b/cos(d*x + c)^9)/d","A",0
413,1,311,0,0.327594," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{495 \, b^{8} \sin\left(d x + c\right)^{13} + 4290 \, a b^{7} \sin\left(d x + c\right)^{12} + 1170 \, {\left(14 \, a^{2} b^{6} - b^{8}\right)} \sin\left(d x + c\right)^{11} + 5148 \, {\left(7 \, a^{3} b^{5} - 2 \, a b^{7}\right)} \sin\left(d x + c\right)^{10} + 25740 \, a^{7} b \sin\left(d x + c\right)^{2} + 715 \, {\left(70 \, a^{4} b^{4} - 56 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)^{9} + 6435 \, a^{8} \sin\left(d x + c\right) + 6435 \, {\left(7 \, a^{5} b^{3} - 14 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(d x + c\right)^{8} + 25740 \, {\left(a^{6} b^{2} - 5 \, a^{4} b^{4} + a^{2} b^{6}\right)} \sin\left(d x + c\right)^{7} + 8580 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 7 \, a^{3} b^{5}\right)} \sin\left(d x + c\right)^{6} + 1287 \, {\left(a^{8} - 56 \, a^{6} b^{2} + 70 \, a^{4} b^{4}\right)} \sin\left(d x + c\right)^{5} - 12870 \, {\left(2 \, a^{7} b - 7 \, a^{5} b^{3}\right)} \sin\left(d x + c\right)^{4} - 4290 \, {\left(a^{8} - 14 \, a^{6} b^{2}\right)} \sin\left(d x + c\right)^{3}}{6435 \, d}"," ",0,"1/6435*(495*b^8*sin(d*x + c)^13 + 4290*a*b^7*sin(d*x + c)^12 + 1170*(14*a^2*b^6 - b^8)*sin(d*x + c)^11 + 5148*(7*a^3*b^5 - 2*a*b^7)*sin(d*x + c)^10 + 25740*a^7*b*sin(d*x + c)^2 + 715*(70*a^4*b^4 - 56*a^2*b^6 + b^8)*sin(d*x + c)^9 + 6435*a^8*sin(d*x + c) + 6435*(7*a^5*b^3 - 14*a^3*b^5 + a*b^7)*sin(d*x + c)^8 + 25740*(a^6*b^2 - 5*a^4*b^4 + a^2*b^6)*sin(d*x + c)^7 + 8580*(a^7*b - 14*a^5*b^3 + 7*a^3*b^5)*sin(d*x + c)^6 + 1287*(a^8 - 56*a^6*b^2 + 70*a^4*b^4)*sin(d*x + c)^5 - 12870*(2*a^7*b - 7*a^5*b^3)*sin(d*x + c)^4 - 4290*(a^8 - 14*a^6*b^2)*sin(d*x + c)^3)/d","B",0
414,1,233,0,0.325953," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{45 \, b^{8} \sin\left(d x + c\right)^{11} + 396 \, a b^{7} \sin\left(d x + c\right)^{10} - 1980 \, a^{7} b \sin\left(d x + c\right)^{2} + 55 \, {\left(28 \, a^{2} b^{6} - b^{8}\right)} \sin\left(d x + c\right)^{9} - 495 \, a^{8} \sin\left(d x + c\right) + 495 \, {\left(7 \, a^{3} b^{5} - a b^{7}\right)} \sin\left(d x + c\right)^{8} + 990 \, {\left(5 \, a^{4} b^{4} - 2 \, a^{2} b^{6}\right)} \sin\left(d x + c\right)^{7} + 4620 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} \sin\left(d x + c\right)^{6} + 1386 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{4} b^{4}\right)} \sin\left(d x + c\right)^{5} + 990 \, {\left(a^{7} b - 7 \, a^{5} b^{3}\right)} \sin\left(d x + c\right)^{4} + 165 \, {\left(a^{8} - 28 \, a^{6} b^{2}\right)} \sin\left(d x + c\right)^{3}}{495 \, d}"," ",0,"-1/495*(45*b^8*sin(d*x + c)^11 + 396*a*b^7*sin(d*x + c)^10 - 1980*a^7*b*sin(d*x + c)^2 + 55*(28*a^2*b^6 - b^8)*sin(d*x + c)^9 - 495*a^8*sin(d*x + c) + 495*(7*a^3*b^5 - a*b^7)*sin(d*x + c)^8 + 990*(5*a^4*b^4 - 2*a^2*b^6)*sin(d*x + c)^7 + 4620*(a^5*b^3 - a^3*b^5)*sin(d*x + c)^6 + 1386*(2*a^6*b^2 - 5*a^4*b^4)*sin(d*x + c)^5 + 990*(a^7*b - 7*a^5*b^3)*sin(d*x + c)^4 + 165*(a^8 - 28*a^6*b^2)*sin(d*x + c)^3)/d","B",0
415,1,20,0,0.340723," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{9}}{9 \, b d}"," ",0,"1/9*(b*sin(d*x + c) + a)^9/(b*d)","A",0
416,1,317,0,0.326030," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{30 \, b^{8} \sin\left(d x + c\right)^{7} + 280 \, a b^{7} \sin\left(d x + c\right)^{6} + 42 \, {\left(28 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)^{5} + 420 \, {\left(7 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(d x + c\right)^{4} + 70 \, {\left(70 \, a^{4} b^{4} + 28 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)^{3} + 840 \, {\left(7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} + a b^{7}\right)} \sin\left(d x + c\right)^{2} - 105 \, {\left(a^{8} - 8 \, a^{7} b + 28 \, a^{6} b^{2} - 56 \, a^{5} b^{3} + 70 \, a^{4} b^{4} - 56 \, a^{3} b^{5} + 28 \, a^{2} b^{6} - 8 \, a b^{7} + b^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, {\left(a^{8} + 8 \, a^{7} b + 28 \, a^{6} b^{2} + 56 \, a^{5} b^{3} + 70 \, a^{4} b^{4} + 56 \, a^{3} b^{5} + 28 \, a^{2} b^{6} + 8 \, a b^{7} + b^{8}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 210 \, {\left(28 \, a^{6} b^{2} + 70 \, a^{4} b^{4} + 28 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)}{210 \, d}"," ",0,"-1/210*(30*b^8*sin(d*x + c)^7 + 280*a*b^7*sin(d*x + c)^6 + 42*(28*a^2*b^6 + b^8)*sin(d*x + c)^5 + 420*(7*a^3*b^5 + a*b^7)*sin(d*x + c)^4 + 70*(70*a^4*b^4 + 28*a^2*b^6 + b^8)*sin(d*x + c)^3 + 840*(7*a^5*b^3 + 7*a^3*b^5 + a*b^7)*sin(d*x + c)^2 - 105*(a^8 - 8*a^7*b + 28*a^6*b^2 - 56*a^5*b^3 + 70*a^4*b^4 - 56*a^3*b^5 + 28*a^2*b^6 - 8*a*b^7 + b^8)*log(sin(d*x + c) + 1) + 105*(a^8 + 8*a^7*b + 28*a^6*b^2 + 56*a^5*b^3 + 70*a^4*b^4 + 56*a^3*b^5 + 28*a^2*b^6 + 8*a*b^7 + b^8)*log(sin(d*x + c) - 1) + 210*(28*a^6*b^2 + 70*a^4*b^4 + 28*a^2*b^6 + b^8)*sin(d*x + c))/d","A",0
417,1,323,0,0.331618," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{12 \, b^{8} \sin\left(d x + c\right)^{5} + 120 \, a b^{7} \sin\left(d x + c\right)^{4} + 40 \, {\left(14 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)^{3} + 240 \, {\left(7 \, a^{3} b^{5} + 2 \, a b^{7}\right)} \sin\left(d x + c\right)^{2} + 15 \, {\left(a^{8} - 28 \, a^{6} b^{2} + 112 \, a^{5} b^{3} - 210 \, a^{4} b^{4} + 224 \, a^{3} b^{5} - 140 \, a^{2} b^{6} + 48 \, a b^{7} - 7 \, b^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(a^{8} - 28 \, a^{6} b^{2} - 112 \, a^{5} b^{3} - 210 \, a^{4} b^{4} - 224 \, a^{3} b^{5} - 140 \, a^{2} b^{6} - 48 \, a b^{7} - 7 \, b^{8}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 60 \, {\left(70 \, a^{4} b^{4} + 56 \, a^{2} b^{6} + 3 \, b^{8}\right)} \sin\left(d x + c\right) - \frac{30 \, {\left(8 \, a^{7} b + 56 \, a^{5} b^{3} + 56 \, a^{3} b^{5} + 8 \, a b^{7} + {\left(a^{8} + 28 \, a^{6} b^{2} + 70 \, a^{4} b^{4} + 28 \, a^{2} b^{6} + b^{8}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{2} - 1}}{60 \, d}"," ",0,"1/60*(12*b^8*sin(d*x + c)^5 + 120*a*b^7*sin(d*x + c)^4 + 40*(14*a^2*b^6 + b^8)*sin(d*x + c)^3 + 240*(7*a^3*b^5 + 2*a*b^7)*sin(d*x + c)^2 + 15*(a^8 - 28*a^6*b^2 + 112*a^5*b^3 - 210*a^4*b^4 + 224*a^3*b^5 - 140*a^2*b^6 + 48*a*b^7 - 7*b^8)*log(sin(d*x + c) + 1) - 15*(a^8 - 28*a^6*b^2 - 112*a^5*b^3 - 210*a^4*b^4 - 224*a^3*b^5 - 140*a^2*b^6 - 48*a*b^7 - 7*b^8)*log(sin(d*x + c) - 1) + 60*(70*a^4*b^4 + 56*a^2*b^6 + 3*b^8)*sin(d*x + c) - 30*(8*a^7*b + 56*a^5*b^3 + 56*a^3*b^5 + 8*a*b^7 + (a^8 + 28*a^6*b^2 + 70*a^4*b^4 + 28*a^2*b^6 + b^8)*sin(d*x + c))/(sin(d*x + c)^2 - 1))/d","A",0
418,1,348,0,0.327666," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{16 \, b^{8} \sin\left(d x + c\right)^{3} + 192 \, a b^{7} \sin\left(d x + c\right)^{2} - 3 \, {\left(3 \, a^{8} - 28 \, a^{6} b^{2} + 210 \, a^{4} b^{4} - 448 \, a^{3} b^{5} + 420 \, a^{2} b^{6} - 192 \, a b^{7} + 35 \, b^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(3 \, a^{8} - 28 \, a^{6} b^{2} + 210 \, a^{4} b^{4} + 448 \, a^{3} b^{5} + 420 \, a^{2} b^{6} + 192 \, a b^{7} + 35 \, b^{8}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 48 \, {\left(28 \, a^{2} b^{6} + 3 \, b^{8}\right)} \sin\left(d x + c\right) - \frac{6 \, {\left(16 \, a^{7} b - 112 \, a^{5} b^{3} - 336 \, a^{3} b^{5} - 80 \, a b^{7} - {\left(3 \, a^{8} - 28 \, a^{6} b^{2} - 350 \, a^{4} b^{4} - 252 \, a^{2} b^{6} - 13 \, b^{8}\right)} \sin\left(d x + c\right)^{3} + 32 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \sin\left(d x + c\right)^{2} + {\left(5 \, a^{8} + 28 \, a^{6} b^{2} - 210 \, a^{4} b^{4} - 196 \, a^{2} b^{6} - 11 \, b^{8}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"-1/48*(16*b^8*sin(d*x + c)^3 + 192*a*b^7*sin(d*x + c)^2 - 3*(3*a^8 - 28*a^6*b^2 + 210*a^4*b^4 - 448*a^3*b^5 + 420*a^2*b^6 - 192*a*b^7 + 35*b^8)*log(sin(d*x + c) + 1) + 3*(3*a^8 - 28*a^6*b^2 + 210*a^4*b^4 + 448*a^3*b^5 + 420*a^2*b^6 + 192*a*b^7 + 35*b^8)*log(sin(d*x + c) - 1) + 48*(28*a^2*b^6 + 3*b^8)*sin(d*x + c) - 6*(16*a^7*b - 112*a^5*b^3 - 336*a^3*b^5 - 80*a*b^7 - (3*a^8 - 28*a^6*b^2 - 350*a^4*b^4 - 252*a^2*b^6 - 13*b^8)*sin(d*x + c)^3 + 32*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*sin(d*x + c)^2 + (5*a^8 + 28*a^6*b^2 - 210*a^4*b^4 - 196*a^2*b^6 - 11*b^8)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
419,1,336,0,0.338223," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{1720320 \, a^{7} b \cos\left(d x + c\right)^{3} - 161280 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{8} - 564480 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{6} b^{2} - 2408448 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{5} b^{3} + 235200 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} b^{4} + 344064 \, {\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^{3} b^{5} + 5880 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 120 \, d x - 120 \, c + 3 \, \sin\left(8 \, d x + 8 \, c\right) + 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} b^{6} - 16384 \, {\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 b^{7} - 21 \, {\left(96 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 640 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 840 \, d x + 840 \, c - 45 \, \sin\left(8 \, d x + 8 \, c\right) - 120 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{8}}{645120 \, d}"," ",0,"-1/645120*(1720320*a^7*b*cos(d*x + c)^3 - 161280*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^8 - 564480*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^6*b^2 - 2408448*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^5*b^3 + 235200*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a^4*b^4 + 344064*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*a^3*b^5 + 5880*(64*sin(2*d*x + 2*c)^3 - 120*d*x - 120*c + 3*sin(8*d*x + 8*c) + 24*sin(4*d*x + 4*c))*a^2*b^6 - 16384*(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*b^7 - 21*(96*sin(2*d*x + 2*c)^5 - 640*sin(2*d*x + 2*c)^3 + 840*d*x + 840*c - 45*sin(8*d*x + 8*c) - 120*sin(4*d*x + 4*c))*b^8)/d","A",0
