1,1,62,0,1.886138," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{35 \, a \cos\left(d x + c\right)^{8} - 8 \, {\left(5 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} + 8 \, a \cos\left(d x + c\right)^{2} + 16 \, a\right)} \sin\left(d x + c\right)}{280 \, d}"," ",0,"-1/280*(35*a*cos(d*x + c)^8 - 8*(5*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 + 8*a*cos(d*x + c)^2 + 16*a)*sin(d*x + c))/d","A",0
2,1,62,0,2.164056," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{48 \, a \cos\left(d x + c\right)^{7} - 105 \, a d x - 7 \, {\left(8 \, a \cos\left(d x + c\right)^{5} + 10 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{336 \, d}"," ",0,"-1/336*(48*a*cos(d*x + c)^7 - 105*a*d*x - 7*(8*a*cos(d*x + c)^5 + 10*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/d","A",0
3,1,51,0,1.563928," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{5 \, a \cos\left(d x + c\right)^{6} - 2 \, {\left(3 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(5*a*cos(d*x + c)^6 - 2*(3*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c))/d","A",0
4,1,51,0,1.696063," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, a \cos\left(d x + c\right)^{5} - 15 \, a d x - 5 \, {\left(2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40 \, d}"," ",0,"-1/40*(8*a*cos(d*x + c)^5 - 15*a*d*x - 5*(2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
5,1,39,0,1.624807," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a \cos\left(d x + c\right)^{4} - 4 \, {\left(a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*a*cos(d*x + c)^4 - 4*(a*cos(d*x + c)^2 + 2*a)*sin(d*x + c))/d","A",0
6,1,37,0,1.287733," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a \cos\left(d x + c\right)^{3} - 3 \, a d x - 3 \, a \cos\left(d x + c\right) \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*a*cos(d*x + c)^3 - 3*a*d*x - 3*a*cos(d*x + c)*sin(d*x + c))/d","A",0
7,1,25,0,1.382337," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(a*cos(d*x + c)^2 - 2*a*sin(d*x + c))/d","A",0
8,1,17,0,1.596503," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a \log\left(-\sin\left(d x + c\right) + 1\right)}{d}"," ",0,"-a*log(-sin(d*x + c) + 1)/d","A",0
9,1,40,0,1.275889," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a}{d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d}"," ",0,"(a*cos(d*x + c) + a*sin(d*x + c) + a)/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
10,1,67,0,1.062318," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a \sin\left(d x + c\right) - a\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a \sin\left(d x + c\right) - a\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, a}{4 \, {\left(d \sin\left(d x + c\right) - d\right)}}"," ",0,"1/4*((a*sin(d*x + c) - a)*log(sin(d*x + c) + 1) - (a*sin(d*x + c) - a)*log(-sin(d*x + c) + 1) - 2*a)/(d*sin(d*x + c) - d)","A",0
11,1,52,0,1.511011," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, a \sin\left(d x + c\right) - a}{3 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(2*a*cos(d*x + c)^2 + 2*a*sin(d*x + c) - a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
12,1,136,0,1.741055," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, a \cos\left(d x + c\right)^{2} - 3 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 6 \, a \sin\left(d x + c\right) - 2 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(6*a*cos(d*x + c)^2 - 3*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 3*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 6*a*sin(d*x + c) - 2*a)/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
13,1,85,0,1.810015," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{256 \, a^{2} \cos\left(d x + c\right)^{7} - 315 \, a^{2} d x + 7 \, {\left(16 \, a^{2} \cos\left(d x + c\right)^{7} - 24 \, a^{2} \cos\left(d x + c\right)^{5} - 30 \, a^{2} \cos\left(d x + c\right)^{3} - 45 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{896 \, d}"," ",0,"-1/896*(256*a^2*cos(d*x + c)^7 - 315*a^2*d*x + 7*(16*a^2*cos(d*x + c)^7 - 24*a^2*cos(d*x + c)^5 - 30*a^2*cos(d*x + c)^3 - 45*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
14,1,71,0,1.561855," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{35 \, a^{2} \cos\left(d x + c\right)^{6} + {\left(15 \, a^{2} \cos\left(d x + c\right)^{6} - 24 \, a^{2} \cos\left(d x + c\right)^{4} - 32 \, a^{2} \cos\left(d x + c\right)^{2} - 64 \, a^{2}\right)} \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(35*a^2*cos(d*x + c)^6 + (15*a^2*cos(d*x + c)^6 - 24*a^2*cos(d*x + c)^4 - 32*a^2*cos(d*x + c)^2 - 64*a^2)*sin(d*x + c))/d","A",0
15,1,72,0,1.435763," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{96 \, a^{2} \cos\left(d x + c\right)^{5} - 105 \, a^{2} d x + 5 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{5} - 14 \, a^{2} \cos\left(d x + c\right)^{3} - 21 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(96*a^2*cos(d*x + c)^5 - 105*a^2*d*x + 5*(8*a^2*cos(d*x + c)^5 - 14*a^2*cos(d*x + c)^3 - 21*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
16,1,58,0,1.244238," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{5 \, a^{2} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} - 4 \, a^{2}\right)} \sin\left(d x + c\right)}{10 \, d}"," ",0,"-1/10*(5*a^2*cos(d*x + c)^4 + 2*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 - 4*a^2)*sin(d*x + c))/d","A",0
17,1,59,0,1.195256," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{16 \, a^{2} \cos\left(d x + c\right)^{3} - 15 \, a^{2} d x + 3 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{3} - 5 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"-1/24*(16*a^2*cos(d*x + c)^3 - 15*a^2*d*x + 3*(2*a^2*cos(d*x + c)^3 - 5*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
18,1,44,0,1.450286," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, a^{2} \cos\left(d x + c\right)^{2} + {\left(a^{2} \cos\left(d x + c\right)^{2} - 4 \, a^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(3*a^2*cos(d*x + c)^2 + (a^2*cos(d*x + c)^2 - 4*a^2)*sin(d*x + c))/d","B",0
19,1,32,0,1.385369," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\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
20,1,74,0,1.563198," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} d x - 2 \, a^{2} + {\left(a^{2} d x - 2 \, a^{2}\right)} \cos\left(d x + c\right) - {\left(a^{2} d x + 2 \, a^{2}\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d}"," ",0,"-(a^2*d*x - 2*a^2 + (a^2*d*x - 2*a^2)*cos(d*x + c) - (a^2*d*x + 2*a^2)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
21,1,19,0,0.940376," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2}}{d \sin\left(d x + c\right) - d}"," ",0,"-a^2/(d*sin(d*x + c) - d)","A",0
22,1,97,0,1.469809," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2} - {\left(a^{2} \cos\left(d x + c\right) - a^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/3*(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2 - (a^2*cos(d*x + c) - a^2)*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","A",0
23,1,125,0,1.295809," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} \sin\left(d x + c\right) - 4 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/8*(2*a^2*sin(d*x + c) - 4*a^2 + (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(sin(d*x + c) + 1) - (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","B",0
24,1,85,0,1.565945," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} - 3 \, a^{2}\right)} \sin\left(d x + c\right)}{5 \, {\left(d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)\right)}}"," ",0,"-1/5*(4*a^2*cos(d*x + c)^2 - 2*a^2 - (2*a^2*cos(d*x + c)^2 - 3*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3 + 2*d*cos(d*x + c)*sin(d*x + c) - 2*d*cos(d*x + c))","A",0
25,1,203,0,0.950635," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{12 \, a^{2} \cos\left(d x + c\right)^{2} - 4 \, a^{2} - 3 \, {\left(a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, a^{2} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, a^{2} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{2} - 4 \, a^{2}\right)} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right)^{4} + 2 \, d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/24*(12*a^2*cos(d*x + c)^2 - 4*a^2 - 3*(a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^2*sin(d*x + c) - 2*a^2*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 3*(a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^2*sin(d*x + c) - 2*a^2*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(3*a^2*cos(d*x + c)^2 - 4*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4 + 2*d*cos(d*x + c)^2*sin(d*x + c) - 2*d*cos(d*x + c)^2)","A",0
26,1,115,0,1.535935," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{16 \, a^{2} \cos\left(d x + c\right)^{4} - 8 \, a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - {\left(8 \, a^{2} \cos\left(d x + c\right)^{4} - 12 \, a^{2} \cos\left(d x + c\right)^{2} - 5 \, a^{2}\right)} \sin\left(d x + c\right)}{21 \, {\left(d \cos\left(d x + c\right)^{5} + 2 \, d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/21*(16*a^2*cos(d*x + c)^4 - 8*a^2*cos(d*x + c)^2 - 2*a^2 - (8*a^2*cos(d*x + c)^4 - 12*a^2*cos(d*x + c)^2 - 5*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5 + 2*d*cos(d*x + c)^3*sin(d*x + c) - 2*d*cos(d*x + c)^3)","A",0
27,1,98,0,1.727788," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{896 \, a^{3} \cos\left(d x + c\right)^{9} - 4608 \, a^{3} \cos\left(d x + c\right)^{7} + 3465 \, a^{3} d x - 21 \, {\left(144 \, a^{3} \cos\left(d x + c\right)^{7} - 88 \, a^{3} \cos\left(d x + c\right)^{5} - 110 \, a^{3} \cos\left(d x + c\right)^{3} - 165 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8064 \, d}"," ",0,"1/8064*(896*a^3*cos(d*x + c)^9 - 4608*a^3*cos(d*x + c)^7 + 3465*a^3*d*x - 21*(144*a^3*cos(d*x + c)^7 - 88*a^3*cos(d*x + c)^5 - 110*a^3*cos(d*x + c)^3 - 165*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
28,1,85,0,1.293514," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{21 \, a^{3} \cos\left(d x + c\right)^{8} - 112 \, a^{3} \cos\left(d x + c\right)^{6} - 8 \, {\left(9 \, a^{3} \cos\left(d x + c\right)^{6} - 6 \, a^{3} \cos\left(d x + c\right)^{4} - 8 \, a^{3} \cos\left(d x + c\right)^{2} - 16 \, a^{3}\right)} \sin\left(d x + c\right)}{168 \, d}"," ",0,"1/168*(21*a^3*cos(d*x + c)^8 - 112*a^3*cos(d*x + c)^6 - 8*(9*a^3*cos(d*x + c)^6 - 6*a^3*cos(d*x + c)^4 - 8*a^3*cos(d*x + c)^2 - 16*a^3)*sin(d*x + c))/d","A",0
29,1,85,0,1.300078," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{80 \, a^{3} \cos\left(d x + c\right)^{7} - 448 \, a^{3} \cos\left(d x + c\right)^{5} + 315 \, a^{3} d x - 35 \, {\left(8 \, a^{3} \cos\left(d x + c\right)^{5} - 6 \, a^{3} \cos\left(d x + c\right)^{3} - 9 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{560 \, d}"," ",0,"1/560*(80*a^3*cos(d*x + c)^7 - 448*a^3*cos(d*x + c)^5 + 315*a^3*d*x - 35*(8*a^3*cos(d*x + c)^5 - 6*a^3*cos(d*x + c)^3 - 9*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
30,1,72,0,1.628683," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{5 \, a^{3} \cos\left(d x + c\right)^{6} - 30 \, a^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(9 \, a^{3} \cos\left(d x + c\right)^{4} - 8 \, a^{3} \cos\left(d x + c\right)^{2} - 16 \, a^{3}\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(5*a^3*cos(d*x + c)^6 - 30*a^3*cos(d*x + c)^4 - 2*(9*a^3*cos(d*x + c)^4 - 8*a^3*cos(d*x + c)^2 - 16*a^3)*sin(d*x + c))/d","A",0
31,1,72,0,1.594614," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{24 \, a^{3} \cos\left(d x + c\right)^{5} - 160 \, a^{3} \cos\left(d x + c\right)^{3} + 105 \, a^{3} d x - 15 \, {\left(6 \, a^{3} \cos\left(d x + c\right)^{3} - 7 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(24*a^3*cos(d*x + c)^5 - 160*a^3*cos(d*x + c)^3 + 105*a^3*d*x - 15*(6*a^3*cos(d*x + c)^3 - 7*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