420,1,348,0,0.432317," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{6720 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{6} b^{2} + 8400 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{4} b^{4} + 4480 \, {\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^{3} b^{5} + 840 \, {\left(15 \, d x + 15 \, c - \frac{9 \, \tan\left(d x + c\right)^{3} + 7 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 8 \, \tan\left(d x + c\right)\right)} a^{2} b^{6} - 384 \, {\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 b^{7} + 5 \, {\left(105 \, d x + 105 \, c - \frac{87 \, \tan\left(d x + c\right)^{5} + 136 \, \tan\left(d x + c\right)^{3} + 57 \, \tan\left(d x + c\right)}{\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 \, \tan\left(d x + c\right)\right)} b^{8} - 13440 \, a^{5} b^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - 240 \, a^{8} \tan\left(d x + c\right) - \frac{1920 \, a^{7} b}{\cos\left(d x + c\right)}}{240 \, d}"," ",0,"-1/240*(6720*(d*x + c - tan(d*x + c))*a^6*b^2 + 8400*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^4*b^4 + 4480*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^3*b^5 + 840*(15*d*x + 15*c - (9*tan(d*x + c)^3 + 7*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 8*tan(d*x + c))*a^2*b^6 - 384*(cos(d*x + c)^5 - 5*cos(d*x + c)^3 + 5/cos(d*x + c) + 15*cos(d*x + c))*a*b^7 + 5*(105*d*x + 105*c - (87*tan(d*x + c)^5 + 136*tan(d*x + c)^3 + 57*tan(d*x + c))/(tan(d*x + c)^6 + 3*tan(d*x + c)^4 + 3*tan(d*x + c)^2 + 1) - 48*tan(d*x + c))*b^8 - 13440*a^5*b^3*(1/cos(d*x + c) + cos(d*x + c)) - 240*a^8*tan(d*x + c) - 1920*a^7*b/cos(d*x + c))/d","A",0
421,1,328,0,0.431413," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{224 \, a^{6} b^{2} \tan\left(d x + c\right)^{3} + 8 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{8} + 560 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{4} b^{4} + 112 \, {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{2} b^{6} + 64 \, {\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 b^{7} + {\left(8 \, \tan\left(d x + c\right)^{3} + 105 \, d x + 105 \, c - \frac{3 \, {\left(13 \, \tan\left(d x + c\right)^{3} + 11 \, \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 72 \, \tan\left(d x + c\right)\right)} b^{8} - 448 \, a^{3} b^{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)} - \frac{448 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{5} b^{3}}{\cos\left(d x + c\right)^{3}} + \frac{64 \, a^{7} b}{\cos\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"1/24*(224*a^6*b^2*tan(d*x + c)^3 + 8*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^8 + 560*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^4*b^4 + 112*(2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^2*b^6 + 64*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*a*b^7 + (8*tan(d*x + c)^3 + 105*d*x + 105*c - 3*(13*tan(d*x + c)^3 + 11*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 72*tan(d*x + c))*b^8 - 448*a^3*b^5*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) - 448*(3*cos(d*x + c)^2 - 1)*a^5*b^3/cos(d*x + c)^3 + 64*a^7*b/cos(d*x + c)^3)/d","A",0
422,1,315,0,0.443455," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{420 \, a^{4} b^{4} \tan\left(d x + c\right)^{5} + 2 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} a^{8} + 56 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} a^{6} b^{2} + 56 \, {\left(3 \, \tan\left(d x + c\right)^{5} - 5 \, \tan\left(d x + c\right)^{3} - 15 \, d x - 15 \, c + 15 \, \tan\left(d x + c\right)\right)} a^{2} b^{6} + {\left(6 \, \tan\left(d x + c\right)^{5} - 20 \, \tan\left(d x + c\right)^{3} - 105 \, d x - 105 \, c + \frac{15 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} + 90 \, \tan\left(d x + c\right)\right)} b^{8} + 48 \, a b^{7} {\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)} - \frac{112 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} a^{5} b^{3}}{\cos\left(d x + c\right)^{5}} + \frac{112 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} + 3\right)} a^{3} b^{5}}{\cos\left(d x + c\right)^{5}} + \frac{48 \, a^{7} b}{\cos\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"1/30*(420*a^4*b^4*tan(d*x + c)^5 + 2*(3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*a^8 + 56*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*a^6*b^2 + 56*(3*tan(d*x + c)^5 - 5*tan(d*x + c)^3 - 15*d*x - 15*c + 15*tan(d*x + c))*a^2*b^6 + (6*tan(d*x + c)^5 - 20*tan(d*x + c)^3 - 105*d*x - 105*c + 15*tan(d*x + c)/(tan(d*x + c)^2 + 1) + 90*tan(d*x + c))*b^8 + 48*a*b^7*((15*cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 1)/cos(d*x + c)^5 + 5*cos(d*x + c)) - 112*(5*cos(d*x + c)^2 - 3)*a^5*b^3/cos(d*x + c)^5 + 112*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 + 3)*a^3*b^5/cos(d*x + c)^5 + 48*a^7*b/cos(d*x + c)^5)/d","A",0
423,1,310,0,0.432163," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{420 \, a^{2} b^{6} \tan\left(d x + c\right)^{7} + 3 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} a^{8} + 28 \, {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} a^{6} b^{2} + 210 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 7 \, \tan\left(d x + c\right)^{5}\right)} a^{4} b^{4} + {\left(15 \, \tan\left(d x + c\right)^{7} - 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 105 \, d x + 105 \, c - 105 \, \tan\left(d x + c\right)\right)} b^{8} - \frac{168 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} a^{5} b^{3}}{\cos\left(d x + c\right)^{7}} + \frac{56 \, {\left(35 \, \cos\left(d x + c\right)^{4} - 42 \, \cos\left(d x + c\right)^{2} + 15\right)} a^{3} b^{5}}{\cos\left(d x + c\right)^{7}} - \frac{24 \, {\left(35 \, \cos\left(d x + c\right)^{6} - 35 \, \cos\left(d x + c\right)^{4} + 21 \, \cos\left(d x + c\right)^{2} - 5\right)} a b^{7}}{\cos\left(d x + c\right)^{7}} + \frac{120 \, a^{7} b}{\cos\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*(420*a^2*b^6*tan(d*x + c)^7 + 3*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*a^8 + 28*(15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*a^6*b^2 + 210*(5*tan(d*x + c)^7 + 7*tan(d*x + c)^5)*a^4*b^4 + (15*tan(d*x + c)^7 - 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 105*d*x + 105*c - 105*tan(d*x + c))*b^8 - 168*(7*cos(d*x + c)^2 - 5)*a^5*b^3/cos(d*x + c)^7 + 56*(35*cos(d*x + c)^4 - 42*cos(d*x + c)^2 + 15)*a^3*b^5/cos(d*x + c)^7 - 24*(35*cos(d*x + c)^6 - 35*cos(d*x + c)^4 + 21*cos(d*x + c)^2 - 5)*a*b^7/cos(d*x + c)^7 + 120*a^7*b/cos(d*x + c)^7)/d","A",0
424,1,315,0,0.334051," ","integrate(sec(d*x+c)^10*(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{35 \, b^{8} \tan\left(d x + c\right)^{9} + {\left(35 \, \tan\left(d x + c\right)^{9} + 180 \, \tan\left(d x + c\right)^{7} + 378 \, \tan\left(d x + c\right)^{5} + 420 \, \tan\left(d x + c\right)^{3} + 315 \, \tan\left(d x + c\right)\right)} a^{8} + 28 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} a^{6} b^{2} + 70 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 90 \, \tan\left(d x + c\right)^{7} + 63 \, \tan\left(d x + c\right)^{5}\right)} a^{4} b^{4} + 140 \, {\left(7 \, \tan\left(d x + c\right)^{9} + 9 \, \tan\left(d x + c\right)^{7}\right)} a^{2} b^{6} - \frac{280 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 7\right)} a^{5} b^{3}}{\cos\left(d x + c\right)^{9}} + \frac{56 \, {\left(63 \, \cos\left(d x + c\right)^{4} - 90 \, \cos\left(d x + c\right)^{2} + 35\right)} a^{3} b^{5}}{\cos\left(d x + c\right)^{9}} - \frac{8 \, {\left(105 \, \cos\left(d x + c\right)^{6} - 189 \, \cos\left(d x + c\right)^{4} + 135 \, \cos\left(d x + c\right)^{2} - 35\right)} a b^{7}}{\cos\left(d x + c\right)^{9}} + \frac{280 \, a^{7} b}{\cos\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"1/315*(35*b^8*tan(d*x + c)^9 + (35*tan(d*x + c)^9 + 180*tan(d*x + c)^7 + 378*tan(d*x + c)^5 + 420*tan(d*x + c)^3 + 315*tan(d*x + c))*a^8 + 28*(35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*a^6*b^2 + 70*(35*tan(d*x + c)^9 + 90*tan(d*x + c)^7 + 63*tan(d*x + c)^5)*a^4*b^4 + 140*(7*tan(d*x + c)^9 + 9*tan(d*x + c)^7)*a^2*b^6 - 280*(9*cos(d*x + c)^2 - 7)*a^5*b^3/cos(d*x + c)^9 + 56*(63*cos(d*x + c)^4 - 90*cos(d*x + c)^2 + 35)*a^3*b^5/cos(d*x + c)^9 - 8*(105*cos(d*x + c)^6 - 189*cos(d*x + c)^4 + 135*cos(d*x + c)^2 - 35)*a*b^7/cos(d*x + c)^9 + 280*a^7*b/cos(d*x + c)^9)/d","A",0
425,1,108,0,0.310961," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{3 \, b^{3} \sin\left(d x + c\right)^{4} - 4 \, a b^{2} \sin\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2} - 12 \, {\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{5}}}{12 \, d}"," ",0,"1/12*((3*b^3*sin(d*x + c)^4 - 4*a*b^2*sin(d*x + c)^3 + 6*(a^2*b - 2*b^3)*sin(d*x + c)^2 - 12*(a^3 - 2*a*b^2)*sin(d*x + c))/b^4 + 12*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/b^5)/d","A",0
426,1,55,0,0.309509," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{b^{2}} + \frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{3}}}{2 \, d}"," ",0,"-1/2*((b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2 + 2*(a^2 - b^2)*log(b*sin(d*x + c) + a)/b^3)/d","A",0
427,1,18,0,0.328347," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\log\left(b \sin\left(d x + c\right) + a\right)}{b d}"," ",0,"log(b*sin(d*x + c) + a)/(b*d)","A",0
428,1,64,0,0.328618," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} - b^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b}}{2 \, d}"," ",0,"-1/2*(2*b*log(b*sin(d*x + c) + a)/(a^2 - b^2) - log(sin(d*x + c) + 1)/(a - b) + log(sin(d*x + c) - 1)/(a + b))/d","A",0
429,1,139,0,0.332660," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{4 \, b^{3} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a - 2 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(a + 2 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(a \sin\left(d x + c\right) - b\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} + b^{2}}}{4 \, d}"," ",0,"1/4*(4*b^3*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) + (a - 2*b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) - (a + 2*b)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) - 2*(a*sin(d*x + c) - b)/((a^2 - b^2)*sin(d*x + c)^2 - a^2 + b^2))/d","A",0
430,1,278,0,0.337159," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{16 \, b^{5} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{{\left(3 \, a^{2} - 9 \, a b + 8 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(3 \, a^{2} + 9 \, a b + 8 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(4 \, b^{3} \sin\left(d x + c\right)^{2} + {\left(3 \, a^{3} - 7 \, a b^{2}\right)} \sin\left(d x + c\right)^{3} + 2 \, a^{2} b - 6 \, b^{3} - {\left(5 \, a^{3} - 9 \, a b^{2}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"-1/16*(16*b^5*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (3*a^2 - 9*a*b + 8*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*a^2 + 9*a*b + 8*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(4*b^3*sin(d*x + c)^2 + (3*a^3 - 7*a*b^2)*sin(d*x + c)^3 + 2*a^2*b - 6*b^3 - (5*a^3 - 9*a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
431,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
432,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
433,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
434,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
435,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
436,-2,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
437,1,190,0,0.314649," ","integrate(cos(d*x+c)^7/(a+b*sin(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} \sin\left(d x + c\right) + a b^{7}} - \frac{2 \, b^{4} \sin\left(d x + c\right)^{5} - 5 \, a b^{3} \sin\left(d x + c\right)^{4} + 10 \, {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(d x + c\right)^{3} - 10 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} \sin\left(d x + c\right)^{2} + 10 \, {\left(5 \, a^{4} - 9 \, a^{2} b^{2} + 3 \, b^{4}\right)} \sin\left(d x + c\right)}{b^{6}} + \frac{60 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \log\left(b \sin\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*sin(d*x + c) + a*b^7) - (2*b^4*sin(d*x + c)^5 - 5*a*b^3*sin(d*x + c)^4 + 10*(a^2*b^2 - b^4)*sin(d*x + c)^3 - 10*(2*a^3*b - 3*a*b^3)*sin(d*x + c)^2 + 10*(5*a^4 - 9*a^2*b^2 + 3*b^4)*sin(d*x + c))/b^6 + 60*(a^5 - 2*a^3*b^2 + a*b^4)*log(b*sin(d*x + c) + a)/b^7)/d","A",0
438,1,116,0,0.314687," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)}}{b^{6} \sin\left(d x + c\right) + a b^{5}} - \frac{b^{2} \sin\left(d x + c\right)^{3} - 3 \, a b \sin\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{3} - a b^{2}\right)} \log\left(b \sin\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*sin(d*x + c) + a*b^5) - (b^2*sin(d*x + c)^3 - 3*a*b*sin(d*x + c)^2 + 3*(3*a^2 - 2*b^2)*sin(d*x + c))/b^4 + 12*(a^3 - a*b^2)*log(b*sin(d*x + c) + a)/b^5)/d","A",0
439,1,61,0,0.310684," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{a^{2} - b^{2}}{b^{4} \sin\left(d x + c\right) + a b^{3}} + \frac{2 \, a \log\left(b \sin\left(d x + c\right) + a\right)}{b^{3}} - \frac{\sin\left(d x + c\right)}{b^{2}}}{d}"," ",0,"((a^2 - b^2)/(b^4*sin(d*x + c) + a*b^3) + 2*a*log(b*sin(d*x + c) + a)/b^3 - sin(d*x + c)/b^2)/d","A",0
440,1,20,0,0.308101," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{1}{{\left(b \sin\left(d x + c\right) + a\right)} b d}"," ",0,"-1/((b*sin(d*x + c) + a)*b*d)","A",0
441,1,118,0,0.317292," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, a b \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, b}{a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}}}{2 \, d}"," ",0,"-1/2*(4*a*b*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) - 2*b/(a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x + c)) - log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2))/d","A",0
442,1,275,0,0.341960," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{16 \, a b^{3} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{{\left(a - 3 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(a + 3 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left(2 \, a^{2} b + 2 \, b^{3} - {\left(a^{2} b + 3 \, b^{3}\right)} \sin\left(d x + c\right)^{2} - {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)\right)}}{a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*(16*a*b^3*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + (a - 3*b)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (a + 3*b)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*(2*a^2*b + 2*b^3 - (a^2*b + 3*b^3)*sin(d*x + c)^2 - (a^3 - a*b^2)*sin(d*x + c))/(a^5 - 2*a^3*b^2 + a*b^4 - (a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c)^3 - (a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c)^2 + (a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c)))/d","A",0
443,1,505,0,0.338331," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{96 \, a b^{5} \log\left(b \sin\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{3 \, {\left(a^{2} - 4 \, a b + 5 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} + \frac{3 \, {\left(a^{2} + 4 \, a b + 5 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{2 \, {\left(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)} \sin\left(d x + c\right)^{4} + 3 \, {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(d x + c\right)^{3} - {\left(5 \, a^{4} b - 28 \, a^{2} b^{3} - 25 \, b^{5}\right)} \sin\left(d x + c\right)^{2} - {\left(5 \, a^{5} - 16 \, a^{3} b^{2} + 11 \, a b^{4}\right)} \sin\left(d x + c\right)\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)} \sin\left(d x + c\right)^{5} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)^{3} - 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)}}{16 \, d}"," ",0,"-1/16*(96*a*b^5*log(b*sin(d*x + c) + a)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - 3*(a^2 - 4*a*b + 5*b^2)*log(sin(d*x + c) + 1)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + 3*(a^2 + 4*a*b + 5*b^2)*log(sin(d*x + c) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 2*(4*a^4*b - 20*a^2*b^3 - 8*b^5 + 3*(a^4*b - 4*a^2*b^3 - 5*b^5)*sin(d*x + c)^4 + 3*(a^5 - 4*a^3*b^2 + 3*a*b^4)*sin(d*x + c)^3 - (5*a^4*b - 28*a^2*b^3 - 25*b^5)*sin(d*x + c)^2 - (5*a^5 - 16*a^3*b^2 + 11*a*b^4)*sin(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)*sin(d*x + c)^5 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sin(d*x + c)^4 - 2*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*sin(d*x + c)^3 - 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sin(d*x + c)^2 + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*sin(d*x + c)))/d","A",0
444,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
445,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
446,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
447,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
448,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
449,1,200,0,0.327508," ","integrate(cos(d*x+c)^7/(a+b*sin(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)} \sin\left(d x + c\right)\right)}}{b^{9} \sin\left(d x + c\right)^{2} + 2 \, a b^{8} \sin\left(d x + c\right) + a^{2} b^{7}} + \frac{b^{3} \sin\left(d x + c\right)^{4} - 4 \, a b^{2} \sin\left(d x + c\right)^{3} + 6 \, {\left(2 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{2} - 4 \, {\left(10 \, a^{3} - 9 \, a b^{2}\right)} \sin\left(d x + c\right)}{b^{6}} + \frac{12 \, {\left(5 \, a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\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)*sin(d*x + c))/(b^9*sin(d*x + c)^2 + 2*a*b^8*sin(d*x + c) + a^2*b^7) + (b^3*sin(d*x + c)^4 - 4*a*b^2*sin(d*x + c)^3 + 6*(2*a^2*b - b^3)*sin(d*x + c)^2 - 4*(10*a^3 - 9*a*b^2)*sin(d*x + c))/b^6 + 12*(5*a^4 - 6*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/b^7)/d","A",0
450,1,131,0,0.317130," ","integrate(cos(d*x+c)^5/(a+b*sin(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)} \sin\left(d x + c\right)}{b^{7} \sin\left(d x + c\right)^{2} + 2 \, a b^{6} \sin\left(d x + c\right) + a^{2} b^{5}} + \frac{b \sin\left(d x + c\right)^{2} - 6 \, a \sin\left(d x + c\right)}{b^{4}} + \frac{4 \, {\left(3 \, a^{2} - b^{2}\right)} \log\left(b \sin\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)*sin(d*x + c))/(b^7*sin(d*x + c)^2 + 2*a*b^6*sin(d*x + c) + a^2*b^5) + (b*sin(d*x + c)^2 - 6*a*sin(d*x + c))/b^4 + 4*(3*a^2 - b^2)*log(b*sin(d*x + c) + a)/b^5)/d","A",0
451,1,76,0,0.317870," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{4 \, a b \sin\left(d x + c\right) + 3 \, a^{2} + b^{2}}{b^{5} \sin\left(d x + c\right)^{2} + 2 \, a b^{4} \sin\left(d x + c\right) + a^{2} b^{3}} + \frac{2 \, \log\left(b \sin\left(d x + c\right) + a\right)}{b^{3}}}{2 \, d}"," ",0,"-1/2*((4*a*b*sin(d*x + c) + 3*a^2 + b^2)/(b^5*sin(d*x + c)^2 + 2*a*b^4*sin(d*x + c) + a^2*b^3) + 2*log(b*sin(d*x + c) + a)/b^3)/d","A",0
452,1,20,0,0.310899," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{2} b d}"," ",0,"-1/2/((b*sin(d*x + c) + a)^2*b*d)","A",0