32,1,57,0,1.638403," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{3} \cos\left(d x + c\right)^{4} - 8 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(a^3*cos(d*x + c)^4 - 8*a^3*cos(d*x + c)^2 - 4*(a^3*cos(d*x + c)^2 - 2*a^3)*sin(d*x + c))/d","B",0
33,1,45,0,1.549087," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{3} \cos\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*cos(d*x + c)^2 - 8*a^3*log(-sin(d*x + c) + 1) - 6*a^3*sin(d*x + c))/d","A",0
34,1,101,0,1.581420," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, a^{3} d x - a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(3 \, a^{3} d x - 5 \, a^{3}\right)} \cos\left(d x + c\right) - {\left(3 \, a^{3} d x - a^{3} \cos\left(d x + c\right) + 4 \, a^{3}\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d}"," ",0,"-(3*a^3*d*x - a^3*cos(d*x + c)^2 - 4*a^3 + (3*a^3*d*x - 5*a^3)*cos(d*x + c) - (3*a^3*d*x - a^3*cos(d*x + c) + 4*a^3)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
35,1,51,0,1.623587," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} - {\left(a^{3} \sin\left(d x + c\right) - a^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{d \sin\left(d x + c\right) - d}"," ",0,"-(2*a^3 - (a^3*sin(d*x + c) - a^3)*log(-sin(d*x + c) + 1))/(d*sin(d*x + c) - d)","A",0
36,1,99,0,1.671310," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right) + 2 \, a^{3}\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/3*(a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3 - (a^3*cos(d*x + c) + 2*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
37,1,30,0,1.407434," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{a^{3}}{2 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/2*a^3/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
38,1,149,0,1.461285," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} \cos\left(d x + c\right)^{3} - 4 \, a^{3} \cos\left(d x + c\right)^{2} - 9 \, a^{3} \cos\left(d x + c\right) - 3 \, a^{3} + {\left(2 \, a^{3} \cos\left(d x + c\right)^{2} + 6 \, a^{3} \cos\left(d x + c\right) - 3 \, a^{3}\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + 3 \, d \cos\left(d x + c\right)^{2} - 2 \, d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{2} - 2 \, d \cos\left(d x + c\right) - 4 \, d\right)} \sin\left(d x + c\right) - 4 \, d\right)}}"," ",0,"1/15*(2*a^3*cos(d*x + c)^3 - 4*a^3*cos(d*x + c)^2 - 9*a^3*cos(d*x + c) - 3*a^3 + (2*a^3*cos(d*x + c)^2 + 6*a^3*cos(d*x + c) - 3*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3 + 3*d*cos(d*x + c)^2 - 2*d*cos(d*x + c) - (d*cos(d*x + c)^2 - 2*d*cos(d*x + c) - 4*d)*sin(d*x + c) - 4*d)","A",0
39,1,185,0,1.135180," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} \cos\left(d x + c\right)^{2} + 18 \, a^{3} \sin\left(d x + c\right) - 26 \, a^{3} + 3 \, {\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{48 \, {\left(3 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{2} - 4 \, d\right)} \sin\left(d x + c\right) - 4 \, d\right)}}"," ",0,"1/48*(6*a^3*cos(d*x + c)^2 + 18*a^3*sin(d*x + c) - 26*a^3 + 3*(3*a^3*cos(d*x + c)^2 - 4*a^3 - (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*log(sin(d*x + c) + 1) - 3*(3*a^3*cos(d*x + c)^2 - 4*a^3 - (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*log(-sin(d*x + c) + 1))/(3*d*cos(d*x + c)^2 - (d*cos(d*x + c)^2 - 4*d)*sin(d*x + c) - 4*d)","B",0
40,1,112,0,1.582893," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, a^{3} \cos\left(d x + c\right)^{4} - 36 \, a^{3} \cos\left(d x + c\right)^{2} + 15 \, a^{3} + 4 \, {\left(6 \, a^{3} \cos\left(d x + c\right)^{2} - 5 \, a^{3}\right)} \sin\left(d x + c\right)}{35 \, {\left(3 \, d \cos\left(d x + c\right)^{3} - 4 \, d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{3} - 4 \, d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/35*(8*a^3*cos(d*x + c)^4 - 36*a^3*cos(d*x + c)^2 + 15*a^3 + 4*(6*a^3*cos(d*x + c)^2 - 5*a^3)*sin(d*x + c))/(3*d*cos(d*x + c)^3 - 4*d*cos(d*x + c) - (d*cos(d*x + c)^3 - 4*d*cos(d*x + c))*sin(d*x + c))","A",0
41,1,149,0,1.526874," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{286 \, a^{8} \cos\left(d x + c\right)^{12} - 3432 \, a^{8} \cos\left(d x + c\right)^{10} + 10296 \, a^{8} \cos\left(d x + c\right)^{8} - 9152 \, a^{8} \cos\left(d x + c\right)^{6} + {\left(33 \, a^{8} \cos\left(d x + c\right)^{12} - 1212 \, a^{8} \cos\left(d x + c\right)^{10} + 6280 \, a^{8} \cos\left(d x + c\right)^{8} - 8512 \, a^{8} \cos\left(d x + c\right)^{6} + 768 \, a^{8} \cos\left(d x + c\right)^{4} + 1024 \, a^{8} \cos\left(d x + c\right)^{2} + 2048 \, a^{8}\right)} \sin\left(d x + c\right)}{429 \, d}"," ",0,"1/429*(286*a^8*cos(d*x + c)^12 - 3432*a^8*cos(d*x + c)^10 + 10296*a^8*cos(d*x + c)^8 - 9152*a^8*cos(d*x + c)^6 + (33*a^8*cos(d*x + c)^12 - 1212*a^8*cos(d*x + c)^10 + 6280*a^8*cos(d*x + c)^8 - 8512*a^8*cos(d*x + c)^6 + 768*a^8*cos(d*x + c)^4 + 1024*a^8*cos(d*x + c)^2 + 2048*a^8)*sin(d*x + c))/d","B",0
42,1,150,0,1.978966," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{2580480 \, a^{8} \cos\left(d x + c\right)^{11} - 31539200 \, a^{8} \cos\left(d x + c\right)^{9} + 97320960 \, a^{8} \cos\left(d x + c\right)^{7} - 90832896 \, a^{8} \cos\left(d x + c\right)^{5} + 14549535 \, a^{8} d x + 231 \, {\left(1280 \, a^{8} \cos\left(d x + c\right)^{11} - 47744 \, a^{8} \cos\left(d x + c\right)^{9} + 253488 \, a^{8} \cos\left(d x + c\right)^{7} - 359624 \, a^{8} \cos\left(d x + c\right)^{5} + 41990 \, a^{8} \cos\left(d x + c\right)^{3} + 62985 \, a^{8} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3548160 \, d}"," ",0,"1/3548160*(2580480*a^8*cos(d*x + c)^11 - 31539200*a^8*cos(d*x + c)^9 + 97320960*a^8*cos(d*x + c)^7 - 90832896*a^8*cos(d*x + c)^5 + 14549535*a^8*d*x + 231*(1280*a^8*cos(d*x + c)^11 - 47744*a^8*cos(d*x + c)^9 + 253488*a^8*cos(d*x + c)^7 - 359624*a^8*cos(d*x + c)^5 + 41990*a^8*cos(d*x + c)^3 + 62985*a^8*cos(d*x + c))*sin(d*x + c))/d","A",0
43,1,136,0,1.609692," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{44 \, a^{8} \cos\left(d x + c\right)^{10} - 550 \, a^{8} \cos\left(d x + c\right)^{8} + 1760 \, a^{8} \cos\left(d x + c\right)^{6} - 1760 \, a^{8} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{8} \cos\left(d x + c\right)^{10} - 190 \, a^{8} \cos\left(d x + c\right)^{8} + 1040 \, a^{8} \cos\left(d x + c\right)^{6} - 1568 \, a^{8} \cos\left(d x + c\right)^{4} + 256 \, a^{8} \cos\left(d x + c\right)^{2} + 512 \, a^{8}\right)} \sin\left(d x + c\right)}{55 \, d}"," ",0,"1/55*(44*a^8*cos(d*x + c)^10 - 550*a^8*cos(d*x + c)^8 + 1760*a^8*cos(d*x + c)^6 - 1760*a^8*cos(d*x + c)^4 + (5*a^8*cos(d*x + c)^10 - 190*a^8*cos(d*x + c)^8 + 1040*a^8*cos(d*x + c)^6 - 1568*a^8*cos(d*x + c)^4 + 256*a^8*cos(d*x + c)^2 + 512*a^8)*sin(d*x + c))/d","B",0
44,1,137,0,1.446401," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{71680 \, a^{8} \cos\left(d x + c\right)^{9} - 921600 \, a^{8} \cos\left(d x + c\right)^{7} + 3096576 \, a^{8} \cos\left(d x + c\right)^{5} - 3440640 \, a^{8} \cos\left(d x + c\right)^{3} + 765765 \, a^{8} d x + 63 \, {\left(128 \, a^{8} \cos\left(d x + c\right)^{9} - 4976 \, a^{8} \cos\left(d x + c\right)^{7} + 28328 \, a^{8} \cos\left(d x + c\right)^{5} - 46510 \, a^{8} \cos\left(d x + c\right)^{3} + 12155 \, a^{8} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(71680*a^8*cos(d*x + c)^9 - 921600*a^8*cos(d*x + c)^7 + 3096576*a^8*cos(d*x + c)^5 - 3440640*a^8*cos(d*x + c)^3 + 765765*a^8*d*x + 63*(128*a^8*cos(d*x + c)^9 - 4976*a^8*cos(d*x + c)^7 + 28328*a^8*cos(d*x + c)^5 - 46510*a^8*cos(d*x + c)^3 + 12155*a^8*cos(d*x + c))*sin(d*x + c))/d","A",0
45,1,122,0,1.680923," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{9 \, a^{8} \cos\left(d x + c\right)^{8} - 120 \, a^{8} \cos\left(d x + c\right)^{6} + 432 \, a^{8} \cos\left(d x + c\right)^{4} - 576 \, a^{8} \cos\left(d x + c\right)^{2} + {\left(a^{8} \cos\left(d x + c\right)^{8} - 40 \, a^{8} \cos\left(d x + c\right)^{6} + 240 \, a^{8} \cos\left(d x + c\right)^{4} - 448 \, a^{8} \cos\left(d x + c\right)^{2} + 256 \, a^{8}\right)} \sin\left(d x + c\right)}{9 \, d}"," ",0,"1/9*(9*a^8*cos(d*x + c)^8 - 120*a^8*cos(d*x + c)^6 + 432*a^8*cos(d*x + c)^4 - 576*a^8*cos(d*x + c)^2 + (a^8*cos(d*x + c)^8 - 40*a^8*cos(d*x + c)^6 + 240*a^8*cos(d*x + c)^4 - 448*a^8*cos(d*x + c)^2 + 256*a^8)*sin(d*x + c))/d","B",0
46,1,114,0,1.822952," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{140 \, a^{8} \cos\left(d x + c\right)^{6} - 2100 \, a^{8} \cos\left(d x + c\right)^{4} + 10080 \, a^{8} \cos\left(d x + c\right)^{2} - 13440 \, a^{8} \log\left(-\sin\left(d x + c\right) + 1\right) + 3 \, {\left(5 \, a^{8} \cos\left(d x + c\right)^{6} - 218 \, a^{8} \cos\left(d x + c\right)^{4} + 1576 \, a^{8} \cos\left(d x + c\right)^{2} - 5808 \, a^{8}\right)} \sin\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(140*a^8*cos(d*x + c)^6 - 2100*a^8*cos(d*x + c)^4 + 10080*a^8*cos(d*x + c)^2 - 13440*a^8*log(-sin(d*x + c) + 1) + 3*(5*a^8*cos(d*x + c)^6 - 218*a^8*cos(d*x + c)^4 + 1576*a^8*cos(d*x + c)^2 - 5808*a^8)*sin(d*x + c))/d","A",0
47,1,231,0,1.620976," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{40 \, a^{8} \cos\left(d x + c\right)^{7} + 384 \, a^{8} \cos\left(d x + c\right)^{6} - 1526 \, a^{8} \cos\left(d x + c\right)^{5} - 6400 \, a^{8} \cos\left(d x + c\right)^{4} + 11865 \, a^{8} \cos\left(d x + c\right)^{3} - 45045 \, a^{8} d x + 46080 \, a^{8} \cos\left(d x + c\right)^{2} + 30720 \, a^{8} - 15 \, {\left(3003 \, a^{8} d x - 4027 \, a^{8}\right)} \cos\left(d x + c\right) + {\left(40 \, a^{8} \cos\left(d x + c\right)^{6} - 344 \, a^{8} \cos\left(d x + c\right)^{5} - 1870 \, a^{8} \cos\left(d x + c\right)^{4} + 4530 \, a^{8} \cos\left(d x + c\right)^{3} + 45045 \, a^{8} d x + 16395 \, a^{8} \cos\left(d x + c\right)^{2} - 29685 \, a^{8} \cos\left(d x + c\right) + 30720 \, a^{8}\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/240*(40*a^8*cos(d*x + c)^7 + 384*a^8*cos(d*x + c)^6 - 1526*a^8*cos(d*x + c)^5 - 6400*a^8*cos(d*x + c)^4 + 11865*a^8*cos(d*x + c)^3 - 45045*a^8*d*x + 46080*a^8*cos(d*x + c)^2 + 30720*a^8 - 15*(3003*a^8*d*x - 4027*a^8)*cos(d*x + c) + (40*a^8*cos(d*x + c)^6 - 344*a^8*cos(d*x + c)^5 - 1870*a^8*cos(d*x + c)^4 + 4530*a^8*cos(d*x + c)^3 + 45045*a^8*d*x + 16395*a^8*cos(d*x + c)^2 - 29685*a^8*cos(d*x + c) + 30720*a^8)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
48,1,130,0,1.457231," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","-\frac{4 \, a^{8} \cos\left(d x + c\right)^{6} - 172 \, a^{8} \cos\left(d x + c\right)^{4} + 2192 \, a^{8} \cos\left(d x + c\right)^{2} - 1119 \, a^{8} - 3840 \, {\left(a^{8} \sin\left(d x + c\right) - a^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(36 \, a^{8} \cos\left(d x + c\right)^{4} - 592 \, a^{8} \cos\left(d x + c\right)^{2} - 2399 \, a^{8}\right)} \sin\left(d x + c\right)}{20 \, {\left(d \sin\left(d x + c\right) - d\right)}}"," ",0,"-1/20*(4*a^8*cos(d*x + c)^6 - 172*a^8*cos(d*x + c)^4 + 2192*a^8*cos(d*x + c)^2 - 1119*a^8 - 3840*(a^8*sin(d*x + c) - a^8)*log(-sin(d*x + c) + 1) - (36*a^8*cos(d*x + c)^4 - 592*a^8*cos(d*x + c)^2 - 2399*a^8)*sin(d*x + c))/(d*sin(d*x + c) - d)","A",0