453,1,223,0,0.340007," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, a^{2} b + b^{3}\right)} \log\left(b \sin\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^{2} \sin\left(d x + c\right) + 5 \, a^{2} b - b^{3}}{a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}}}{2 \, d}"," ",0,"-1/2*(2*(3*a^2*b + b^3)*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (4*a*b^2*sin(d*x + c) + 5*a^2*b - b^3)/(a^6 - 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 - 2*a^2*b^4 + b^6)*sin(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c)) - log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3))/d","A",0
454,1,438,0,0.355626," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(5 \, a^{2} b^{3} + b^{5}\right)} \log\left(b \sin\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{{\left(a - 4 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(a + 4 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} - \frac{2 \, {\left(3 \, a^{4} b + 10 \, a^{2} b^{3} - b^{5} - {\left(a^{3} b^{2} + 11 \, a b^{4}\right)} \sin\left(d x + c\right)^{3} - 2 \, {\left(a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \sin\left(d x + c\right)^{2} - {\left(a^{5} - 3 \, a^{3} b^{2} - 10 \, a b^{4}\right)} \sin\left(d x + c\right)\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)} \sin\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)} \sin\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)} \sin\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)} \sin\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*(8*(5*a^2*b^3 + b^5)*log(b*sin(d*x + c) + a)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + (a - 4*b)*log(sin(d*x + c) + 1)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (a + 4*b)*log(sin(d*x + c) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) - 2*(3*a^4*b + 10*a^2*b^3 - b^5 - (a^3*b^2 + 11*a*b^4)*sin(d*x + c)^3 - 2*(a^4*b + 6*a^2*b^3 - b^5)*sin(d*x + c)^2 - (a^5 - 3*a^3*b^2 - 10*a*b^4)*sin(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)*sin(d*x + c)^4 - 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*sin(d*x + c)^3 - (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*sin(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*sin(d*x + c)))/d","B",0
455,1,725,0,0.373112," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{48 \, {\left(7 \, a^{2} b^{5} + b^{7}\right)} \log\left(b \sin\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{3 \, {\left(a^{2} - 5 \, a b + 8 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}} + \frac{3 \, {\left(a^{2} + 5 \, a b + 8 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} + \frac{2 \, {\left(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)} \sin\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)} \sin\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)} \sin\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)} \sin\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)} \sin\left(d x + c\right)\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)} \sin\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)} \sin\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)} \sin\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)} \sin\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)} \sin\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)} \sin\left(d x + c\right)}}{16 \, d}"," ",0,"-1/16*(48*(7*a^2*b^5 + b^7)*log(b*sin(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) - 3*(a^2 - 5*a*b + 8*b^2)*log(sin(d*x + c) + 1)/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) + 3*(a^2 + 5*a*b + 8*b^2)*log(sin(d*x + c) - 1)/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) + 2*(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)*sin(d*x + c)^5 + 6*(a^6*b - 6*a^4*b^3 - 13*a^2*b^5 + 2*b^7)*sin(d*x + c)^4 + (3*a^7 - 23*a^5*b^2 + 61*a^3*b^4 + 151*a*b^6)*sin(d*x + c)^3 - 2*(5*a^6*b - 37*a^4*b^3 - 73*a^2*b^5 + 9*b^7)*sin(d*x + c)^2 - (5*a^7 - 26*a^5*b^2 + 49*a^3*b^4 + 68*a*b^6)*sin(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)*sin(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)*sin(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)*sin(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)*sin(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)*sin(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)*sin(d*x + c)))/d","B",0
456,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
457,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
458,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
459,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
460,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
461,1,279,0,0.329823," ","integrate(cos(d*x+c)^7/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{35 \, b^{6} \sin\left(d x + c\right)^{6} + 105 \, a b^{5} \sin\left(d x + c\right)^{5} + 5 \, a^{6} - a^{4} b^{2} + a^{2} b^{4} - 5 \, b^{6} + 35 \, {\left(5 \, a^{2} b^{4} - b^{6}\right)} \sin\left(d x + c\right)^{4} + 35 \, {\left(5 \, a^{3} b^{3} - a b^{5}\right)} \sin\left(d x + c\right)^{3} + 21 \, {\left(5 \, a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{2} + 7 \, {\left(5 \, a^{5} b - a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)}{35 \, {\left(b^{14} \sin\left(d x + c\right)^{7} + 7 \, a b^{13} \sin\left(d x + c\right)^{6} + 21 \, a^{2} b^{12} \sin\left(d x + c\right)^{5} + 35 \, a^{3} b^{11} \sin\left(d x + c\right)^{4} + 35 \, a^{4} b^{10} \sin\left(d x + c\right)^{3} + 21 \, a^{5} b^{9} \sin\left(d x + c\right)^{2} + 7 \, a^{6} b^{8} \sin\left(d x + c\right) + a^{7} b^{7}\right)} d}"," ",0,"1/35*(35*b^6*sin(d*x + c)^6 + 105*a*b^5*sin(d*x + c)^5 + 5*a^6 - a^4*b^2 + a^2*b^4 - 5*b^6 + 35*(5*a^2*b^4 - b^6)*sin(d*x + c)^4 + 35*(5*a^3*b^3 - a*b^5)*sin(d*x + c)^3 + 21*(5*a^4*b^2 - a^2*b^4 + b^6)*sin(d*x + c)^2 + 7*(5*a^5*b - a^3*b^3 + a*b^5)*sin(d*x + c))/((b^14*sin(d*x + c)^7 + 7*a*b^13*sin(d*x + c)^6 + 21*a^2*b^12*sin(d*x + c)^5 + 35*a^3*b^11*sin(d*x + c)^4 + 35*a^4*b^10*sin(d*x + c)^3 + 21*a^5*b^9*sin(d*x + c)^2 + 7*a^6*b^8*sin(d*x + c) + a^7*b^7)*d)","A",0
462,1,206,0,0.330823," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{35 \, b^{4} \sin\left(d x + c\right)^{4} + 35 \, a b^{3} \sin\left(d x + c\right)^{3} + a^{4} - 2 \, a^{2} b^{2} + 15 \, b^{4} + 21 \, {\left(a^{2} b^{2} - 2 \, b^{4}\right)} \sin\left(d x + c\right)^{2} + 7 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)}{105 \, {\left(b^{12} \sin\left(d x + c\right)^{7} + 7 \, a b^{11} \sin\left(d x + c\right)^{6} + 21 \, a^{2} b^{10} \sin\left(d x + c\right)^{5} + 35 \, a^{3} b^{9} \sin\left(d x + c\right)^{4} + 35 \, a^{4} b^{8} \sin\left(d x + c\right)^{3} + 21 \, a^{5} b^{7} \sin\left(d x + c\right)^{2} + 7 \, a^{6} b^{6} \sin\left(d x + c\right) + a^{7} b^{5}\right)} d}"," ",0,"-1/105*(35*b^4*sin(d*x + c)^4 + 35*a*b^3*sin(d*x + c)^3 + a^4 - 2*a^2*b^2 + 15*b^4 + 21*(a^2*b^2 - 2*b^4)*sin(d*x + c)^2 + 7*(a^3*b - 2*a*b^3)*sin(d*x + c))/((b^12*sin(d*x + c)^7 + 7*a*b^11*sin(d*x + c)^6 + 21*a^2*b^10*sin(d*x + c)^5 + 35*a^3*b^9*sin(d*x + c)^4 + 35*a^4*b^8*sin(d*x + c)^3 + 21*a^5*b^7*sin(d*x + c)^2 + 7*a^6*b^6*sin(d*x + c) + a^7*b^5)*d)","A",0
463,1,151,0,1.518244," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{21 \, b^{2} \sin\left(d x + c\right)^{2} + 7 \, a b \sin\left(d x + c\right) + a^{2} - 15 \, b^{2}}{105 \, {\left(b^{10} \sin\left(d x + c\right)^{7} + 7 \, a b^{9} \sin\left(d x + c\right)^{6} + 21 \, a^{2} b^{8} \sin\left(d x + c\right)^{5} + 35 \, a^{3} b^{7} \sin\left(d x + c\right)^{4} + 35 \, a^{4} b^{6} \sin\left(d x + c\right)^{3} + 21 \, a^{5} b^{5} \sin\left(d x + c\right)^{2} + 7 \, a^{6} b^{4} \sin\left(d x + c\right) + a^{7} b^{3}\right)} d}"," ",0,"1/105*(21*b^2*sin(d*x + c)^2 + 7*a*b*sin(d*x + c) + a^2 - 15*b^2)/((b^10*sin(d*x + c)^7 + 7*a*b^9*sin(d*x + c)^6 + 21*a^2*b^8*sin(d*x + c)^5 + 35*a^3*b^7*sin(d*x + c)^4 + 35*a^4*b^6*sin(d*x + c)^3 + 21*a^5*b^5*sin(d*x + c)^2 + 7*a^6*b^4*sin(d*x + c) + a^7*b^3)*d)","B",0
464,1,20,0,0.308538," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{1}{7 \, {\left(b \sin\left(d x + c\right) + a\right)}^{7} b d}"," ",0,"-1/7/((b*sin(d*x + c) + a)^7*b*d)","A",0
465,1,1160,0,0.395657," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","-\frac{\frac{1680 \, {\left(a^{7} b + 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} + a b^{7}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{16} - 8 \, a^{14} b^{2} + 28 \, a^{12} b^{4} - 56 \, a^{10} b^{6} + 70 \, a^{8} b^{8} - 56 \, a^{6} b^{10} + 28 \, a^{4} b^{12} - 8 \, a^{2} b^{14} + b^{16}} - \frac{2 \, {\left(1443 \, a^{12} b + 3704 \, a^{10} b^{3} + 1849 \, a^{8} b^{5} - 496 \, a^{6} b^{7} + 309 \, a^{4} b^{9} - 104 \, a^{2} b^{11} + 15 \, b^{13} + 105 \, {\left(7 \, a^{6} b^{7} + 35 \, a^{4} b^{9} + 21 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)^{6} + 105 \, {\left(45 \, a^{7} b^{6} + 217 \, a^{5} b^{8} + 119 \, a^{3} b^{10} + 3 \, a b^{12}\right)} \sin\left(d x + c\right)^{5} + 35 \, {\left(365 \, a^{8} b^{5} + 1680 \, a^{6} b^{7} + 826 \, a^{4} b^{9} + 8 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)^{4} + 35 \, {\left(533 \, a^{9} b^{4} + 2304 \, a^{7} b^{6} + 994 \, a^{5} b^{8} + 8 \, a^{3} b^{10} + a b^{12}\right)} \sin\left(d x + c\right)^{3} + 21 \, {\left(743 \, a^{10} b^{3} + 2934 \, a^{8} b^{5} + 1099 \, a^{6} b^{7} + 29 \, a^{4} b^{9} - 6 \, a^{2} b^{11} + b^{13}\right)} \sin\left(d x + c\right)^{2} + 7 \, {\left(1023 \, a^{11} b^{2} + 3494 \, a^{9} b^{4} + 1219 \, a^{7} b^{6} + 29 \, a^{5} b^{8} - 6 \, a^{3} b^{10} + a b^{12}\right)} \sin\left(d x + c\right)\right)}}{a^{21} - 7 \, a^{19} b^{2} + 21 \, a^{17} b^{4} - 35 \, a^{15} b^{6} + 35 \, a^{13} b^{8} - 21 \, a^{11} b^{10} + 7 \, a^{9} b^{12} - a^{7} b^{14} + {\left(a^{14} b^{7} - 7 \, a^{12} b^{9} + 21 \, a^{10} b^{11} - 35 \, a^{8} b^{13} + 35 \, a^{6} b^{15} - 21 \, a^{4} b^{17} + 7 \, a^{2} b^{19} - b^{21}\right)} \sin\left(d x + c\right)^{7} + 7 \, {\left(a^{15} b^{6} - 7 \, a^{13} b^{8} + 21 \, a^{11} b^{10} - 35 \, a^{9} b^{12} + 35 \, a^{7} b^{14} - 21 \, a^{5} b^{16} + 7 \, a^{3} b^{18} - a b^{20}\right)} \sin\left(d x + c\right)^{6} + 21 \, {\left(a^{16} b^{5} - 7 \, a^{14} b^{7} + 21 \, a^{12} b^{9} - 35 \, a^{10} b^{11} + 35 \, a^{8} b^{13} - 21 \, a^{6} b^{15} + 7 \, a^{4} b^{17} - a^{2} b^{19}\right)} \sin\left(d x + c\right)^{5} + 35 \, {\left(a^{17} b^{4} - 7 \, a^{15} b^{6} + 21 \, a^{13} b^{8} - 35 \, a^{11} b^{10} + 35 \, a^{9} b^{12} - 21 \, a^{7} b^{14} + 7 \, a^{5} b^{16} - a^{3} b^{18}\right)} \sin\left(d x + c\right)^{4} + 35 \, {\left(a^{18} b^{3} - 7 \, a^{16} b^{5} + 21 \, a^{14} b^{7} - 35 \, a^{12} b^{9} + 35 \, a^{10} b^{11} - 21 \, a^{8} b^{13} + 7 \, a^{6} b^{15} - a^{4} b^{17}\right)} \sin\left(d x + c\right)^{3} + 21 \, {\left(a^{19} b^{2} - 7 \, a^{17} b^{4} + 21 \, a^{15} b^{6} - 35 \, a^{13} b^{8} + 35 \, a^{11} b^{10} - 21 \, a^{9} b^{12} + 7 \, a^{7} b^{14} - a^{5} b^{16}\right)} \sin\left(d x + c\right)^{2} + 7 \, {\left(a^{20} b - 7 \, a^{18} b^{3} + 21 \, a^{16} b^{5} - 35 \, a^{14} b^{7} + 35 \, a^{12} b^{9} - 21 \, a^{10} b^{11} + 7 \, a^{8} b^{13} - a^{6} b^{15}\right)} \sin\left(d x + c\right)} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{8} - 8 \, a^{7} b + 28 \, a^{6} b^{2} - 56 \, a^{5} b^{3} + 70 \, a^{4} b^{4} - 56 \, a^{3} b^{5} + 28 \, a^{2} b^{6} - 8 \, a b^{7} + b^{8}} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a^{8} + 8 \, a^{7} b + 28 \, a^{6} b^{2} + 56 \, a^{5} b^{3} + 70 \, a^{4} b^{4} + 56 \, a^{3} b^{5} + 28 \, a^{2} b^{6} + 8 \, a b^{7} + b^{8}}}{210 \, d}"," ",0,"-1/210*(1680*(a^7*b + 7*a^5*b^3 + 7*a^3*b^5 + a*b^7)*log(b*sin(d*x + c) + a)/(a^16 - 8*a^14*b^2 + 28*a^12*b^4 - 56*a^10*b^6 + 70*a^8*b^8 - 56*a^6*b^10 + 28*a^4*b^12 - 8*a^2*b^14 + b^16) - 2*(1443*a^12*b + 3704*a^10*b^3 + 1849*a^8*b^5 - 496*a^6*b^7 + 309*a^4*b^9 - 104*a^2*b^11 + 15*b^13 + 105*(7*a^6*b^7 + 35*a^4*b^9 + 21*a^2*b^11 + b^13)*sin(d*x + c)^6 + 105*(45*a^7*b^6 + 217*a^5*b^8 + 119*a^3*b^10 + 3*a*b^12)*sin(d*x + c)^5 + 35*(365*a^8*b^5 + 1680*a^6*b^7 + 826*a^4*b^9 + 8*a^2*b^11 + b^13)*sin(d*x + c)^4 + 35*(533*a^9*b^4 + 2304*a^7*b^6 + 994*a^5*b^8 + 8*a^3*b^10 + a*b^12)*sin(d*x + c)^3 + 21*(743*a^10*b^3 + 2934*a^8*b^5 + 1099*a^6*b^7 + 29*a^4*b^9 - 6*a^2*b^11 + b^13)*sin(d*x + c)^2 + 7*(1023*a^11*b^2 + 3494*a^9*b^4 + 1219*a^7*b^6 + 29*a^5*b^8 - 6*a^3*b^10 + a*b^12)*sin(d*x + c))/(a^21 - 7*a^19*b^2 + 21*a^17*b^4 - 35*a^15*b^6 + 35*a^13*b^8 - 21*a^11*b^10 + 7*a^9*b^12 - a^7*b^14 + (a^14*b^7 - 7*a^12*b^9 + 21*a^10*b^11 - 35*a^8*b^13 + 35*a^6*b^15 - 21*a^4*b^17 + 7*a^2*b^19 - b^21)*sin(d*x + c)^7 + 7*(a^15*b^6 - 7*a^13*b^8 + 21*a^11*b^10 - 35*a^9*b^12 + 35*a^7*b^14 - 21*a^5*b^16 + 7*a^3*b^18 - a*b^20)*sin(d*x + c)^6 + 21*(a^16*b^5 - 7*a^14*b^7 + 21*a^12*b^9 - 35*a^10*b^11 + 35*a^8*b^13 - 21*a^6*b^15 + 7*a^4*b^17 - a^2*b^19)*sin(d*x + c)^5 + 35*(a^17*b^4 - 7*a^15*b^6 + 21*a^13*b^8 - 35*a^11*b^10 + 35*a^9*b^12 - 21*a^7*b^14 + 7*a^5*b^16 - a^3*b^18)*sin(d*x + c)^4 + 35*(a^18*b^3 - 7*a^16*b^5 + 21*a^14*b^7 - 35*a^12*b^9 + 35*a^10*b^11 - 21*a^8*b^13 + 7*a^6*b^15 - a^4*b^17)*sin(d*x + c)^3 + 21*(a^19*b^2 - 7*a^17*b^4 + 21*a^15*b^6 - 35*a^13*b^8 + 35*a^11*b^10 - 21*a^9*b^12 + 7*a^7*b^14 - a^5*b^16)*sin(d*x + c)^2 + 7*(a^20*b - 7*a^18*b^3 + 21*a^16*b^5 - 35*a^14*b^7 + 35*a^12*b^9 - 21*a^10*b^11 + 7*a^8*b^13 - a^6*b^15)*sin(d*x + c)) - 105*log(sin(d*x + c) + 1)/(a^8 - 8*a^7*b + 28*a^6*b^2 - 56*a^5*b^3 + 70*a^4*b^4 - 56*a^3*b^5 + 28*a^2*b^6 - 8*a*b^7 + b^8) + 105*log(sin(d*x + c) - 1)/(a^8 + 8*a^7*b + 28*a^6*b^2 + 56*a^5*b^3 + 70*a^4*b^4 + 56*a^3*b^5 + 28*a^2*b^6 + 8*a*b^7 + b^8))/d","B",0
466,1,1670,0,0.438267," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\frac{\frac{3360 \, {\left(15 \, a^{7} b^{3} + 63 \, a^{5} b^{5} + 45 \, a^{3} b^{7} + 5 \, a b^{9}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{18} - 9 \, a^{16} b^{2} + 36 \, a^{14} b^{4} - 84 \, a^{12} b^{6} + 126 \, a^{10} b^{8} - 126 \, a^{8} b^{10} + 84 \, a^{6} b^{12} - 36 \, a^{4} b^{14} + 9 \, a^{2} b^{16} - b^{18}} + \frac{105 \, {\left(a - 9 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{9} - 9 \, a^{8} b + 36 \, a^{7} b^{2} - 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} - 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} - 36 \, a^{2} b^{7} + 9 \, a b^{8} - b^{9}} - \frac{105 \, {\left(a + 9 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{9} + 9 \, a^{8} b + 36 \, a^{7} b^{2} + 84 \, a^{6} b^{3} + 126 \, a^{5} b^{4} + 126 \, a^{4} b^{5} + 84 \, a^{3} b^{6} + 36 \, a^{2} b^{7} + 9 \, a b^{8} + b^{9}} - \frac{2 \, {\left(840 \, a^{14} b + 33490 \, a^{12} b^{3} + 57724 \, a^{10} b^{5} + 16354 \, a^{8} b^{7} - 1496 \, a^{6} b^{9} + 814 \, a^{4} b^{11} - 236 \, a^{2} b^{13} + 30 \, b^{15} - 105 \, {\left(a^{8} b^{7} + 196 \, a^{6} b^{9} + 574 \, a^{4} b^{11} + 244 \, a^{2} b^{13} + 9 \, b^{15}\right)} \sin\left(d x + c\right)^{8} - 105 \, {\left(7 \, a^{9} b^{6} + 1252 \, a^{7} b^{8} + 3514 \, a^{5} b^{10} + 1348 \, a^{3} b^{12} + 23 \, a b^{14}\right)} \sin\left(d x + c\right)^{7} - 35 \, {\left(63 \, a^{10} b^{5} + 10066 \, a^{8} b^{7} + 26194 \, a^{6} b^{9} + 7384 \, a^{4} b^{11} - 681 \, a^{2} b^{13} - 18 \, b^{15}\right)} \sin\left(d x + c\right)^{6} - 35 \, {\left(105 \, a^{11} b^{4} + 14506 \, a^{9} b^{6} + 32254 \, a^{7} b^{8} + 160 \, a^{5} b^{10} - 3951 \, a^{3} b^{12} - 66 \, a b^{14}\right)} \sin\left(d x + c\right)^{5} - 7 \, {\left(525 \, a^{12} b^{3} + 59310 \, a^{10} b^{5} + 83812 \, a^{8} b^{7} - 98528 \, a^{6} b^{9} - 44663 \, a^{4} b^{11} - 438 \, a^{2} b^{13} - 18 \, b^{15}\right)} \sin\left(d x + c\right)^{4} - 7 \, {\left(315 \, a^{13} b^{2} + 25930 \, a^{11} b^{4} - 20896 \, a^{9} b^{6} - 166336 \, a^{7} b^{8} - 53641 \, a^{5} b^{10} - 386 \, a^{3} b^{12} - 26 \, a b^{14}\right)} \sin\left(d x + c\right)^{3} - {\left(735 \, a^{14} b + 30550 \, a^{12} b^{3} - 361856 \, a^{10} b^{5} - 919070 \, a^{8} b^{7} - 252845 \, a^{6} b^{9} - 3050 \, a^{4} b^{11} + 310 \, a^{2} b^{13} - 54 \, b^{15}\right)} \sin\left(d x + c\right)^{2} - 7 \, {\left(15 \, a^{15} - 420 \, a^{13} b^{2} - 26140 \, a^{11} b^{4} - 52264 \, a^{9} b^{6} - 13189 \, a^{7} b^{8} - 184 \, a^{5} b^{10} + 26 \, a^{3} b^{12} - 4 \, a b^{14}\right)} \sin\left(d x + c\right)\right)}}{a^{23} - 8 \, a^{21} b^{2} + 28 \, a^{19} b^{4} - 56 \, a^{17} b^{6} + 70 \, a^{15} b^{8} - 56 \, a^{13} b^{10} + 28 \, a^{11} b^{12} - 8 \, a^{9} b^{14} + a^{7} b^{16} - {\left(a^{16} b^{7} - 8 \, a^{14} b^{9} + 28 \, a^{12} b^{11} - 56 \, a^{10} b^{13} + 70 \, a^{8} b^{15} - 56 \, a^{6} b^{17} + 28 \, a^{4} b^{19} - 8 \, a^{2} b^{21} + b^{23}\right)} \sin\left(d x + c\right)^{9} - 7 \, {\left(a^{17} b^{6} - 8 \, a^{15} b^{8} + 28 \, a^{13} b^{10} - 56 \, a^{11} b^{12} + 70 \, a^{9} b^{14} - 56 \, a^{7} b^{16} + 28 \, a^{5} b^{18} - 8 \, a^{3} b^{20} + a b^{22}\right)} \sin\left(d x + c\right)^{8} - {\left(21 \, a^{18} b^{5} - 169 \, a^{16} b^{7} + 596 \, a^{14} b^{9} - 1204 \, a^{12} b^{11} + 1526 \, a^{10} b^{13} - 1246 \, a^{8} b^{15} + 644 \, a^{6} b^{17} - 196 \, a^{4} b^{19} + 29 \, a^{2} b^{21} - b^{23}\right)} \sin\left(d x + c\right)^{7} - 7 \, {\left(5 \, a^{19} b^{4} - 41 \, a^{17} b^{6} + 148 \, a^{15} b^{8} - 308 \, a^{13} b^{10} + 406 \, a^{11} b^{12} - 350 \, a^{9} b^{14} + 196 \, a^{7} b^{16} - 68 \, a^{5} b^{18} + 13 \, a^{3} b^{20} - a b^{22}\right)} \sin\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{20} b^{3} - 43 \, a^{18} b^{5} + 164 \, a^{16} b^{7} - 364 \, a^{14} b^{9} + 518 \, a^{12} b^{11} - 490 \, a^{10} b^{13} + 308 \, a^{8} b^{15} - 124 \, a^{6} b^{17} + 29 \, a^{4} b^{19} - 3 \, a^{2} b^{21}\right)} \sin\left(d x + c\right)^{5} - 7 \, {\left(3 \, a^{21} b^{2} - 29 \, a^{19} b^{4} + 124 \, a^{17} b^{6} - 308 \, a^{15} b^{8} + 490 \, a^{13} b^{10} - 518 \, a^{11} b^{12} + 364 \, a^{9} b^{14} - 164 \, a^{7} b^{16} + 43 \, a^{5} b^{18} - 5 \, a^{3} b^{20}\right)} \sin\left(d x + c\right)^{4} - 7 \, {\left(a^{22} b - 13 \, a^{20} b^{3} + 68 \, a^{18} b^{5} - 196 \, a^{16} b^{7} + 350 \, a^{14} b^{9} - 406 \, a^{12} b^{11} + 308 \, a^{10} b^{13} - 148 \, a^{8} b^{15} + 41 \, a^{6} b^{17} - 5 \, a^{4} b^{19}\right)} \sin\left(d x + c\right)^{3} - {\left(a^{23} - 29 \, a^{21} b^{2} + 196 \, a^{19} b^{4} - 644 \, a^{17} b^{6} + 1246 \, a^{15} b^{8} - 1526 \, a^{13} b^{10} + 1204 \, a^{11} b^{12} - 596 \, a^{9} b^{14} + 169 \, a^{7} b^{16} - 21 \, a^{5} b^{18}\right)} \sin\left(d x + c\right)^{2} + 7 \, {\left(a^{22} b - 8 \, a^{20} b^{3} + 28 \, a^{18} b^{5} - 56 \, a^{16} b^{7} + 70 \, a^{14} b^{9} - 56 \, a^{12} b^{11} + 28 \, a^{10} b^{13} - 8 \, a^{8} b^{15} + a^{6} b^{17}\right)} \sin\left(d x + c\right)}}{420 \, d}"," ",0,"1/420*(3360*(15*a^7*b^3 + 63*a^5*b^5 + 45*a^3*b^7 + 5*a*b^9)*log(b*sin(d*x + c) + a)/(a^18 - 9*a^16*b^2 + 36*a^14*b^4 - 84*a^12*b^6 + 126*a^10*b^8 - 126*a^8*b^10 + 84*a^6*b^12 - 36*a^4*b^14 + 9*a^2*b^16 - b^18) + 105*(a - 9*b)*log(sin(d*x + c) + 1)/(a^9 - 9*a^8*b + 36*a^7*b^2 - 84*a^6*b^3 + 126*a^5*b^4 - 126*a^4*b^5 + 84*a^3*b^6 - 36*a^2*b^7 + 9*a*b^8 - b^9) - 105*(a + 9*b)*log(sin(d*x + c) - 1)/(a^9 + 9*a^8*b + 36*a^7*b^2 + 84*a^6*b^3 + 126*a^5*b^4 + 126*a^4*b^5 + 84*a^3*b^6 + 36*a^2*b^7 + 9*a*b^8 + b^9) - 2*(840*a^14*b + 33490*a^12*b^3 + 57724*a^10*b^5 + 16354*a^8*b^7 - 1496*a^6*b^9 + 814*a^4*b^11 - 236*a^2*b^13 + 30*b^15 - 105*(a^8*b^7 + 196*a^6*b^9 + 574*a^4*b^11 + 244*a^2*b^13 + 9*b^15)*sin(d*x + c)^8 - 105*(7*a^9*b^6 + 1252*a^7*b^8 + 3514*a^5*b^10 + 1348*a^3*b^12 + 23*a*b^14)*sin(d*x + c)^7 - 35*(63*a^10*b^5 + 10066*a^8*b^7 + 26194*a^6*b^9 + 7384*a^4*b^11 - 681*a^2*b^13 - 