49,1,247,0,1.646499," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","-\frac{6 \, a^{8} \cos\left(d x + c\right)^{6} - 52 \, a^{8} \cos\left(d x + c\right)^{5} - 317 \, a^{8} \cos\left(d x + c\right)^{4} + 1286 \, a^{8} \cos\left(d x + c\right)^{3} + 6930 \, a^{8} d x + 512 \, a^{8} - {\left(3465 \, a^{8} d x + 5641 \, a^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(3465 \, a^{8} d x - 6674 \, a^{8}\right)} \cos\left(d x + c\right) - {\left(6 \, a^{8} \cos\left(d x + c\right)^{5} + 58 \, a^{8} \cos\left(d x + c\right)^{4} - 259 \, a^{8} \cos\left(d x + c\right)^{3} + 6930 \, a^{8} d x - 1545 \, a^{8} \cos\left(d x + c\right)^{2} - 512 \, a^{8} + {\left(3465 \, a^{8} d x - 7186 \, a^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/24*(6*a^8*cos(d*x + c)^6 - 52*a^8*cos(d*x + c)^5 - 317*a^8*cos(d*x + c)^4 + 1286*a^8*cos(d*x + c)^3 + 6930*a^8*d*x + 512*a^8 - (3465*a^8*d*x + 5641*a^8)*cos(d*x + c)^2 + (3465*a^8*d*x - 6674*a^8)*cos(d*x + c) - (6*a^8*cos(d*x + c)^5 + 58*a^8*cos(d*x + c)^4 - 259*a^8*cos(d*x + c)^3 + 6930*a^8*d*x - 1545*a^8*cos(d*x + c)^2 - 512*a^8 + (3465*a^8*d*x - 7186*a^8)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","A",0
50,1,139,0,1.577549," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{10 \, a^{8} \cos\left(d x + c\right)^{4} + 160 \, a^{8} \cos\left(d x + c\right)^{2} + 16 \, a^{8} - 240 \, {\left(a^{8} \cos\left(d x + c\right)^{2} + 2 \, a^{8} \sin\left(d x + c\right) - 2 \, a^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(a^{8} \cos\left(d x + c\right)^{4} - 72 \, a^{8} \cos\left(d x + c\right)^{2} - 64 \, a^{8}\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/3*(10*a^8*cos(d*x + c)^4 + 160*a^8*cos(d*x + c)^2 + 16*a^8 - 240*(a^8*cos(d*x + c)^2 + 2*a^8*sin(d*x + c) - 2*a^8)*log(-sin(d*x + c) + 1) + (a^8*cos(d*x + c)^4 - 72*a^8*cos(d*x + c)^2 - 64*a^8)*sin(d*x + c))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
51,1,50,0,1.467076," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{5} + 15 \, d x + 5 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40 \, a d}"," ",0,"1/40*(8*cos(d*x + c)^5 + 15*d*x + 5*(2*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
52,1,37,0,1.680180," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{4} + 4 \, {\left(\cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right)}{12 \, a d}"," ",0,"1/12*(3*cos(d*x + c)^4 + 4*(cos(d*x + c)^2 + 2)*sin(d*x + c))/(a*d)","A",0
53,1,37,0,1.900208," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{3} + 3 \, d x + 3 \, \cos\left(d x + c\right) \sin\left(d x + c\right)}{6 \, a d}"," ",0,"1/6*(2*cos(d*x + c)^3 + 3*d*x + 3*cos(d*x + c)*sin(d*x + c))/(a*d)","A",0
54,1,25,0,1.516159," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"1/2*(cos(d*x + c)^2 + 2*sin(d*x + c))/(a*d)","A",0
55,1,17,0,1.192644," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d x + \cos\left(d x + c\right)}{a d}"," ",0,"(d*x + cos(d*x + c))/(a*d)","A",0
56,1,16,0,1.298750," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a d}"," ",0,"log(sin(d*x + c) + 1)/(a*d)","A",0
57,1,58,0,1.536874," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(\sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(\sin\left(d x + c\right) + 1\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2}{4 \, {\left(a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"1/4*((sin(d*x + c) + 1)*log(sin(d*x + c) + 1) - (sin(d*x + c) + 1)*log(-sin(d*x + c) + 1) - 2)/(a*d*sin(d*x + c) + a*d)","A",0
58,1,49,0,1.505319," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 1}{3 \, {\left(a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(2*cos(d*x + c)^2 - 2*sin(d*x + c) - 1)/(a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))","A",0
59,1,125,0,1.523966," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(\cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(\cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 6 \, \sin\left(d x + c\right) - 2}{16 \, {\left(a d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(6*cos(d*x + c)^2 - 3*(cos(d*x + c)^2*sin(d*x + c) + cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 3*(cos(d*x + c)^2*sin(d*x + c) + cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 6*sin(d*x + c) - 2)/(a*d*cos(d*x + c)^2*sin(d*x + c) + a*d*cos(d*x + c)^2)","A",0
60,1,75,0,1.485995," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) - 1}{15 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/15*(8*cos(d*x + c)^4 - 4*cos(d*x + c)^2 - 4*(2*cos(d*x + c)^2 + 1)*sin(d*x + c) - 1)/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
61,1,147,0,1.610489," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{30 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(\cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 10 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right) - 4}{96 \, {\left(a d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"-1/96*(30*cos(d*x + c)^4 - 10*cos(d*x + c)^2 - 15*(cos(d*x + c)^4*sin(d*x + c) + cos(d*x + c)^4)*log(sin(d*x + c) + 1) + 15*(cos(d*x + c)^4*sin(d*x + c) + cos(d*x + c)^4)*log(-sin(d*x + c) + 1) - 10*(3*cos(d*x + c)^2 + 2)*sin(d*x + c) - 4)/(a*d*cos(d*x + c)^4*sin(d*x + c) + a*d*cos(d*x + c)^4)","A",0
62,1,60,0,1.226492," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{96 \, \cos\left(d x + c\right)^{5} + 105 \, d x - 5 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 14 \, \cos\left(d x + c\right)^{3} - 21 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, a^{2} d}"," ",0,"1/240*(96*cos(d*x + c)^5 + 105*d*x - 5*(8*cos(d*x + c)^5 - 14*cos(d*x + c)^3 - 21*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
63,1,47,0,1.355485," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5 \, \cos\left(d x + c\right)^{4} - 2 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right)}{10 \, a^{2} d}"," ",0,"1/10*(5*cos(d*x + c)^4 - 2*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - 4)*sin(d*x + c))/(a^2*d)","A",0
64,1,50,0,1.362214," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, \cos\left(d x + c\right)^{3} + 15 \, d x - 3 \, {\left(2 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, a^{2} d}"," ",0,"1/24*(16*cos(d*x + c)^3 + 15*d*x - 3*(2*cos(d*x + c)^3 - 5*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
65,1,37,0,1.434307," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"1/3*(3*cos(d*x + c)^2 - (cos(d*x + c)^2 - 4)*sin(d*x + c))/(a^2*d)","A",0
66,1,35,0,1.372378," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, d x - \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right)}{2 \, a^{2} d}"," ",0,"1/2*(3*d*x - cos(d*x + c)*sin(d*x + c) + 4*cos(d*x + c))/(a^2*d)","A",0
67,1,27,0,1.486267," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right) - \sin\left(d x + c\right)}{a^{2} d}"," ",0,"(2*log(sin(d*x + c) + 1) - sin(d*x + c))/(a^2*d)","A",0
68,1,61,0,1.220845," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{d x + {\left(d x + 2\right)} \cos\left(d x + c\right) + {\left(d x - 2\right)} \sin\left(d x + c\right) + 2}{a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"-(d*x + (d*x + 2)*cos(d*x + c) + (d*x - 2)*sin(d*x + c) + 2)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
69,1,21,0,1.361077," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{1}{a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"-1/(a^2*d*sin(d*x + c) + a^2*d)","A",0
70,1,105,0,1.435631," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, \sin\left(d x + c\right) + 4}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - 2 \, a^{2} d \sin\left(d x + c\right) - 2 \, a^{2} d\right)}}"," ",0,"1/8*((cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*log(sin(d*x + c) + 1) - (cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*log(-sin(d*x + c) + 1) + 2*sin(d*x + c) + 4)/(a^2*d*cos(d*x + c)^2 - 2*a^2*d*sin(d*x + c) - 2*a^2*d)","A",0
71,1,79,0,1.129791," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, \cos\left(d x + c\right)^{2} + {\left(2 \, \cos\left(d x + c\right)^{2} - 3\right)} \sin\left(d x + c\right) - 2}{5 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"1/5*(4*cos(d*x + c)^2 + (2*cos(d*x + c)^2 - 3)*sin(d*x + c) - 2)/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","A",0
72,1,178,0,1.229696," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{12 \, \cos\left(d x + c\right)^{2} + 3 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/24*(12*cos(d*x + c)^2 + 3*(cos(d*x + c)^4 - 2*cos(d*x + c)^2*sin(d*x + c) - 2*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*(cos(d*x + c)^4 - 2*cos(d*x + c)^2*sin(d*x + c) - 2*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(3*cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^2)","A",0
73,1,103,0,1.377016," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, \cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + {\left(8 \, \cos\left(d x + c\right)^{4} - 12 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) - 2}{21 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/21*(16*cos(d*x + c)^4 - 8*cos(d*x + c)^2 + (8*cos(d*x + c)^4 - 12*cos(d*x + c)^2 - 5)*sin(d*x + c) - 2)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
74,1,198,0,1.918272," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{60 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{2} + 15 \, {\left(\cos\left(d x + c\right)^{6} - 2 \, \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(\cos\left(d x + c\right)^{6} - 2 \, \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{2} - 12\right)} \sin\left(d x + c\right) - 8}{128 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 2 \, a^{2} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/128*(60*cos(d*x + c)^4 - 20*cos(d*x + c)^2 + 15*(cos(d*x + c)^6 - 2*cos(d*x + c)^4*sin(d*x + c) - 2*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - 15*(cos(d*x + c)^6 - 2*cos(d*x + c)^4*sin(d*x + c) - 2*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) + 2*(15*cos(d*x + c)^4 - 20*cos(d*x + c)^2 - 12)*sin(d*x + c) - 8)/(a^2*d*cos(d*x + c)^6 - 2*a^2*d*cos(d*x + c)^4*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^4)","A",0
75,1,60,0,1.451232," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{24 \, \cos\left(d x + c\right)^{5} - 160 \, \cos\left(d x + c\right)^{3} - 105 \, d x + 15 \, {\left(6 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, a^{3} d}"," ",0,"-1/120*(24*cos(d*x + c)^5 - 160*cos(d*x + c)^3 - 105*d*x + 15*(6*cos(d*x + c)^3 - 7*cos(d*x + c))*sin(d*x + c))/(a^3*d)","A",0
76,1,45,0,1.469532," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right)}{4 \, a^{3} d}"," ",0,"-1/4*(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c))/(a^3*d)","B",0
77,1,45,0,1.453061," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{3} - 15 \, d x + 9 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 24 \, \cos\left(d x + c\right)}{6 \, a^{3} d}"," ",0,"-1/6*(2*cos(d*x + c)^3 - 15*d*x + 9*cos(d*x + c)*sin(d*x + c) - 24*cos(d*x + c))/(a^3*d)","A",0
78,1,36,0,1.375777," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} - 8 \, \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, \sin\left(d x + c\right)}{2 \, a^{3} d}"," ",0,"-1/2*(cos(d*x + c)^2 - 8*log(sin(d*x + c) + 1) + 6*sin(d*x + c))/(a^3*d)","A",0
79,1,78,0,1.356939," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, d x + {\left(3 \, d x + 5\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + {\left(3 \, d x + \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) + 4}{a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d}"," ",0,"-(3*d*x + (3*d*x + 5)*cos(d*x + c) + cos(d*x + c)^2 + (3*d*x + cos(d*x + c) - 4)*sin(d*x + c) + 4)/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","A",0
80,1,41,0,1.460301," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(\sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2}{a^{3} d \sin\left(d x + c\right) + a^{3} d}"," ",0,"-((sin(d*x + c) + 1)*log(sin(d*x + c) + 1) + 2)/(a^3*d*sin(d*x + c) + a^3*d)","A",0