18*b^15)*sin(d*x + c)^6 - 35*(105*a^11*b^4 + 14506*a^9*b^6 + 32254*a^7*b^8 + 160*a^5*b^10 - 3951*a^3*b^12 - 66*a*b^14)*sin(d*x + c)^5 - 7*(525*a^12*b^3 + 59310*a^10*b^5 + 83812*a^8*b^7 - 98528*a^6*b^9 - 44663*a^4*b^11 - 438*a^2*b^13 - 18*b^15)*sin(d*x + c)^4 - 7*(315*a^13*b^2 + 25930*a^11*b^4 - 20896*a^9*b^6 - 166336*a^7*b^8 - 53641*a^5*b^10 - 386*a^3*b^12 - 26*a*b^14)*sin(d*x + c)^3 - (735*a^14*b + 30550*a^12*b^3 - 361856*a^10*b^5 - 919070*a^8*b^7 - 252845*a^6*b^9 - 3050*a^4*b^11 + 310*a^2*b^13 - 54*b^15)*sin(d*x + c)^2 - 7*(15*a^15 - 420*a^13*b^2 - 26140*a^11*b^4 - 52264*a^9*b^6 - 13189*a^7*b^8 - 184*a^5*b^10 + 26*a^3*b^12 - 4*a*b^14)*sin(d*x + c))/(a^23 - 8*a^21*b^2 + 28*a^19*b^4 - 56*a^17*b^6 + 70*a^15*b^8 - 56*a^13*b^10 + 28*a^11*b^12 - 8*a^9*b^14 + a^7*b^16 - (a^16*b^7 - 8*a^14*b^9 + 28*a^12*b^11 - 56*a^10*b^13 + 70*a^8*b^15 - 56*a^6*b^17 + 28*a^4*b^19 - 8*a^2*b^21 + b^23)*sin(d*x + c)^9 - 7*(a^17*b^6 - 8*a^15*b^8 + 28*a^13*b^10 - 56*a^11*b^12 + 70*a^9*b^14 - 56*a^7*b^16 + 28*a^5*b^18 - 8*a^3*b^20 + a*b^22)*sin(d*x + c)^8 - (21*a^18*b^5 - 169*a^16*b^7 + 596*a^14*b^9 - 1204*a^12*b^11 + 1526*a^10*b^13 - 1246*a^8*b^15 + 644*a^6*b^17 - 196*a^4*b^19 + 29*a^2*b^21 - b^23)*sin(d*x + c)^7 - 7*(5*a^19*b^4 - 41*a^17*b^6 + 148*a^15*b^8 - 308*a^13*b^10 + 406*a^11*b^12 - 350*a^9*b^14 + 196*a^7*b^16 - 68*a^5*b^18 + 13*a^3*b^20 - a*b^22)*sin(d*x + c)^6 - 7*(5*a^20*b^3 - 43*a^18*b^5 + 164*a^16*b^7 - 364*a^14*b^9 + 518*a^12*b^11 - 490*a^10*b^13 + 308*a^8*b^15 - 124*a^6*b^17 + 29*a^4*b^19 - 3*a^2*b^21)*sin(d*x + c)^5 - 7*(3*a^21*b^2 - 29*a^19*b^4 + 124*a^17*b^6 - 308*a^15*b^8 + 490*a^13*b^10 - 518*a^11*b^12 + 364*a^9*b^14 - 164*a^7*b^16 + 43*a^5*b^18 - 5*a^3*b^20)*sin(d*x + c)^4 - 7*(a^22*b - 13*a^20*b^3 + 68*a^18*b^5 - 196*a^16*b^7 + 350*a^14*b^9 - 406*a^12*b^11 + 308*a^10*b^13 - 148*a^8*b^15 + 41*a^6*b^17 - 5*a^4*b^19)*sin(d*x + c)^3 - (a^23 - 29*a^21*b^2 + 196*a^19*b^4 - 644*a^17*b^6 + 1246*a^15*b^8 - 1526*a^13*b^10 + 1204*a^11*b^12 - 596*a^9*b^14 + 169*a^7*b^16 - 21*a^5*b^18)*sin(d*x + c)^2 + 7*(a^22*b - 8*a^20*b^3 + 28*a^18*b^5 - 56*a^16*b^7 + 70*a^14*b^9 - 56*a^12*b^11 + 28*a^10*b^13 - 8*a^8*b^15 + a^6*b^17)*sin(d*x + c)))/d","B",0
467,-2,0,0,0.000000," ","integrate(cos(d*x+c)^8/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
468,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
469,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
470,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
471,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
472,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
473,1,116,0,0.321253," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(315 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 1540 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 990 \, {\left(3 \, a^{2} - b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 2772 \, {\left(a^{3} - a b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} + 1155 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\right)}}{3465 \, b^{5} d}"," ",0,"2/3465*(315*(b*sin(d*x + c) + a)^(11/2) - 1540*(b*sin(d*x + c) + a)^(9/2)*a + 990*(3*a^2 - b^2)*(b*sin(d*x + c) + a)^(7/2) - 2772*(a^3 - a*b^2)*(b*sin(d*x + c) + a)^(5/2) + 1155*(a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c) + a)^(3/2))/(b^5*d)","A",0
474,1,61,0,0.323323," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(15 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 42 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 35 \, {\left(a^{2} - b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\right)}}{105 \, b^{3} d}"," ",0,"-2/105*(15*(b*sin(d*x + c) + a)^(7/2) - 42*(b*sin(d*x + c) + a)^(5/2)*a + 35*(a^2 - b^2)*(b*sin(d*x + c) + a)^(3/2))/(b^3*d)","A",0
475,1,20,0,0.332295," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{3 \, b d}"," ",0,"2/3*(b*sin(d*x + c) + a)^(3/2)/(b*d)","A",0
476,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
477,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
478,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
479,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4, x)","F",0
480,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
481,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
482,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
483,1,116,0,0.345391," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3465 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} - 16380 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} a + 10010 \, {\left(3 \, a^{2} - b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 25740 \, {\left(a^{3} - a b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} + 9009 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\right)}}{45045 \, b^{5} d}"," ",0,"2/45045*(3465*(b*sin(d*x + c) + a)^(13/2) - 16380*(b*sin(d*x + c) + a)^(11/2)*a + 10010*(3*a^2 - b^2)*(b*sin(d*x + c) + a)^(9/2) - 25740*(a^3 - a*b^2)*(b*sin(d*x + c) + a)^(7/2) + 9009*(a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c) + a)^(5/2))/(b^5*d)","A",0
484,1,61,0,0.318895," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(35 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 90 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 63 \, {\left(a^{2} - b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\right)}}{315 \, b^{3} d}"," ",0,"-2/315*(35*(b*sin(d*x + c) + a)^(9/2) - 90*(b*sin(d*x + c) + a)^(7/2)*a + 63*(a^2 - b^2)*(b*sin(d*x + c) + a)^(5/2))/(b^3*d)","A",0
485,1,20,0,0.322577," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{5 \, b d}"," ",0,"2/5*(b*sin(d*x + c) + a)^(5/2)/(b*d)","A",0
486,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
487,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
488,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
489,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
490,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
491,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
492,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
493,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*sec(d*x + c)^6, x)","F",0
494,1,116,0,0.327972," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(3003 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{15}{2}} - 13860 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{13}{2}} a + 8190 \, {\left(3 \, a^{2} - b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 20020 \, {\left(a^{3} - a b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} + 6435 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}}\right)}}{45045 \, b^{5} d}"," ",0,"2/45045*(3003*(b*sin(d*x + c) + a)^(15/2) - 13860*(b*sin(d*x + c) + a)^(13/2)*a + 8190*(3*a^2 - b^2)*(b*sin(d*x + c) + a)^(11/2) - 20020*(a^3 - a*b^2)*(b*sin(d*x + c) + a)^(9/2) + 6435*(a^4 - 2*a^2*b^2 + b^4)*(b*sin(d*x + c) + a)^(7/2))/(b^5*d)","A",0
495,1,61,0,0.361138," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(63 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{11}{2}} - 154 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} a + 99 \, {\left(a^{2} - b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}}\right)}}{693 \, b^{3} d}"," ",0,"-2/693*(63*(b*sin(d*x + c) + a)^(11/2) - 154*(b*sin(d*x + c) + a)^(9/2)*a + 99*(a^2 - b^2)*(b*sin(d*x + c) + a)^(7/2))/(b^3*d)","A",0
496,1,20,0,0.338229," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}}}{7 \, b d}"," ",0,"2/7*(b*sin(d*x + c) + a)^(7/2)/(b*d)","A",0
497,-2,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
498,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
499,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
500,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^4, x)","F",0
501,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^2, x)","F",0
502,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
503,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
504,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*sec(d*x + c)^6, x)","F",0
505,0,0,0,0.000000," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{8}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*sec(d*x + c)^8, x)","F",0
506,1,160,0,0.339627," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(315 \, \sqrt{b \sin\left(d x + c\right) + a} - \frac{42 \, {\left(3 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b \sin\left(d x + c\right) + a} a^{2}\right)}}{b^{2}} + \frac{35 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{9}{2}} - 180 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} a + 378 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 420 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 315 \, \sqrt{b \sin\left(d x + c\right) + a} a^{4}}{b^{4}}\right)}}{315 \, b d}"," ",0,"2/315*(315*sqrt(b*sin(d*x + c) + a) - 42*(3*(b*sin(d*x + c) + a)^(5/2) - 10*(b*sin(d*x + c) + a)^(3/2)*a + 15*sqrt(b*sin(d*x + c) + a)*a^2)/b^2 + (35*(b*sin(d*x + c) + a)^(9/2) - 180*(b*sin(d*x + c) + a)^(7/2)*a + 378*(b*sin(d*x + c) + a)^(5/2)*a^2 - 420*(b*sin(d*x + c) + a)^(3/2)*a^3 + 315*sqrt(b*sin(d*x + c) + a)*a^4)/b^4)/(b*d)","A",0
507,1,75,0,0.317193," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, \sqrt{b \sin\left(d x + c\right) + a} - \frac{3 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 10 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 15 \, \sqrt{b \sin\left(d x + c\right) + a} a^{2}}{b^{2}}\right)}}{15 \, b d}"," ",0,"2/15*(15*sqrt(b*sin(d*x + c) + a) - (3*(b*sin(d*x + c) + a)^(5/2) - 10*(b*sin(d*x + c) + a)^(3/2)*a + 15*sqrt(b*sin(d*x + c) + a)*a^2)/b^2)/(b*d)","A",0
508,1,20,0,0.318109," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{b \sin\left(d x + c\right) + a}}{b d}"," ",0,"2*sqrt(b*sin(d*x + c) + a)/(b*d)","A",0