81,1,95,0,1.263331," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}{3 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right) + 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(cos(d*x + c)^2 + (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)/(a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d - (a^3*d*cos(d*x + c) + 2*a^3*d)*sin(d*x + c))","B",0
82,1,36,0,1.109778," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{1}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"1/2/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","A",0
83,1,154,0,1.265703," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 18 \, \sin\left(d x + c\right) - 26}{48 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{2} - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/48*(6*cos(d*x + c)^2 - 3*(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)*log(sin(d*x + c) + 1) + 3*(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)*log(-sin(d*x + c) + 1) - 18*sin(d*x + c) - 26)/(3*a^3*d*cos(d*x + c)^2 - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 4*a^3*d)*sin(d*x + c))","B",0
84,1,106,0,1.186076," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{4} - 36 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(6 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) + 15}{35 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/35*(8*cos(d*x + c)^4 - 36*cos(d*x + c)^2 - 4*(6*cos(d*x + c)^2 - 5)*sin(d*x + c) + 15)/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
85,1,228,0,1.321817," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{30 \, \cos\left(d x + c\right)^{4} - 130 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 30 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 36}{192 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{4} - 4 \, a^{3} d \cos\left(d x + c\right)^{2} + {\left(a^{3} d \cos\left(d x + c\right)^{4} - 4 \, a^{3} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/192*(30*cos(d*x + c)^4 - 130*cos(d*x + c)^2 - 15*(3*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + (cos(d*x + c)^4 - 4*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) + 15*(3*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + (cos(d*x + c)^4 - 4*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) - 30*(3*cos(d*x + c)^2 - 2)*sin(d*x + c) + 36)/(3*a^3*d*cos(d*x + c)^4 - 4*a^3*d*cos(d*x + c)^2 + (a^3*d*cos(d*x + c)^4 - 4*a^3*d*cos(d*x + c)^2)*sin(d*x + c))","A",0
86,1,130,0,1.388104," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{16 \, \cos\left(d x + c\right)^{6} - 72 \, \cos\left(d x + c\right)^{4} + 30 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(24 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{2} - 7\right)} \sin\left(d x + c\right) + 7}{63 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/63*(16*cos(d*x + c)^6 - 72*cos(d*x + c)^4 + 30*cos(d*x + c)^2 - 2*(24*cos(d*x + c)^4 - 20*cos(d*x + c)^2 - 7)*sin(d*x + c) + 7)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
87,1,248,0,1.611169," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{210 \, \cos\left(d x + c\right)^{6} - 910 \, \cos\left(d x + c\right)^{4} + 252 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(3 \, \cos\left(d x + c\right)^{6} - 4 \, \cos\left(d x + c\right)^{4} + {\left(\cos\left(d x + c\right)^{6} - 4 \, \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, {\left(3 \, \cos\left(d x + c\right)^{6} - 4 \, \cos\left(d x + c\right)^{4} + {\left(\cos\left(d x + c\right)^{6} - 4 \, \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 14 \, {\left(45 \, \cos\left(d x + c\right)^{4} - 30 \, \cos\left(d x + c\right)^{2} - 16\right)} \sin\left(d x + c\right) + 96}{1280 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{6} - 4 \, a^{3} d \cos\left(d x + c\right)^{4} + {\left(a^{3} d \cos\left(d x + c\right)^{6} - 4 \, a^{3} d \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/1280*(210*cos(d*x + c)^6 - 910*cos(d*x + c)^4 + 252*cos(d*x + c)^2 - 105*(3*cos(d*x + c)^6 - 4*cos(d*x + c)^4 + (cos(d*x + c)^6 - 4*cos(d*x + c)^4)*sin(d*x + c))*log(sin(d*x + c) + 1) + 105*(3*cos(d*x + c)^6 - 4*cos(d*x + c)^4 + (cos(d*x + c)^6 - 4*cos(d*x + c)^4)*sin(d*x + c))*log(-sin(d*x + c) + 1) - 14*(45*cos(d*x + c)^4 - 30*cos(d*x + c)^2 - 16)*sin(d*x + c) + 96)/(3*a^3*d*cos(d*x + c)^6 - 4*a^3*d*cos(d*x + c)^4 + (a^3*d*cos(d*x + c)^6 - 4*a^3*d*cos(d*x + c)^4)*sin(d*x + c))","A",0
88,1,244,0,1.278871," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(105 \, d x - 352\right)} \cos\left(d x + c\right)^{4} - {\left(315 \, d x + 568\right)} \cos\left(d x + c\right)^{3} - 24 \, {\left(35 \, d x - 31\right)} \cos\left(d x + c\right)^{2} + 840 \, d x + 60 \, {\left(7 \, d x + 12\right)} \cos\left(d x + c\right) - {\left({\left(105 \, d x + 352\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(35 \, d x - 18\right)} \cos\left(d x + c\right)^{2} - 840 \, d x - 60 \, {\left(7 \, d x + 16\right)} \cos\left(d x + c\right) - 240\right)} \sin\left(d x + c\right) - 240}{105 \, {\left(a^{8} d \cos\left(d x + c\right)^{4} - 3 \, a^{8} d \cos\left(d x + c\right)^{3} - 8 \, a^{8} d \cos\left(d x + c\right)^{2} + 4 \, a^{8} d \cos\left(d x + c\right) + 8 \, a^{8} d - {\left(a^{8} d \cos\left(d x + c\right)^{3} + 4 \, a^{8} d \cos\left(d x + c\right)^{2} - 4 \, a^{8} d \cos\left(d x + c\right) - 8 \, a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/105*((105*d*x - 352)*cos(d*x + c)^4 - (315*d*x + 568)*cos(d*x + c)^3 - 24*(35*d*x - 31)*cos(d*x + c)^2 + 840*d*x + 60*(7*d*x + 12)*cos(d*x + c) - ((105*d*x + 352)*cos(d*x + c)^3 + 12*(35*d*x - 18)*cos(d*x + c)^2 - 840*d*x - 60*(7*d*x + 16)*cos(d*x + c) - 240)*sin(d*x + c) - 240)/(a^8*d*cos(d*x + c)^4 - 3*a^8*d*cos(d*x + c)^3 - 8*a^8*d*cos(d*x + c)^2 + 4*a^8*d*cos(d*x + c) + 8*a^8*d - (a^8*d*cos(d*x + c)^3 + 4*a^8*d*cos(d*x + c)^2 - 4*a^8*d*cos(d*x + c) - 8*a^8*d)*sin(d*x + c))","B",0
89,1,82,0,1.060165," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right)}{a^{8} d \cos\left(d x + c\right)^{4} - 8 \, a^{8} d \cos\left(d x + c\right)^{2} + 8 \, a^{8} d - 4 \, {\left(a^{8} d \cos\left(d x + c\right)^{2} - 2 \, a^{8} d\right)} \sin\left(d x + c\right)}"," ",0,"-(cos(d*x + c)^2 - 2)*sin(d*x + c)/(a^8*d*cos(d*x + c)^4 - 8*a^8*d*cos(d*x + c)^2 + 8*a^8*d - 4*(a^8*d*cos(d*x + c)^2 - 2*a^8*d)*sin(d*x + c))","B",0
90,1,239,0,1.306943," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{4} + 19 \, \cos\left(d x + c\right)^{3} + 52 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{3} + 24 \, \cos\left(d x + c\right)^{2} - 28 \, \cos\left(d x + c\right) - 56\right)} \sin\left(d x + c\right) - 28 \, \cos\left(d x + c\right) - 56}{63 \, {\left(a^{8} d \cos\left(d x + c\right)^{5} + 5 \, a^{8} d \cos\left(d x + c\right)^{4} - 8 \, a^{8} d \cos\left(d x + c\right)^{3} - 20 \, a^{8} d \cos\left(d x + c\right)^{2} + 8 \, a^{8} d \cos\left(d x + c\right) + 16 \, a^{8} d + {\left(a^{8} d \cos\left(d x + c\right)^{4} - 4 \, a^{8} d \cos\left(d x + c\right)^{3} - 12 \, a^{8} d \cos\left(d x + c\right)^{2} + 8 \, a^{8} d \cos\left(d x + c\right) + 16 \, a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/63*(cos(d*x + c)^5 - 4*cos(d*x + c)^4 + 19*cos(d*x + c)^3 + 52*cos(d*x + c)^2 - (cos(d*x + c)^4 + 5*cos(d*x + c)^3 + 24*cos(d*x + c)^2 - 28*cos(d*x + c) - 56)*sin(d*x + c) - 28*cos(d*x + c) - 56)/(a^8*d*cos(d*x + c)^5 + 5*a^8*d*cos(d*x + c)^4 - 8*a^8*d*cos(d*x + c)^3 - 20*a^8*d*cos(d*x + c)^2 + 8*a^8*d*cos(d*x + c) + 16*a^8*d + (a^8*d*cos(d*x + c)^4 - 4*a^8*d*cos(d*x + c)^3 - 12*a^8*d*cos(d*x + c)^2 + 8*a^8*d*cos(d*x + c) + 16*a^8*d)*sin(d*x + c))","B",0
91,1,100,0,1.466051," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{5 \, \cos\left(d x + c\right)^{2} + 5 \, \sin\left(d x + c\right) - 7}{15 \, {\left(5 \, a^{8} d \cos\left(d x + c\right)^{4} - 20 \, a^{8} d \cos\left(d x + c\right)^{2} + 16 \, a^{8} d + {\left(a^{8} d \cos\left(d x + c\right)^{4} - 12 \, a^{8} d \cos\left(d x + c\right)^{2} + 16 \, a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/15*(5*cos(d*x + c)^2 + 5*sin(d*x + c) - 7)/(5*a^8*d*cos(d*x + c)^4 - 20*a^8*d*cos(d*x + c)^2 + 16*a^8*d + (a^8*d*cos(d*x + c)^4 - 12*a^8*d*cos(d*x + c)^2 + 16*a^8*d)*sin(d*x + c))","A",0
92,1,291,0,1.436823," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{6} + 12 \, \cos\left(d x + c\right)^{5} - 25 \, \cos\left(d x + c\right)^{4} - 70 \, \cos\left(d x + c\right)^{3} - 245 \, \cos\left(d x + c\right)^{2} + {\left(2 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{4} - 35 \, \cos\left(d x + c\right)^{3} + 35 \, \cos\left(d x + c\right)^{2} - 210 \, \cos\left(d x + c\right) - 420\right)} \sin\left(d x + c\right) + 210 \, \cos\left(d x + c\right) + 420}{1155 \, {\left(a^{8} d \cos\left(d x + c\right)^{6} - 5 \, a^{8} d \cos\left(d x + c\right)^{5} - 18 \, a^{8} d \cos\left(d x + c\right)^{4} + 20 \, a^{8} d \cos\left(d x + c\right)^{3} + 48 \, a^{8} d \cos\left(d x + c\right)^{2} - 16 \, a^{8} d \cos\left(d x + c\right) - 32 \, a^{8} d - {\left(a^{8} d \cos\left(d x + c\right)^{5} + 6 \, a^{8} d \cos\left(d x + c\right)^{4} - 12 \, a^{8} d \cos\left(d x + c\right)^{3} - 32 \, a^{8} d \cos\left(d x + c\right)^{2} + 16 \, a^{8} d \cos\left(d x + c\right) + 32 \, a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/1155*(2*cos(d*x + c)^6 + 12*cos(d*x + c)^5 - 25*cos(d*x + c)^4 - 70*cos(d*x + c)^3 - 245*cos(d*x + c)^2 + (2*cos(d*x + c)^5 - 10*cos(d*x + c)^4 - 35*cos(d*x + c)^3 + 35*cos(d*x + c)^2 - 210*cos(d*x + c) - 420)*sin(d*x + c) + 210*cos(d*x + c) + 420)/(a^8*d*cos(d*x + c)^6 - 5*a^8*d*cos(d*x + c)^5 - 18*a^8*d*cos(d*x + c)^4 + 20*a^8*d*cos(d*x + c)^3 + 48*a^8*d*cos(d*x + c)^2 - 16*a^8*d*cos(d*x + c) - 32*a^8*d - (a^8*d*cos(d*x + c)^5 + 6*a^8*d*cos(d*x + c)^4 - 12*a^8*d*cos(d*x + c)^3 - 32*a^8*d*cos(d*x + c)^2 + 16*a^8*d*cos(d*x + c) + 32*a^8*d)*sin(d*x + c))","B",0
93,1,105,0,0.782490," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","-\frac{3 \, \sin\left(d x + c\right) - 2}{15 \, {\left(a^{8} d \cos\left(d x + c\right)^{6} - 18 \, a^{8} d \cos\left(d x + c\right)^{4} + 48 \, a^{8} d \cos\left(d x + c\right)^{2} - 32 \, a^{8} d - 2 \, {\left(3 \, a^{8} d \cos\left(d x + c\right)^{4} - 16 \, a^{8} d \cos\left(d x + c\right)^{2} + 16 \, a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/15*(3*sin(d*x + c) - 2)/(a^8*d*cos(d*x + c)^6 - 18*a^8*d*cos(d*x + c)^4 + 48*a^8*d*cos(d*x + c)^2 - 32*a^8*d - 2*(3*a^8*d*cos(d*x + c)^4 - 16*a^8*d*cos(d*x + c)^2 + 16*a^8*d)*sin(d*x + c))","B",0
94,1,339,0,1.205001," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{7} - 48 \, \cos\left(d x + c\right)^{6} - 196 \, \cos\left(d x + c\right)^{5} + 280 \, \cos\left(d x + c\right)^{4} + 735 \, \cos\left(d x + c\right)^{3} - 378 \, \cos\left(d x + c\right)^{2} - {\left(8 \, \cos\left(d x + c\right)^{6} + 56 \, \cos\left(d x + c\right)^{5} - 140 \, \cos\left(d x + c\right)^{4} - 420 \, \cos\left(d x + c\right)^{3} + 315 \, \cos\left(d x + c\right)^{2} + 693 \, \cos\left(d x + c\right) + 1386\right)} \sin\left(d x + c\right) + 693 \, \cos\left(d x + c\right) + 1386}{9009 \, {\left(a^{8} d \cos\left(d x + c\right)^{7} + 7 \, a^{8} d \cos\left(d x + c\right)^{6} - 18 \, a^{8} d \cos\left(d x + c\right)^{5} - 56 \, a^{8} d \cos\left(d x + c\right)^{4} + 48 \, a^{8} d \cos\left(d x + c\right)^{3} + 112 \, a^{8} d \cos\left(d x + c\right)^{2} - 32 \, a^{8} d \cos\left(d x + c\right) - 64 \, a^{8} d + {\left(a^{8} d \cos\left(d x + c\right)^{6} - 6 \, a^{8} d \cos\left(d x + c\right)^{5} - 24 \, a^{8} d \cos\left(d x + c\right)^{4} + 32 \, a^{8} d \cos\left(d x + c\right)^{3} + 80 \, a^{8} d \cos\left(d x + c\right)^{2} - 32 \, a^{8} d \cos\left(d x + c\right) - 64 \, a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/9009*(8*cos(d*x + c)^7 - 48*cos(d*x + c)^6 - 196*cos(d*x + c)^5 + 280*cos(d*x + c)^4 + 735*cos(d*x + c)^3 - 378*cos(d*x + c)^2 - (8*cos(d*x + c)^6 + 56*cos(d*x + c)^5 - 140*cos(d*x + c)^4 - 420*cos(d*x + c)^3 + 315*cos(d*x + c)^2 + 693*cos(d*x + c) + 1386)*sin(d*x + c) + 693*cos(d*x + c) + 1386)/(a^8*d*cos(d*x + c)^7 + 7*a^8*d*cos(d*x + c)^6 - 18*a^8*d*cos(d*x + c)^5 - 56*a^8*d*cos(d*x + c)^4 + 48*a^8*d*cos(d*x + c)^3 + 112*a^8*d*cos(d*x + c)^2 - 32*a^8*d*cos(d*x + c) - 64*a^8*d + (a^8*d*cos(d*x + c)^6 - 6*a^8*d*cos(d*x + c)^5 - 24*a^8*d*cos(d*x + c)^4 + 32*a^8*d*cos(d*x + c)^3 + 80*a^8*d*cos(d*x + c)^2 - 32*a^8*d*cos(d*x + c) - 64*a^8*d)*sin(d*x + c))","A",0
95,1,108,0,1.418814," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{1}{7 \, {\left(7 \, a^{8} d \cos\left(d x + c\right)^{6} - 56 \, a^{8} d \cos\left(d x + c\right)^{4} + 112 \, a^{8} d \cos\left(d x + c\right)^{2} - 64 \, a^{8} d + {\left(a^{8} d \cos\left(d x + c\right)^{6} - 24 \, a^{8} d \cos\left(d x + c\right)^{4} + 80 \, a^{8} d \cos\left(d x + c\right)^{2} - 64 \, a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/7/(7*a^8*d*cos(d*x + c)^6 - 56*a^8*d*cos(d*x + c)^4 + 112*a^8*d*cos(d*x + c)^2 - 64*a^8*d + (a^8*d*cos(d*x + c)^6 - 24*a^8*d*cos(d*x + c)^4 + 80*a^8*d*cos(d*x + c)^2 - 64*a^8*d)*sin(d*x + c))","B",0
96,1,374,0,1.334296," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{1680 \, \cos\left(d x + c\right)^{6} - 17360 \, \cos\left(d x + c\right)^{4} + 45696 \, \cos\left(d x + c\right)^{2} + 105 \, {\left(\cos\left(d x + c\right)^{8} - 32 \, \cos\left(d x + c\right)^{6} + 160 \, \cos\left(d x + c\right)^{4} - 256 \, \cos\left(d x + c\right)^{2} - 8 \, {\left(\cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 24 \, \cos\left(d x + c\right)^{2} - 16\right)} \sin\left(d x + c\right) + 128\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(\cos\left(d x + c\right)^{8} - 32 \, \cos\left(d x + c\right)^{6} + 160 \, \cos\left(d x + c\right)^{4} - 256 \, \cos\left(d x + c\right)^{2} - 8 \, {\left(\cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 24 \, \cos\left(d x + c\right)^{2} - 16\right)} \sin\left(d x + c\right) + 128\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(105 \, \cos\left(d x + c\right)^{6} - 3290 \, \cos\left(d x + c\right)^{4} + 14616 \, \cos\left(d x + c\right)^{2} - 17424\right)} \sin\left(d x + c\right) - 38208}{53760 \, {\left(a^{8} d \cos\left(d x + c\right)^{8} - 32 \, a^{8} d \cos\left(d x + c\right)^{6} + 160 \, a^{8} d \cos\left(d x + c\right)^{4} - 256 \, a^{8} d \cos\left(d x + c\right)^{2} + 128 \, a^{8} d - 8 \, {\left(a^{8} d \cos\left(d x + c\right)^{6} - 10 \, a^{8} d \cos\left(d x + c\right)^{4} + 24 \, a^{8} d \cos\left(d x + c\right)^{2} - 16 \, a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/53760*(1680*cos(d*x + c)^6 - 17360*cos(d*x + c)^4 + 45696*cos(d*x + c)^2 + 105*(cos(d*x + c)^8 - 32*cos(d*x + c)^6 + 160*cos(d*x + c)^4 - 256*cos(d*x + c)^2 - 8*(cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 24*cos(d*x + c)^2 - 16)*sin(d*x + c) + 128)*log(sin(d*x + c) + 1) - 105*(cos(d*x + c)^8 - 32*cos(d*x + c)^6 + 160*cos(d*x + c)^4 - 256*cos(d*x + c)^2 - 8*(cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 24*cos(d*x + c)^2 - 16)*sin(d*x + c) + 128)*log(-sin(d*x + c) + 1) + 2*(105*cos(d*x + c)^6 - 3290*cos(d*x + c)^4 + 14616*cos(d*x + c)^2 - 17424)*sin(d*x + c) - 38208)/(a^8*d*cos(d*x + c)^8 - 32*a^8*d*cos(d*x + c)^6 + 160*a^8*d*cos(d*x + c)^4 - 256*a^8*d*cos(d*x + c)^2 + 128*a^8*d - 8*(a^8*d*cos(d*x + c)^6 - 10*a^8*d*cos(d*x + c)^4 + 24*a^8*d*cos(d*x + c)^2 - 16*a^8*d)*sin(d*x + c))","B",0
97,1,225,0,1.498664," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{1024 \, \cos\left(d x + c\right)^{8} - 10752 \, \cos\left(d x + c\right)^{6} + 29568 \, \cos\left(d x + c\right)^{4} - 27456 \, \cos\left(d x + c\right)^{2} + {\left(128 \, \cos\left(d x + c\right)^{8} - 4032 \, \cos\left(d x + c\right)^{6} + 18480 \, \cos\left(d x + c\right)^{4} - 24024 \, \cos\left(d x + c\right)^{2} + 6435\right)} \sin\left(d x + c\right) + 5720}{12155 \, {\left(a^{8} d \cos\left(d x + c\right)^{9} - 32 \, a^{8} d \cos\left(d x + c\right)^{7} + 160 \, a^{8} d \cos\left(d x + c\right)^{5} - 256 \, a^{8} d \cos\left(d x + c\right)^{3} + 128 \, a^{8} d \cos\left(d x + c\right) - 8 \, {\left(a^{8} d \cos\left(d x + c\right)^{7} - 10 \, a^{8} d \cos\left(d x + c\right)^{5} + 24 \, a^{8} d \cos\left(d x + c\right)^{3} - 16 \, a^{8} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12155*(1024*cos(d*x + c)^8 - 10752*cos(d*x + c)^6 + 29568*cos(d*x + c)^4 - 27456*cos(d*x + c)^2 + (128*cos(d*x + c)^8 - 4032*cos(d*x + c)^6 + 18480*cos(d*x + c)^4 - 24024*cos(d*x + c)^2 + 6435)*sin(d*x + c) + 5720)/(a^8*d*cos(d*x + c)^9 - 32*a^8*d*cos(d*x + c)^7 + 160*a^8*d*cos(d*x + c)^5 - 256*a^8*d*cos(d*x + c)^3 + 128*a^8*d*cos(d*x + c) - 8*(a^8*d*cos(d*x + c)^7 - 10*a^8*d*cos(d*x + c)^5 + 24*a^8*d*cos(d*x + c)^3 - 16*a^8*d*cos(d*x + c))*sin(d*x + c))","A",0
98,1,446,0,1.143330," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{5040 \, \cos\left(d x + c\right)^{8} - 52080 \, \cos\left(d x + c\right)^{6} + 137088 \, \cos\left(d x + c\right)^{4} - 114624 \, \cos\left(d x + c\right)^{2} + 315 \, {\left(\cos\left(d x + c\right)^{10} - 32 \, \cos\left(d x + c\right)^{8} + 160 \, \cos\left(d x + c\right)^{6} - 256 \, \cos\left(d x + c\right)^{4} + 128 \, \cos\left(d x + c\right)^{2} - 8 \, {\left(\cos\left(d x + c\right)^{8} - 10 \, \cos\left(d x + c\right)^{6} + 24 \, \cos\left(d x + c\right)^{4} - 16 \, \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 315 \, {\left(\cos\left(d x + c\right)^{10} - 32 \, \cos\left(d x + c\right)^{8} + 160 \, \cos\left(d x + c\right)^{6} - 256 \, \cos\left(d x + c\right)^{4} + 128 \, \cos\left(d x + c\right)^{2} - 8 \, {\left(\cos\left(d x + c\right)^{8} - 10 \, \cos\left(d x + c\right)^{6} + 24 \, \cos\left(d x + c\right)^{4} - 16 \, \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(315 \, \cos\left(d x + c\right)^{8} - 9870 \, \cos\left(d x + c\right)^{6} + 43848 \, \cos\left(d x + c\right)^{4} - 52272 \, \cos\left(d x + c\right)^{2} + 8960\right)} \sin\left(d x + c\right) + 14336}{64512 \, {\left(a^{8} d \cos\left(d x + c\right)^{10} - 32 \, a^{8} d \cos\left(d x + c\right)^{8} + 160 \, a^{8} d \cos\left(d x + c\right)^{6} - 256 \, a^{8} d \cos\left(d x + c\right)^{4} + 128 \, a^{8} d \cos\left(d x + c\right)^{2} - 8 \, {\left(a^{8} d \cos\left(d x + c\right)^{8} - 10 \, a^{8} d \cos\left(d x + c\right)^{6} + 24 \, a^{8} d \cos\left(d x + c\right)^{4} - 16 \, a^{8} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/64512*(5040*cos(d*x + c)^8 - 52080*cos(d*x + c)^6 + 137088*cos(d*x + c)^4 - 114624*cos(d*x + c)^2 + 315*(cos(d*x + c)^10 - 32*cos(d*x + c)^8 + 160*cos(d*x + c)^6 - 256*cos(d*x + c)^4 + 128*cos(d*x + c)^2 - 8*(cos(d*x + c)^8 - 10*cos(d*x + c)^6 + 24*cos(d*x + c)^4 - 16*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) - 315*(cos(d*x + c)^10 - 32*cos(d*x + c)^8 + 160*cos(d*x + c)^6 - 256*cos(d*x + c)^4 + 128*cos(d*x + c)^2 - 8*(cos(d*x + c)^8 - 10*cos(d*x + c)^6 + 24*cos(d*x + c)^4 - 16*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 2*(315*cos(d*x + c)^8 - 9870*cos(d*x + c)^6 + 43848*cos(d*x + c)^4 - 52272*cos(d*x + c)^2 + 8960)*sin(d*x + c) + 14336)/(a^8*d*cos(d*x + c)^10 - 32*a^8*d*cos(d*x + c)^8 + 160*a^8*d*cos(d*x + c)^6 - 256*a^8*d*cos(d*x + c)^4 + 128*a^8*d*cos(d*x + c)^2 - 8*(a^8*d*cos(d*x + c)^8 - 10*a^8*d*cos(d*x + c)^6 + 24*a^8*d*cos(d*x + c)^4 - 16*a^8*d*cos(d*x + c)^2)*sin(d*x + c))","B",0
99,1,249,0,1.792910," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{2048 \, \cos\left(d x + c\right)^{10} - 21504 \, \cos\left(d x + c\right)^{8} + 59136 \, \cos\left(d x + c\right)^{6} - 54912 \, \cos\left(d x + c\right)^{4} + 11440 \, \cos\left(d x + c\right)^{2} + {\left(256 \, \cos\left(d x + c\right)^{10} - 8064 \, \cos\left(d x + c\right)^{8} + 36960 \, \cos\left(d x + c\right)^{6} - 48048 \, \cos\left(d x + c\right)^{4} + 12870 \, \cos\left(d x + c\right)^{2} + 2431\right)} \sin\left(d x + c\right) + 1768}{12597 \, {\left(a^{8} d \cos\left(d x + c\right)^{11} - 32 \, a^{8} d \cos\left(d x + c\right)^{9} + 160 \, a^{8} d \cos\left(d x + c\right)^{7} - 256 \, a^{8} d \cos\left(d x + c\right)^{5} + 128 \, a^{8} d \cos\left(d x + c\right)^{3} - 8 \, {\left(a^{8} d \cos\left(d x + c\right)^{9} - 10 \, a^{8} d \cos\left(d x + c\right)^{7} + 24 \, a^{8} d \cos\left(d x + c\right)^{5} - 16 \, a^{8} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12597*(2048*cos(d*x + c)^10 - 21504*cos(d*x + c)^8 + 59136*cos(d*x + c)^6 - 54912*cos(d*x + c)^4 + 11440*cos(d*x + c)^2 + (256*cos(d*x + c)^10 - 8064*cos(d*x + c)^8 + 36960*cos(d*x + c)^6 - 48048*cos(d*x + c)^4 + 12870*cos(d*x + c)^2 + 2431)*sin(d*x + c) + 1768)/(a^8*d*cos(d*x + c)^11 - 32*a^8*d*cos(d*x + c)^9 + 160*a^8*d*cos(d*x + c)^7 - 256*a^8*d*cos(d*x + c)^5 + 128*a^8*d*cos(d*x + c)^3 - 8*(a^8*d*cos(d*x + c)^9 - 10*a^8*d*cos(d*x + c)^7 + 24*a^8*d*cos(d*x + c)^5 - 16*a^8*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
100,1,466,0,1.485817," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{55440 \, \cos\left(d x + c\right)^{10} - 572880 \, \cos\left(d x + c\right)^{8} + 1507968 \, \cos\left(d x + c\right)^{6} - 1260864 \, \cos\left(d x + c\right)^{4} + 157696 \, \cos\left(d x + c\right)^{2} + 3465 \, {\left(\cos\left(d x + c\right)^{12} - 32 \, \cos\left(d x + c\right)^{10} + 160 \, \cos\left(d x + c\right)^{8} - 256 \, \cos\left(d x + c\right)^{6} + 128 \, \cos\left(d x + c\right)^{4} - 8 \, {\left(\cos\left(d x + c\right)^{10} - 10 \, \cos\left(d x + c\right)^{8} + 24 \, \cos\left(d x + c\right)^{6} - 16 \, \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3465 \, {\left(\cos\left(d x + c\right)^{12} - 32 \, \cos\left(d x + c\right)^{10} + 160 \, \cos\left(d x + c\right)^{8} - 256 \, \cos\left(d x + c\right)^{6} + 128 \, \cos\left(d x + c\right)^{4} - 8 \, {\left(\cos\left(d x + c\right)^{10} - 10 \, \cos\left(d x + c\right)^{8} + 24 \, \cos\left(d x + c\right)^{6} - 16 \, \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3465 \, \cos\left(d x + c\right)^{10} - 108570 \, \cos\left(d x + c\right)^{8} + 482328 \, \cos\left(d x + c\right)^{6} - 574992 \, \cos\left(d x + c\right)^{4} + 98560 \, \cos\left(d x + c\right)^{2} + 32256\right)} \sin\left(d x + c\right) + 43008}{430080 \, {\left(a^{8} d \cos\left(d x + c\right)^{12} - 32 \, a^{8} d \cos\left(d x + c\right)^{10} + 160 \, a^{8} d \cos\left(d x + c\right)^{8} - 256 \, a^{8} d \cos\left(d x + c\right)^{6} + 128 \, a^{8} d \cos\left(d x + c\right)^{4} - 8 \, {\left(a^{8} d \cos\left(d x + c\right)^{10} - 10 \, a^{8} d \cos\left(d x + c\right)^{8} + 24 \, a^{8} d \cos\left(d x + c\right)^{6} - 16 \, a^{8} d \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/430080*(55440*cos(d*x + c)^10 - 572880*cos(d*x + c)^8 + 1507968*cos(d*x + c)^6 - 1260864*cos(d*x + c)^4 + 157696*cos(d*x + c)^2 + 3465*(cos(d*x + c)^12 - 32*cos(d*x + c)^10 + 160*cos(d*x + c)^8 - 256*cos(d*x + c)^6 + 128*cos(d*x + c)^4 - 8*(cos(d*x + c)^10 - 10*cos(d*x + c)^8 + 24*cos(d*x + c)^6 - 16*cos(d*x + c)^4)*sin(d*x + c))*log(sin(d*x + c) + 1) - 3465*(cos(d*x + c)^12 - 32*cos(d*x + c)^10 + 160*cos(d*x + c)^8 - 256*cos(d*x + c)^6 + 128*cos(d*x + c)^4 - 8*(cos(d*x + c)^10 - 10*cos(d*x + c)^8 + 24*cos(d*x + c)^6 - 16*cos(d*x + c)^4)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 2*(3465*cos(d*x + c)^10 - 108570*cos(d*x + c)^8 + 482328*cos(d*x + c)^6 - 574992*cos(d*x + c)^4 + 98560*cos(d*x + c)^2 + 32256)*sin(d*x + c) + 43008)/(a^8*d*cos(d*x + c)^12 - 32*a^8*d*cos(d*x + c)^10 + 160*a^8*d*cos(d*x + c)^8 - 256*a^8*d*cos(d*x + c)^6 + 128*a^8*d*cos(d*x + c)^4 - 8*(a^8*d*cos(d*x + c)^10 - 10*a^8*d*cos(d*x + c)^8 + 24*a^8*d*cos(d*x + c)^6 - 16*a^8*d*cos(d*x + c)^4)*sin(d*x + c))","A",0