509,-2,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
510,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
511,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
512,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/sqrt(b*sin(d*x + c) + a), x)","F",0
513,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
514,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
515,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(b*sin(d*x + c) + a), x)","F",0
516,1,124,0,0.321002," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{15 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{7}{2}} - 84 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} a + 70 \, {\left(3 \, a^{2} - b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 420 \, {\left(a^{3} - a b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}}{b^{4}} - \frac{105 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)}}{\sqrt{b \sin\left(d x + c\right) + a} b^{4}}\right)}}{105 \, b d}"," ",0,"2/105*((15*(b*sin(d*x + c) + a)^(7/2) - 84*(b*sin(d*x + c) + a)^(5/2)*a + 70*(3*a^2 - b^2)*(b*sin(d*x + c) + a)^(3/2) - 420*(a^3 - a*b^2)*sqrt(b*sin(d*x + c) + a))/b^4 - 105*(a^4 - 2*a^2*b^2 + b^4)/(sqrt(b*sin(d*x + c) + a)*b^4))/(b*d)","A",0
517,1,67,0,0.325398," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 6 \, \sqrt{b \sin\left(d x + c\right) + a} a}{b^{2}} - \frac{3 \, {\left(a^{2} - b^{2}\right)}}{\sqrt{b \sin\left(d x + c\right) + a} b^{2}}\right)}}{3 \, b d}"," ",0,"-2/3*(((b*sin(d*x + c) + a)^(3/2) - 6*sqrt(b*sin(d*x + c) + a)*a)/b^2 - 3*(a^2 - b^2)/(sqrt(b*sin(d*x + c) + a)*b^2))/(b*d)","A",0
518,1,20,0,0.320319," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2}{\sqrt{b \sin\left(d x + c\right) + a} b d}"," ",0,"-2/(sqrt(b*sin(d*x + c) + a)*b*d)","A",0
519,-2,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
520,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
521,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
522,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{6}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(b*sin(d*x + c) + a)^(3/2), x)","F",0
523,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(b*sin(d*x + c) + a)^(3/2), x)","F",0
524,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sin(d*x + c) + a)^(3/2), x)","F",0
525,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sin(d*x + c) + a)^(3/2), x)","F",0
526,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,1,122,0,0.753905," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 20 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 30 \, {\left(3 \, a^{2} - b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}}{b^{4}} - \frac{5 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - 12 \, {\left(a^{3} - a b^{2}\right)} {\left(b \sin\left(d x + c\right) + a\right)}\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} b^{4}}\right)}}{15 \, b d}"," ",0,"2/15*((3*(b*sin(d*x + c) + a)^(5/2) - 20*(b*sin(d*x + c) + a)^(3/2)*a + 30*(3*a^2 - b^2)*sqrt(b*sin(d*x + c) + a))/b^4 - 5*(a^4 - 2*a^2*b^2 + b^4 - 12*(a^3 - a*b^2)*(b*sin(d*x + c) + a))/((b*sin(d*x + c) + a)^(3/2)*b^4))/(b*d)","A",0
528,1,64,0,0.732782," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, \sqrt{b \sin\left(d x + c\right) + a}}{b^{2}} + \frac{6 \, {\left(b \sin\left(d x + c\right) + a\right)} a - a^{2} + b^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{3 \, b d}"," ",0,"-2/3*(3*sqrt(b*sin(d*x + c) + a)/b^2 + (6*(b*sin(d*x + c) + a)*a - a^2 + b^2)/((b*sin(d*x + c) + a)^(3/2)*b^2))/(b*d)","A",0
529,1,20,0,0.468457," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2}{3 \, {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} b d}"," ",0,"-2/3/((b*sin(d*x + c) + a)^(3/2)*b*d)","A",0
530,-2,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
531,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
532,-2,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
533,0,0,0,0.000000," ","integrate(cos(d*x+c)^8/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{8}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^8/(b*sin(d*x + c) + a)^(5/2), x)","F",0
534,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{6}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(b*sin(d*x + c) + a)^(5/2), x)","F",0
535,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(b*sin(d*x + c) + a)^(5/2), x)","F",0
536,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(b*sin(d*x + c) + a)^(5/2), x)","F",0
537,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(b*sin(d*x + c) + a)^(5/2), x)","F",0
538,-1,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a), x)","F",0
540,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a), x)","F",0
541,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a), x)","F",0
542,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a), x)","F",0
543,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(d x + c\right) + a}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
544,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)/(e*cos(d*x + c))^(3/2), x)","F",0
545,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)/(e*cos(d*x + c))^(5/2), x)","F",0
546,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{b \sin\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)/(e*cos(d*x + c))^(7/2), x)","F",0
547,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)^2, x)","F",0
548,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^2, x)","F",0
549,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^2, x)","F",0
550,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^2, x)","F",0
551,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2/sqrt(e*cos(d*x + c)), x)","F",0
552,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(3/2), x)","F",0
553,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(5/2), x)","F",0
554,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2/(e*cos(d*x + c))^(7/2), x)","F",0
555,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)^3, x)","F",0
556,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^3, x)","F",0
557,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^3, x)","F",0
558,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^3, x)","F",0
559,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/sqrt(e*cos(d*x + c)), x)","F",0
560,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(3/2), x)","F",0
561,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(5/2), x)","F",0
562,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(7/2), x)","F",0
563,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3/(e*cos(d*x + c))^(9/2), x)","F",0
564,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)^4, x)","F",0
565,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^4, x)","F",0
566,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^4, x)","F",0
567,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4*(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{4}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^4, x)","F",0
568,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/sqrt(e*cos(d*x + c)), x)","F",0
569,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(3/2), x)","F",0
570,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(5/2), x)","F",0
571,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(7/2), x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(9/2), x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4/(e*cos(d*x + c))^(11/2), x)","F",0
574,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(11/2)/(b*sin(d*x + c) + a), x)","F",0
575,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(9/2)/(b*sin(d*x + c) + a), x)","F",0
576,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(b*sin(d*x + c) + a), x)","F",0
577,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(b*sin(d*x + c) + a), x)","F",0
578,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(b*sin(d*x + c) + a), x)","F",0
579,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(b*sin(d*x + c) + a), x)","F",0
580,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)), x)","F",0
581,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)), x)","F",0
582,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)), x)","F",0
583,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(b \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(b*sin(d*x + c) + a)), x)","F",0
584,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(11/2)/(b*sin(d*x + c) + a)^2, x)","F",0
585,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(9/2)/(b*sin(d*x + c) + a)^2, x)","F",0
586,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(b*sin(d*x + c) + a)^2, x)","F",0
587,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(b*sin(d*x + c) + a)^2, x)","F",0
588,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(b*sin(d*x + c) + a)^2, x)","F",0
589,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(b*sin(d*x + c) + a)^2, x)","F",0
590,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^2), x)","F",0
591,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^2), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^2), x)","F",0
593,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{13}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(13/2)/(b*sin(d*x + c) + a)^3, x)","F",0
595,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(11/2)/(b*sin(d*x + c) + a)^3, x)","F",0
596,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(9/2)/(b*sin(d*x + c) + a)^3, x)","F",0
597,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(b*sin(d*x + c) + a)^3, x)","F",0
598,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(b*sin(d*x + c) + a)^3, x)","F",0