101,1,88,0,1.449754," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(33 \, \cos\left(d x + c\right)^{6} + 56 \, \cos\left(d x + c\right)^{4} + 128 \, \cos\left(d x + c\right)^{2} + {\left(429 \, \cos\left(d x + c\right)^{6} + 504 \, \cos\left(d x + c\right)^{4} + 640 \, \cos\left(d x + c\right)^{2} + 1024\right)} \sin\left(d x + c\right) + 1024\right)} \sqrt{a \sin\left(d x + c\right) + a}}{6435 \, d}"," ",0,"2/6435*(33*cos(d*x + c)^6 + 56*cos(d*x + c)^4 + 128*cos(d*x + c)^2 + (429*cos(d*x + c)^6 + 504*cos(d*x + c)^4 + 640*cos(d*x + c)^2 + 1024)*sin(d*x + c) + 1024)*sqrt(a*sin(d*x + c) + a)/d","A",0
102,1,172,0,1.495891," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(231 \, \cos\left(d x + c\right)^{7} - 21 \, \cos\left(d x + c\right)^{6} + 28 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{4} + 64 \, \cos\left(d x + c\right)^{3} - 128 \, \cos\left(d x + c\right)^{2} - {\left(231 \, \cos\left(d x + c\right)^{6} + 252 \, \cos\left(d x + c\right)^{5} + 280 \, \cos\left(d x + c\right)^{4} + 320 \, \cos\left(d x + c\right)^{3} + 384 \, \cos\left(d x + c\right)^{2} + 512 \, \cos\left(d x + c\right) + 1024\right)} \sin\left(d x + c\right) + 512 \, \cos\left(d x + c\right) + 1024\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3003 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/3003*(231*cos(d*x + c)^7 - 21*cos(d*x + c)^6 + 28*cos(d*x + c)^5 - 40*cos(d*x + c)^4 + 64*cos(d*x + c)^3 - 128*cos(d*x + c)^2 - (231*cos(d*x + c)^6 + 252*cos(d*x + c)^5 + 280*cos(d*x + c)^4 + 320*cos(d*x + c)^3 + 384*cos(d*x + c)^2 + 512*cos(d*x + c) + 1024)*sin(d*x + c) + 512*cos(d*x + c) + 1024)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
103,1,68,0,1.450062," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, \cos\left(d x + c\right)^{4} + 16 \, \cos\left(d x + c\right)^{2} + {\left(63 \, \cos\left(d x + c\right)^{4} + 80 \, \cos\left(d x + c\right)^{2} + 128\right)} \sin\left(d x + c\right) + 128\right)} \sqrt{a \sin\left(d x + c\right) + a}}{693 \, d}"," ",0,"2/693*(7*cos(d*x + c)^4 + 16*cos(d*x + c)^2 + (63*cos(d*x + c)^4 + 80*cos(d*x + c)^2 + 128)*sin(d*x + c) + 128)*sqrt(a*sin(d*x + c) + a)/d","A",0
104,1,132,0,1.233986," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{4} + 8 \, \cos\left(d x + c\right)^{3} - 16 \, \cos\left(d x + c\right)^{2} - {\left(35 \, \cos\left(d x + c\right)^{4} + 40 \, \cos\left(d x + c\right)^{3} + 48 \, \cos\left(d x + c\right)^{2} + 64 \, \cos\left(d x + c\right) + 128\right)} \sin\left(d x + c\right) + 64 \, \cos\left(d x + c\right) + 128\right)} \sqrt{a \sin\left(d x + c\right) + a}}{315 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/315*(35*cos(d*x + c)^5 - 5*cos(d*x + c)^4 + 8*cos(d*x + c)^3 - 16*cos(d*x + c)^2 - (35*cos(d*x + c)^4 + 40*cos(d*x + c)^3 + 48*cos(d*x + c)^2 + 64*cos(d*x + c) + 128)*sin(d*x + c) + 64*cos(d*x + c) + 128)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
105,1,46,0,1.265593," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + {\left(5 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 8\right)} \sqrt{a \sin\left(d x + c\right) + a}}{35 \, d}"," ",0,"2/35*(cos(d*x + c)^2 + (5*cos(d*x + c)^2 + 8)*sin(d*x + c) + 8)*sqrt(a*sin(d*x + c) + a)/d","A",0
106,1,92,0,1.278208," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right) + 8\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/15*(3*cos(d*x + c)^3 - cos(d*x + c)^2 - (3*cos(d*x + c)^2 + 4*cos(d*x + c) + 8)*sin(d*x + c) + 4*cos(d*x + c) + 8)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
107,1,25,0,1.103274," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sin\left(d x + c\right) + 1\right)}}{3 \, d}"," ",0,"2/3*sqrt(a*sin(d*x + c) + a)*(sin(d*x + c) + 1)/d","A",0
108,1,92,0,1.402577," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right)}{2 \, d}, -\frac{\sqrt{2} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a}}{\sqrt{a \sin\left(d x + c\right) + a}}\right)}{d}\right]"," ",0,"[1/2*sqrt(2)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1))/d, -sqrt(2)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)/sqrt(a*sin(d*x + c) + a))/d]","A",0
109,1,159,0,1.188428," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \cos\left(d x + c\right) \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a}}{4 \, d \cos\left(d x + c\right)}"," ",0,"1/4*(sqrt(2)*sqrt(a)*cos(d*x + c)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c))","B",0
110,1,99,0,1.574845," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \sqrt{a} \cos\left(d x + c\right)^{2} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(3 \, \sin\left(d x + c\right) - 1\right)}}{16 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/16*(3*sqrt(2)*sqrt(a)*cos(d*x + c)^2*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + 4*sqrt(a*sin(d*x + c) + a)*(3*sin(d*x + c) - 1))/(d*cos(d*x + c)^2)","A",0
111,1,188,0,0.849375," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} \sqrt{a} \cos\left(d x + c\right)^{3} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sqrt{2} \cos\left(d x + c\right) - \sqrt{2} \sin\left(d x + c\right) + \sqrt{2}\right)} \sqrt{a} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(15 \, \cos\left(d x + c\right)^{2} + 10 \, \sin\left(d x + c\right) - 2\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/96*(15*sqrt(2)*sqrt(a)*cos(d*x + c)^3*log(-(a*cos(d*x + c)^2 - 2*sqrt(a*sin(d*x + c) + a)*(sqrt(2)*cos(d*x + c) - sqrt(2)*sin(d*x + c) + sqrt(2))*sqrt(a) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(15*cos(d*x + c)^2 + 10*sin(d*x + c) - 2)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^3)","A",0
112,1,121,0,1.566666," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} \sqrt{a} \cos\left(d x + c\right)^{4} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, {\left(35 \, \cos\left(d x + c\right)^{2} - 7 \, {\left(15 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 8\right)} \sqrt{a \sin\left(d x + c\right) + a}}{768 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/768*(105*sqrt(2)*sqrt(a)*cos(d*x + c)^4*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*(35*cos(d*x + c)^2 - 7*(15*cos(d*x + c)^2 + 8)*sin(d*x + c) + 8)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^4)","A",0
113,1,210,0,0.868454," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{315 \, \sqrt{2} \sqrt{a} \cos\left(d x + c\right)^{5} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sqrt{2} \cos\left(d x + c\right) - \sqrt{2} \sin\left(d x + c\right) + \sqrt{2}\right)} \sqrt{a} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(315 \, \cos\left(d x + c\right)^{4} - 42 \, \cos\left(d x + c\right)^{2} + 6 \, {\left(35 \, \cos\left(d x + c\right)^{2} + 24\right)} \sin\left(d x + c\right) - 16\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2560 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/2560*(315*sqrt(2)*sqrt(a)*cos(d*x + c)^5*log(-(a*cos(d*x + c)^2 - 2*sqrt(a*sin(d*x + c) + a)*(sqrt(2)*cos(d*x + c) - sqrt(2)*sin(d*x + c) + sqrt(2))*sqrt(a) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(315*cos(d*x + c)^4 - 42*cos(d*x + c)^2 + 6*(35*cos(d*x + c)^2 + 24)*sin(d*x + c) - 16)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^5)","A",0
114,1,110,0,1.483432," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(715 \, a \cos\left(d x + c\right)^{8} - 66 \, a \cos\left(d x + c\right)^{6} - 112 \, a \cos\left(d x + c\right)^{4} - 256 \, a \cos\left(d x + c\right)^{2} - 2 \, {\left(429 \, a \cos\left(d x + c\right)^{6} + 504 \, a \cos\left(d x + c\right)^{4} + 640 \, a \cos\left(d x + c\right)^{2} + 1024 \, a\right)} \sin\left(d x + c\right) - 2048 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{12155 \, d}"," ",0,"-2/12155*(715*a*cos(d*x + c)^8 - 66*a*cos(d*x + c)^6 - 112*a*cos(d*x + c)^4 - 256*a*cos(d*x + c)^2 - 2*(429*a*cos(d*x + c)^6 + 504*a*cos(d*x + c)^4 + 640*a*cos(d*x + c)^2 + 1024*a)*sin(d*x + c) - 2048*a)*sqrt(a*sin(d*x + c) + a)/d","A",0
115,1,210,0,1.156314," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, a \cos\left(d x + c\right)^{8} + 6699 \, a \cos\left(d x + c\right)^{7} - 336 \, a \cos\left(d x + c\right)^{6} + 448 \, a \cos\left(d x + c\right)^{5} - 640 \, a \cos\left(d x + c\right)^{4} + 1024 \, a \cos\left(d x + c\right)^{3} - 2048 \, a \cos\left(d x + c\right)^{2} + 8192 \, a \cos\left(d x + c\right) + {\left(3003 \, a \cos\left(d x + c\right)^{7} - 3696 \, a \cos\left(d x + c\right)^{6} - 4032 \, a \cos\left(d x + c\right)^{5} - 4480 \, a \cos\left(d x + c\right)^{4} - 5120 \, a \cos\left(d x + c\right)^{3} - 6144 \, a \cos\left(d x + c\right)^{2} - 8192 \, a \cos\left(d x + c\right) - 16384 \, a\right)} \sin\left(d x + c\right) + 16384 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{45045 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/45045*(3003*a*cos(d*x + c)^8 + 6699*a*cos(d*x + c)^7 - 336*a*cos(d*x + c)^6 + 448*a*cos(d*x + c)^5 - 640*a*cos(d*x + c)^4 + 1024*a*cos(d*x + c)^3 - 2048*a*cos(d*x + c)^2 + 8192*a*cos(d*x + c) + (3003*a*cos(d*x + c)^7 - 3696*a*cos(d*x + c)^6 - 4032*a*cos(d*x + c)^5 - 4480*a*cos(d*x + c)^4 - 5120*a*cos(d*x + c)^3 - 6144*a*cos(d*x + c)^2 - 8192*a*cos(d*x + c) - 16384*a)*sin(d*x + c) + 16384*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
116,1,88,0,1.332577," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(99 \, a \cos\left(d x + c\right)^{6} - 14 \, a \cos\left(d x + c\right)^{4} - 32 \, a \cos\left(d x + c\right)^{2} - 2 \, {\left(63 \, a \cos\left(d x + c\right)^{4} + 80 \, a \cos\left(d x + c\right)^{2} + 128 \, a\right)} \sin\left(d x + c\right) - 256 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{1287 \, d}"," ",0,"-2/1287*(99*a*cos(d*x + c)^6 - 14*a*cos(d*x + c)^4 - 32*a*cos(d*x + c)^2 - 2*(63*a*cos(d*x + c)^4 + 80*a*cos(d*x + c)^2 + 128*a)*sin(d*x + c) - 256*a)*sqrt(a*sin(d*x + c) + a)/d","A",0
117,1,166,0,1.375963," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, a \cos\left(d x + c\right)^{6} + 245 \, a \cos\left(d x + c\right)^{5} - 20 \, a \cos\left(d x + c\right)^{4} + 32 \, a \cos\left(d x + c\right)^{3} - 64 \, a \cos\left(d x + c\right)^{2} + 256 \, a \cos\left(d x + c\right) + {\left(105 \, a \cos\left(d x + c\right)^{5} - 140 \, a \cos\left(d x + c\right)^{4} - 160 \, a \cos\left(d x + c\right)^{3} - 192 \, a \cos\left(d x + c\right)^{2} - 256 \, a \cos\left(d x + c\right) - 512 \, a\right)} \sin\left(d x + c\right) + 512 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{1155 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/1155*(105*a*cos(d*x + c)^6 + 245*a*cos(d*x + c)^5 - 20*a*cos(d*x + c)^4 + 32*a*cos(d*x + c)^3 - 64*a*cos(d*x + c)^2 + 256*a*cos(d*x + c) + (105*a*cos(d*x + c)^5 - 140*a*cos(d*x + c)^4 - 160*a*cos(d*x + c)^3 - 192*a*cos(d*x + c)^2 - 256*a*cos(d*x + c) - 512*a)*sin(d*x + c) + 512*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
118,1,66,0,1.095256," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} - 2 \, {\left(5 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right) - 16 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{63 \, d}"," ",0,"-2/63*(7*a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 - 2*(5*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c) - 16*a)*sqrt(a*sin(d*x + c) + a)/d","A",0
119,1,122,0,1.088825," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, a \cos\left(d x + c\right)^{4} + 39 \, a \cos\left(d x + c\right)^{3} - 8 \, a \cos\left(d x + c\right)^{2} + 32 \, a \cos\left(d x + c\right) + {\left(15 \, a \cos\left(d x + c\right)^{3} - 24 \, a \cos\left(d x + c\right)^{2} - 32 \, a \cos\left(d x + c\right) - 64 \, a\right)} \sin\left(d x + c\right) + 64 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{105 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/105*(15*a*cos(d*x + c)^4 + 39*a*cos(d*x + c)^3 - 8*a*cos(d*x + c)^2 + 32*a*cos(d*x + c) + (15*a*cos(d*x + c)^3 - 24*a*cos(d*x + c)^2 - 32*a*cos(d*x + c) - 64*a)*sin(d*x + c) + 64*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
120,1,40,0,0.969106," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a \cos\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right) - 2 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{5 \, d}"," ",0,"-2/5*(a*cos(d*x + c)^2 - 2*a*sin(d*x + c) - 2*a)*sqrt(a*sin(d*x + c) + a)/d","A",0
121,1,72,0,1.503956," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 2 \, \sqrt{a \sin\left(d x + c\right) + a} a}{d}"," ",0,"(sqrt(2)*a^(3/2)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 2*sqrt(a*sin(d*x + c) + a)*a)/d","A",0
122,1,26,0,1.168530," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a} a}{d \cos\left(d x + c\right)}"," ",0,"2*sqrt(a*sin(d*x + c) + a)*a/(d*cos(d*x + c))","A",0
123,1,99,0,1.000722," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} a \sin\left(d x + c\right) - \sqrt{2} a\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, \sqrt{a \sin\left(d x + c\right) + a} a}{8 \, {\left(d \sin\left(d x + c\right) - d\right)}}"," ",0,"1/8*((sqrt(2)*a*sin(d*x + c) - sqrt(2)*a)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*sqrt(a*sin(d*x + c) + a)*a)/(d*sin(d*x + c) - d)","A",0
124,1,215,0,1.240830," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\sqrt{2} a \cos\left(d x + c\right) \sin\left(d x + c\right) - \sqrt{2} a \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sqrt{2} \cos\left(d x + c\right) - \sqrt{2} \sin\left(d x + c\right) + \sqrt{2}\right)} \sqrt{a} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(3 \, a \sin\left(d x + c\right) - 5 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{24 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"1/24*(3*(sqrt(2)*a*cos(d*x + c)*sin(d*x + c) - sqrt(2)*a*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(a*sin(d*x + c) + a)*(sqrt(2)*cos(d*x + c) - sqrt(2)*sin(d*x + c) + sqrt(2))*sqrt(a) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(3*a*sin(d*x + c) - 5*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","B",0
125,1,155,0,1.534597," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{15 \, {\left(\sqrt{2} a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - \sqrt{2} a \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, {\left(15 \, a \cos\left(d x + c\right)^{2} + 20 \, a \sin\left(d x + c\right) - 12 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{128 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/128*(15*(sqrt(2)*a*cos(d*x + c)^2*sin(d*x + c) - sqrt(2)*a*cos(d*x + c)^2)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*(15*a*cos(d*x + c)^2 + 20*a*sin(d*x + c) - 12*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
126,1,248,0,1.342812," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{105 \, {\left(\sqrt{2} a \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - \sqrt{2} a \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sqrt{2} \cos\left(d x + c\right) - \sqrt{2} \sin\left(d x + c\right) + \sqrt{2}\right)} \sqrt{a} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) - 4 \, {\left(175 \, a \cos\left(d x + c\right)^{2} - 21 \, {\left(5 \, a \cos\left(d x + c\right)^{2} - 4 \, a\right)} \sin\left(d x + c\right) - 36 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{960 \, {\left(d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/960*(105*(sqrt(2)*a*cos(d*x + c)^3*sin(d*x + c) - sqrt(2)*a*cos(d*x + c)^3)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(a*sin(d*x + c) + a)*(sqrt(2)*cos(d*x + c) - sqrt(2)*sin(d*x + c) + sqrt(2))*sqrt(a) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) - 4*(175*a*cos(d*x + c)^2 - 21*(5*a*cos(d*x + c)^2 - 4*a)*sin(d*x + c) - 36*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^3*sin(d*x + c) - d*cos(d*x + c)^3)","A",0
127,1,114,0,1.317509," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(341 \, a^{2} \cos\left(d x + c\right)^{6} - 28 \, a^{2} \cos\left(d x + c\right)^{4} - 64 \, a^{2} \cos\left(d x + c\right)^{2} - 512 \, a^{2} + {\left(143 \, a^{2} \cos\left(d x + c\right)^{6} - 252 \, a^{2} \cos\left(d x + c\right)^{4} - 320 \, a^{2} \cos\left(d x + c\right)^{2} - 512 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2145 \, d}"," ",0,"-2/2145*(341*a^2*cos(d*x + c)^6 - 28*a^2*cos(d*x + c)^4 - 64*a^2*cos(d*x + c)^2 - 512*a^2 + (143*a^2*cos(d*x + c)^6 - 252*a^2*cos(d*x + c)^4 - 320*a^2*cos(d*x + c)^2 - 512*a^2)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/d","A",0
128,1,219,0,1.180550," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, a^{2} \cos\left(d x + c\right)^{7} - 2835 \, a^{2} \cos\left(d x + c\right)^{6} - 6230 \, a^{2} \cos\left(d x + c\right)^{5} + 320 \, a^{2} \cos\left(d x + c\right)^{4} - 512 \, a^{2} \cos\left(d x + c\right)^{3} + 1024 \, a^{2} \cos\left(d x + c\right)^{2} - 4096 \, a^{2} \cos\left(d x + c\right) - 8192 \, a^{2} - {\left(1155 \, a^{2} \cos\left(d x + c\right)^{6} + 3990 \, a^{2} \cos\left(d x + c\right)^{5} - 2240 \, a^{2} \cos\left(d x + c\right)^{4} - 2560 \, a^{2} \cos\left(d x + c\right)^{3} - 3072 \, a^{2} \cos\left(d x + c\right)^{2} - 4096 \, a^{2} \cos\left(d x + c\right) - 8192 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15015 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/15015*(1155*a^2*cos(d*x + c)^7 - 2835*a^2*cos(d*x + c)^6 - 6230*a^2*cos(d*x + c)^5 + 320*a^2*cos(d*x + c)^4 - 512*a^2*cos(d*x + c)^3 + 1024*a^2*cos(d*x + c)^2 - 4096*a^2*cos(d*x + c) - 8192*a^2 - (1155*a^2*cos(d*x + c)^6 + 3990*a^2*cos(d*x + c)^5 - 2240*a^2*cos(d*x + c)^4 - 2560*a^2*cos(d*x + c)^3 - 3072*a^2*cos(d*x + c)^2 - 4096*a^2*cos(d*x + c) - 8192*a^2)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
129,1,88,0,1.236133," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(23 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} - 32 \, a^{2} + {\left(9 \, a^{2} \cos\left(d x + c\right)^{4} - 20 \, a^{2} \cos\left(d x + c\right)^{2} - 32 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{99 \, d}"," ",0,"-2/99*(23*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 - 32*a^2 + (9*a^2*cos(d*x + c)^4 - 20*a^2*cos(d*x + c)^2 - 32*a^2)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/d","B",0
130,1,167,0,1.427494," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a^{2} \cos\left(d x + c\right)^{5} - 95 \, a^{2} \cos\left(d x + c\right)^{4} - 226 \, a^{2} \cos\left(d x + c\right)^{3} + 32 \, a^{2} \cos\left(d x + c\right)^{2} - 128 \, a^{2} \cos\left(d x + c\right) - 256 \, a^{2} - {\left(35 \, a^{2} \cos\left(d x + c\right)^{4} + 130 \, a^{2} \cos\left(d x + c\right)^{3} - 96 \, a^{2} \cos\left(d x + c\right)^{2} - 128 \, a^{2} \cos\left(d x + c\right) - 256 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{315 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*a^2*cos(d*x + c)^5 - 95*a^2*cos(d*x + c)^4 - 226*a^2*cos(d*x + c)^3 + 32*a^2*cos(d*x + c)^2 - 128*a^2*cos(d*x + c) - 256*a^2 - (35*a^2*cos(d*x + c)^4 + 130*a^2*cos(d*x + c)^3 - 96*a^2*cos(d*x + c)^2 - 128*a^2*cos(d*x + c) - 256*a^2)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
131,1,61,0,1.337157," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{2} - 4 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right)^{2} - 4 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{7 \, d}"," ",0,"-2/7*(3*a^2*cos(d*x + c)^2 - 4*a^2 + (a^2*cos(d*x + c)^2 - 4*a^2)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/d","B",0
132,1,89,0,1.054409," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - {\left(a^{2} \sin\left(d x + c\right) + 7 \, a^{2}\right)} \sqrt{a \sin\left(d x + c\right) + a}\right)}}{3 \, d}"," ",0,"2/3*(3*sqrt(2)*a^(5/2)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - (a^2*sin(d*x + c) + 7*a^2)*sqrt(a*sin(d*x + c) + a))/d","A",0
133,1,41,0,0.686891," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} \sin\left(d x + c\right) - 3 \, a^{2}\right)} \sqrt{a \sin\left(d x + c\right) + a}}{d \cos\left(d x + c\right)}"," ",0,"-2*(a^2*sin(d*x + c) - 3*a^2)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c))","A",0
134,1,102,0,1.340457," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(a^{2} \sin\left(d x + c\right) - a^{2}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}}{4 \, {\left(d \sin\left(d x + c\right) - d\right)}}"," ",0,"1/4*(sqrt(2)*(a^2*sin(d*x + c) - a^2)*sqrt(a)*log(-(a*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*sqrt(a*sin(d*x + c) + a)*a^2)/(d*sin(d*x + c) - d)","A",0
135,1,43,0,1.002027," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a} a^{2}}{3 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"-2/3*sqrt(a*sin(d*x + c) + a)*a^2/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
136,1,147,0,1.314129," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\sqrt{2} a^{2} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} a^{2} \sin\left(d x + c\right) - 2 \, \sqrt{2} a^{2}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + 4 \, {\left(3 \, a^{2} \sin\left(d x + c\right) - 7 \, a^{2}\right)} \sqrt{a \sin\left(d x + c\right) + a}}{64 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/64*(3*(sqrt(2)*a^2*cos(d*x + c)^2 + 2*sqrt(2)*a^2*sin(d*x + c) - 2*sqrt(2)*a^2)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + 4*(3*a^2*sin(d*x + c) - 7*a^2)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
137,1,263,0,1.468845," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{15 \, {\left(\sqrt{2} a^{2} \cos\left(d x + c\right)^{3} + 2 \, \sqrt{2} a^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \sqrt{2} a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sqrt{2} \cos\left(d x + c\right) - \sqrt{2} \sin\left(d x + c\right) + \sqrt{2}\right)} \sqrt{a} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(15 \, a^{2} \cos\left(d x + c\right)^{2} + 40 \, a^{2} \sin\left(d x + c\right) - 52 \, a^{2}\right)} \sqrt{a \sin\left(d x + c\right) + a}}{240 \, {\left(d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)\right)}}"," ",0,"1/240*(15*(sqrt(2)*a^2*cos(d*x + c)^3 + 2*sqrt(2)*a^2*cos(d*x + c)*sin(d*x + c) - 2*sqrt(2)*a^2*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(a*sin(d*x + c) + a)*(sqrt(2)*cos(d*x + c) - sqrt(2)*sin(d*x + c) + sqrt(2))*sqrt(a) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(15*a^2*cos(d*x + c)^2 + 40*a^2*sin(d*x + c) - 52*a^2)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^3 + 2*d*cos(d*x + c)*sin(d*x + c) - 2*d*cos(d*x + c))","B",0
138,1,208,0,1.500831," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{105 \, {\left(\sqrt{2} a^{2} \cos\left(d x + c\right)^{4} + 2 \, \sqrt{2} a^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, \sqrt{2} a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, {\left(245 \, a^{2} \cos\left(d x + c\right)^{2} - 160 \, a^{2} - 7 \, {\left(15 \, a^{2} \cos\left(d x + c\right)^{2} - 32 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{1536 \, {\left(d \cos\left(d x + c\right)^{4} + 2 \, d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/1536*(105*(sqrt(2)*a^2*cos(d*x + c)^4 + 2*sqrt(2)*a^2*cos(d*x + c)^2*sin(d*x + c) - 2*sqrt(2)*a^2*cos(d*x + c)^2)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*(245*a^2*cos(d*x + c)^2 - 160*a^2 - 7*(15*a^2*cos(d*x + c)^2 - 32*a^2)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^4 + 2*d*cos(d*x + c)^2*sin(d*x + c) - 2*d*cos(d*x + c)^2)","A",0