599,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(b*sin(d*x + c) + a)^3, x)","F",0
600,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(b*sin(d*x + c) + a)^3, x)","F",0
601,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^3), x)","F",0
602,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(15/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(b*sin(d*x + c) + a)^4, x)","F",0
612,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(b \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(b*sin(d*x + c) + a)^4, x)","F",0
613,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,0,0,0,0.000000," ","integrate(1/(c*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c \cos\left(f x + e\right)} \sqrt{b \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(1/(sqrt(c*cos(f*x + e))*sqrt(b*sin(f*x + e) + a)), x)","F",0
616,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{3} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3*(e*cos(d*x + c))^p, x)","F",0
617,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{2} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2*(e*cos(d*x + c))^p, x)","F",0
618,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
619,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a), x)","F",0
620,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^2, x)","F",0
621,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^3, x)","F",0
622,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^8,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*(e*cos(d*x + c))^p, x)","F",0
624,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*(e*cos(d*x + c))^p, x)","F",0
625,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
626,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/sqrt(b*sin(d*x + c) + a), x)","F",0
627,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^(3/2), x)","F",0
628,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{p}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p/(b*sin(d*x + c) + a)^(5/2), x)","F",0
629,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{p} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^p*(b*sin(d*x + c) + a)^m, x)","F",0
630,1,558,0,0.997499," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m + 1}}{b {\left(m + 1\right)}} - \frac{3 \, {\left({\left(m^{2} + 3 \, m + 2\right)} b^{3} \sin\left(d x + c\right)^{3} + {\left(m^{2} + m\right)} a b^{2} \sin\left(d x + c\right)^{2} - 2 \, a^{2} b m \sin\left(d x + c\right) + 2 \, a^{3}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} b^{3}} + \frac{3 \, {\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} b^{5} \sin\left(d x + c\right)^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a b^{4} \sin\left(d x + c\right)^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{2} b^{3} \sin\left(d x + c\right)^{3} + 12 \, {\left(m^{2} + m\right)} a^{3} b^{2} \sin\left(d x + c\right)^{2} - 24 \, a^{4} b m \sin\left(d x + c\right) + 24 \, a^{5}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} b^{5}} - \frac{{\left({\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} b^{7} \sin\left(d x + c\right)^{7} + {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} a b^{6} \sin\left(d x + c\right)^{6} - 6 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} a^{2} b^{5} \sin\left(d x + c\right)^{5} + 30 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{3} b^{4} \sin\left(d x + c\right)^{4} - 120 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{4} b^{3} \sin\left(d x + c\right)^{3} + 360 \, {\left(m^{2} + m\right)} a^{5} b^{2} \sin\left(d x + c\right)^{2} - 720 \, a^{6} b m \sin\left(d x + c\right) + 720 \, a^{7}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040\right)} b^{7}}}{d}"," ",0,"((b*sin(d*x + c) + a)^(m + 1)/(b*(m + 1)) - 3*((m^2 + 3*m + 2)*b^3*sin(d*x + c)^3 + (m^2 + m)*a*b^2*sin(d*x + c)^2 - 2*a^2*b*m*sin(d*x + c) + 2*a^3)*(b*sin(d*x + c) + a)^m/((m^3 + 6*m^2 + 11*m + 6)*b^3) + 3*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*b^5*sin(d*x + c)^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*a*b^4*sin(d*x + c)^4 - 4*(m^3 + 3*m^2 + 2*m)*a^2*b^3*sin(d*x + c)^3 + 12*(m^2 + m)*a^3*b^2*sin(d*x + c)^2 - 24*a^4*b*m*sin(d*x + c) + 24*a^5)*(b*sin(d*x + c) + a)^m/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*b^5) - ((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*b^7*sin(d*x + c)^7 + (m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*a*b^6*sin(d*x + c)^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*a^2*b^5*sin(d*x + c)^5 + 30*(m^4 + 6*m^3 + 11*m^2 + 6*m)*a^3*b^4*sin(d*x + c)^4 - 120*(m^3 + 3*m^2 + 2*m)*a^4*b^3*sin(d*x + c)^3 + 360*(m^2 + m)*a^5*b^2*sin(d*x + c)^2 - 720*a^6*b*m*sin(d*x + c) + 720*a^7)*(b*sin(d*x + c) + a)^m/((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*b^7))/d","B",0
631,1,286,0,1.062625," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m + 1}}{b {\left(m + 1\right)}} - \frac{2 \, {\left({\left(m^{2} + 3 \, m + 2\right)} b^{3} \sin\left(d x + c\right)^{3} + {\left(m^{2} + m\right)} a b^{2} \sin\left(d x + c\right)^{2} - 2 \, a^{2} b m \sin\left(d x + c\right) + 2 \, a^{3}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} b^{3}} + \frac{{\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} b^{5} \sin\left(d x + c\right)^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a b^{4} \sin\left(d x + c\right)^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{2} b^{3} \sin\left(d x + c\right)^{3} + 12 \, {\left(m^{2} + m\right)} a^{3} b^{2} \sin\left(d x + c\right)^{2} - 24 \, a^{4} b m \sin\left(d x + c\right) + 24 \, a^{5}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} b^{5}}}{d}"," ",0,"((b*sin(d*x + c) + a)^(m + 1)/(b*(m + 1)) - 2*((m^2 + 3*m + 2)*b^3*sin(d*x + c)^3 + (m^2 + m)*a*b^2*sin(d*x + c)^2 - 2*a^2*b*m*sin(d*x + c) + 2*a^3)*(b*sin(d*x + c) + a)^m/((m^3 + 6*m^2 + 11*m + 6)*b^3) + ((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*b^5*sin(d*x + c)^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*a*b^4*sin(d*x + c)^4 - 4*(m^3 + 3*m^2 + 2*m)*a^2*b^3*sin(d*x + c)^3 + 12*(m^2 + m)*a^3*b^2*sin(d*x + c)^2 - 24*a^4*b*m*sin(d*x + c) + 24*a^5)*(b*sin(d*x + c) + a)^m/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*b^5))/d","A",0
632,1,117,0,0.783514," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m + 1}}{b {\left(m + 1\right)}} - \frac{{\left({\left(m^{2} + 3 \, m + 2\right)} b^{3} \sin\left(d x + c\right)^{3} + {\left(m^{2} + m\right)} a b^{2} \sin\left(d x + c\right)^{2} - 2 \, a^{2} b m \sin\left(d x + c\right) + 2 \, a^{3}\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{{\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} b^{3}}}{d}"," ",0,"((b*sin(d*x + c) + a)^(m + 1)/(b*(m + 1)) - ((m^2 + 3*m + 2)*b^3*sin(d*x + c)^3 + (m^2 + m)*a*b^2*sin(d*x + c)^2 - 2*a^2*b*m*sin(d*x + c) + 2*a^3)*(b*sin(d*x + c) + a)^m/((m^3 + 6*m^2 + 11*m + 6)*b^3))/d","A",0
633,1,26,0,0.294456," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m + 1}}{b d {\left(m + 1\right)}}"," ",0,"(b*sin(d*x + c) + a)^(m + 1)/(b*d*(m + 1))","A",0
634,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c), x)","F",0
635,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c)^3, x)","F",0
636,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c)^5, x)","F",0
637,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*cos(d*x + c)^4, x)","F",0
638,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*cos(d*x + c)^2, x)","F",0
639,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c)^2, x)","F",0
640,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m*sec(d*x + c)^4, x)","F",0
641,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(b*sin(d*x + c) + a)^m, x)","F",0
642,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)*(b*sin(d*x + c) + a)^m, x)","F",0
643,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^m, x)","F",0
644,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m/sqrt(e*cos(d*x + c)), x)","F",0
645,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(3/2), x)","F",0
646,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(5/2), x)","F",0
647,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-4-m)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 4} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 4)*(b*sin(d*x + c) + a)^m, x)","F",0
648,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-3-m)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 3} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 3)*(b*sin(d*x + c) + a)^m, x)","F",0
649,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-2-m)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 2} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 2)*(b*sin(d*x + c) + a)^m, x)","F",0
650,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(-1-m)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m - 1} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m - 1)*(b*sin(d*x + c) + a)^m, x)","F",0
651,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))^m/((e*cos(d*x+c))^m),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{m}}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^m/(e*cos(d*x + c))^m, x)","F",0
652,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1-m)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m + 1} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m + 1)*(b*sin(d*x + c) + a)^m, x)","F",0
653,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(2-m)*(a+b*sin(d*x+c))^m,x, algorithm=""maxima"")","\int \left(e \cos\left(d x + c\right)\right)^{-m + 2} {\left(b \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(-m + 2)*(b*sin(d*x + c) + a)^m, x)","F",0