139,1,154,0,1.515214," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1615 \, a^{3} \cos\left(d x + c\right)^{10} - 8300 \, a^{3} \cos\left(d x + c\right)^{8} + 264 \, a^{3} \cos\left(d x + c\right)^{6} + 448 \, a^{3} \cos\left(d x + c\right)^{4} + 1024 \, a^{3} \cos\left(d x + c\right)^{2} + 8192 \, a^{3} - 8 \, {\left(680 \, a^{3} \cos\left(d x + c\right)^{8} - 429 \, a^{3} \cos\left(d x + c\right)^{6} - 504 \, a^{3} \cos\left(d x + c\right)^{4} - 640 \, a^{3} \cos\left(d x + c\right)^{2} - 1024 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{33915 \, d}"," ",0,"2/33915*(1615*a^3*cos(d*x + c)^10 - 8300*a^3*cos(d*x + c)^8 + 264*a^3*cos(d*x + c)^6 + 448*a^3*cos(d*x + c)^4 + 1024*a^3*cos(d*x + c)^2 + 8192*a^3 - 8*(680*a^3*cos(d*x + c)^8 - 429*a^3*cos(d*x + c)^6 - 504*a^3*cos(d*x + c)^4 - 640*a^3*cos(d*x + c)^2 - 1024*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/d","A",0
140,1,296,0,1.262267," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(51051 \, a^{3} \cos\left(d x + c\right)^{10} + 225225 \, a^{3} \cos\left(d x + c\right)^{9} - 270270 \, a^{3} \cos\left(d x + c\right)^{8} - 562716 \, a^{3} \cos\left(d x + c\right)^{7} + 10752 \, a^{3} \cos\left(d x + c\right)^{6} - 14336 \, a^{3} \cos\left(d x + c\right)^{5} + 20480 \, a^{3} \cos\left(d x + c\right)^{4} - 32768 \, a^{3} \cos\left(d x + c\right)^{3} + 65536 \, a^{3} \cos\left(d x + c\right)^{2} - 262144 \, a^{3} \cos\left(d x + c\right) - 524288 \, a^{3} + {\left(51051 \, a^{3} \cos\left(d x + c\right)^{9} - 174174 \, a^{3} \cos\left(d x + c\right)^{8} - 444444 \, a^{3} \cos\left(d x + c\right)^{7} + 118272 \, a^{3} \cos\left(d x + c\right)^{6} + 129024 \, a^{3} \cos\left(d x + c\right)^{5} + 143360 \, a^{3} \cos\left(d x + c\right)^{4} + 163840 \, a^{3} \cos\left(d x + c\right)^{3} + 196608 \, a^{3} \cos\left(d x + c\right)^{2} + 262144 \, a^{3} \cos\left(d x + c\right) + 524288 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{969969 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/969969*(51051*a^3*cos(d*x + c)^10 + 225225*a^3*cos(d*x + c)^9 - 270270*a^3*cos(d*x + c)^8 - 562716*a^3*cos(d*x + c)^7 + 10752*a^3*cos(d*x + c)^6 - 14336*a^3*cos(d*x + c)^5 + 20480*a^3*cos(d*x + c)^4 - 32768*a^3*cos(d*x + c)^3 + 65536*a^3*cos(d*x + c)^2 - 262144*a^3*cos(d*x + c) - 524288*a^3 + (51051*a^3*cos(d*x + c)^9 - 174174*a^3*cos(d*x + c)^8 - 444444*a^3*cos(d*x + c)^7 + 118272*a^3*cos(d*x + c)^6 + 129024*a^3*cos(d*x + c)^5 + 143360*a^3*cos(d*x + c)^4 + 163840*a^3*cos(d*x + c)^3 + 196608*a^3*cos(d*x + c)^2 + 262144*a^3*cos(d*x + c) + 524288*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
141,1,128,0,1.565629," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(195 \, a^{3} \cos\left(d x + c\right)^{8} - 1072 \, a^{3} \cos\left(d x + c\right)^{6} + 56 \, a^{3} \cos\left(d x + c\right)^{4} + 128 \, a^{3} \cos\left(d x + c\right)^{2} + 1024 \, a^{3} - 4 \, {\left(169 \, a^{3} \cos\left(d x + c\right)^{6} - 126 \, a^{3} \cos\left(d x + c\right)^{4} - 160 \, a^{3} \cos\left(d x + c\right)^{2} - 256 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3315 \, d}"," ",0,"2/3315*(195*a^3*cos(d*x + c)^8 - 1072*a^3*cos(d*x + c)^6 + 56*a^3*cos(d*x + c)^4 + 128*a^3*cos(d*x + c)^2 + 1024*a^3 - 4*(169*a^3*cos(d*x + c)^6 - 126*a^3*cos(d*x + c)^4 - 160*a^3*cos(d*x + c)^2 - 256*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/d","B",0
142,1,244,0,0.772766," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, a^{3} \cos\left(d x + c\right)^{8} + 13629 \, a^{3} \cos\left(d x + c\right)^{7} - 17346 \, a^{3} \cos\left(d x + c\right)^{6} - 36932 \, a^{3} \cos\left(d x + c\right)^{5} + 1280 \, a^{3} \cos\left(d x + c\right)^{4} - 2048 \, a^{3} \cos\left(d x + c\right)^{3} + 4096 \, a^{3} \cos\left(d x + c\right)^{2} - 16384 \, a^{3} \cos\left(d x + c\right) - 32768 \, a^{3} + {\left(3003 \, a^{3} \cos\left(d x + c\right)^{7} - 10626 \, a^{3} \cos\left(d x + c\right)^{6} - 27972 \, a^{3} \cos\left(d x + c\right)^{5} + 8960 \, a^{3} \cos\left(d x + c\right)^{4} + 10240 \, a^{3} \cos\left(d x + c\right)^{3} + 12288 \, a^{3} \cos\left(d x + c\right)^{2} + 16384 \, a^{3} \cos\left(d x + c\right) + 32768 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{45045 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/45045*(3003*a^3*cos(d*x + c)^8 + 13629*a^3*cos(d*x + c)^7 - 17346*a^3*cos(d*x + c)^6 - 36932*a^3*cos(d*x + c)^5 + 1280*a^3*cos(d*x + c)^4 - 2048*a^3*cos(d*x + c)^3 + 4096*a^3*cos(d*x + c)^2 - 16384*a^3*cos(d*x + c) - 32768*a^3 + (3003*a^3*cos(d*x + c)^7 - 10626*a^3*cos(d*x + c)^6 - 27972*a^3*cos(d*x + c)^5 + 8960*a^3*cos(d*x + c)^4 + 10240*a^3*cos(d*x + c)^3 + 12288*a^3*cos(d*x + c)^2 + 16384*a^3*cos(d*x + c) + 32768*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
143,1,102,0,1.389118," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(11 \, a^{3} \cos\left(d x + c\right)^{6} - 68 \, a^{3} \cos\left(d x + c\right)^{4} + 8 \, a^{3} \cos\left(d x + c\right)^{2} + 64 \, a^{3} - 8 \, {\left(5 \, a^{3} \cos\left(d x + c\right)^{4} - 5 \, a^{3} \cos\left(d x + c\right)^{2} - 8 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{143 \, d}"," ",0,"2/143*(11*a^3*cos(d*x + c)^6 - 68*a^3*cos(d*x + c)^4 + 8*a^3*cos(d*x + c)^2 + 64*a^3 - 8*(5*a^3*cos(d*x + c)^4 - 5*a^3*cos(d*x + c)^2 - 8*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/d","B",0
144,1,192,0,1.416214," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, a^{3} \cos\left(d x + c\right)^{6} + 1505 \, a^{3} \cos\left(d x + c\right)^{5} - 2150 \, a^{3} \cos\left(d x + c\right)^{4} - 4876 \, a^{3} \cos\left(d x + c\right)^{3} + 512 \, a^{3} \cos\left(d x + c\right)^{2} - 2048 \, a^{3} \cos\left(d x + c\right) - 4096 \, a^{3} + {\left(315 \, a^{3} \cos\left(d x + c\right)^{5} - 1190 \, a^{3} \cos\left(d x + c\right)^{4} - 3340 \, a^{3} \cos\left(d x + c\right)^{3} + 1536 \, a^{3} \cos\left(d x + c\right)^{2} + 2048 \, a^{3} \cos\left(d x + c\right) + 4096 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3465 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/3465*(315*a^3*cos(d*x + c)^6 + 1505*a^3*cos(d*x + c)^5 - 2150*a^3*cos(d*x + c)^4 - 4876*a^3*cos(d*x + c)^3 + 512*a^3*cos(d*x + c)^2 - 2048*a^3*cos(d*x + c) - 4096*a^3 + (315*a^3*cos(d*x + c)^5 - 1190*a^3*cos(d*x + c)^4 - 3340*a^3*cos(d*x + c)^3 + 1536*a^3*cos(d*x + c)^2 + 2048*a^3*cos(d*x + c) + 4096*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
145,1,74,0,1.307792," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 8 \, a^{3} \cos\left(d x + c\right)^{2} + 8 \, a^{3} - 4 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{9 \, d}"," ",0,"2/9*(a^3*cos(d*x + c)^4 - 8*a^3*cos(d*x + c)^2 + 8*a^3 - 4*(a^3*cos(d*x + c)^2 - 2*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/d","B",0
146,1,102,0,0.985445," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(30 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + {\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 16 \, a^{3} \sin\left(d x + c\right) - 76 \, a^{3}\right)} \sqrt{a \sin\left(d x + c\right) + a}\right)}}{15 \, d}"," ",0,"2/15*(30*sqrt(2)*a^(7/2)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + (3*a^3*cos(d*x + c)^2 - 16*a^3*sin(d*x + c) - 76*a^3)*sqrt(a*sin(d*x + c) + a))/d","A",0
147,1,54,0,1.391726," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - 10 \, a^{3} \sin\left(d x + c\right) + 22 \, a^{3}\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3 \, d \cos\left(d x + c\right)}"," ",0,"2/3*(a^3*cos(d*x + c)^2 - 10*a^3*sin(d*x + c) + 22*a^3)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c))","A",0
148,1,116,0,1.004902," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(a^{3} \sin\left(d x + c\right) - a^{3}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + 4 \, {\left(a^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2 \, {\left(d \sin\left(d x + c\right) - d\right)}}"," ",0,"1/2*(3*sqrt(2)*(a^3*sin(d*x + c) - a^3)*sqrt(a)*log(-(a*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + 4*(a^3*sin(d*x + c) - 2*a^3)*sqrt(a*sin(d*x + c) + a))/(d*sin(d*x + c) - d)","A",0
149,1,57,0,1.361360," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a^{3} \sin\left(d x + c\right) - a^{3}\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"-2/3*(3*a^3*sin(d*x + c) - a^3)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
150,1,145,0,1.232203," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} a^{3} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} a^{3} \sin\left(d x + c\right) - 2 \, \sqrt{2} a^{3}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, {\left(a^{3} \sin\left(d x + c\right) + 3 \, a^{3}\right)} \sqrt{a \sin\left(d x + c\right) + a}}{32 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/32*((sqrt(2)*a^3*cos(d*x + c)^2 + 2*sqrt(2)*a^3*sin(d*x + c) - 2*sqrt(2)*a^3)*sqrt(a)*log(-(a*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*(a^3*sin(d*x + c) + 3*a^3)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
151,1,54,0,1.488530," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a} a^{3}}{5 \, {\left(d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)\right)}}"," ",0,"-2/5*sqrt(a*sin(d*x + c) + a)*a^3/(d*cos(d*x + c)^3 + 2*d*cos(d*x + c)*sin(d*x + c) - 2*d*cos(d*x + c))","B",0
152,1,193,0,1.177894," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, \sqrt{2} a^{3} \cos\left(d x + c\right)^{2} - 4 \, \sqrt{2} a^{3} - {\left(\sqrt{2} a^{3} \cos\left(d x + c\right)^{2} - 4 \, \sqrt{2} a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + 4 \, {\left(15 \, a^{3} \cos\left(d x + c\right)^{2} + 50 \, a^{3} \sin\left(d x + c\right) - 82 \, a^{3}\right)} \sqrt{a \sin\left(d x + c\right) + a}}{768 \, {\left(3 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{2} - 4 \, d\right)} \sin\left(d x + c\right) - 4 \, d\right)}}"," ",0,"1/768*(15*(3*sqrt(2)*a^3*cos(d*x + c)^2 - 4*sqrt(2)*a^3 - (sqrt(2)*a^3*cos(d*x + c)^2 - 4*sqrt(2)*a^3)*sin(d*x + c))*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + 4*(15*a^3*cos(d*x + c)^2 + 50*a^3*sin(d*x + c) - 82*a^3)*sqrt(a*sin(d*x + c) + a))/(3*d*cos(d*x + c)^2 - (d*cos(d*x + c)^2 - 4*d)*sin(d*x + c) - 4*d)","A",0
153,1,312,0,1.516718," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{105 \, {\left(3 \, \sqrt{2} a^{3} \cos\left(d x + c\right)^{3} - 4 \, \sqrt{2} a^{3} \cos\left(d x + c\right) - {\left(\sqrt{2} a^{3} \cos\left(d x + c\right)^{3} - 4 \, \sqrt{2} a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sqrt{2} \cos\left(d x + c\right) - \sqrt{2} \sin\left(d x + c\right) + \sqrt{2}\right)} \sqrt{a} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(385 \, a^{3} \cos\left(d x + c\right)^{2} - 764 \, a^{3} - 7 \, {\left(15 \, a^{3} \cos\left(d x + c\right)^{2} - 92 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3360 \, {\left(3 \, d \cos\left(d x + c\right)^{3} - 4 \, d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{3} - 4 \, d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/3360*(105*(3*sqrt(2)*a^3*cos(d*x + c)^3 - 4*sqrt(2)*a^3*cos(d*x + c) - (sqrt(2)*a^3*cos(d*x + c)^3 - 4*sqrt(2)*a^3*cos(d*x + c))*sin(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(a*sin(d*x + c) + a)*(sqrt(2)*cos(d*x + c) - sqrt(2)*sin(d*x + c) + sqrt(2))*sqrt(a) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(385*a^3*cos(d*x + c)^2 - 764*a^3 - 7*(15*a^3*cos(d*x + c)^2 - 92*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a))/(3*d*cos(d*x + c)^3 - 4*d*cos(d*x + c) - (d*cos(d*x + c)^3 - 4*d*cos(d*x + c))*sin(d*x + c))","B",0
154,1,254,0,1.544988," ","integrate(sec(d*x+c)^9*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{315 \, {\left(3 \, \sqrt{2} a^{3} \cos\left(d x + c\right)^{4} - 4 \, \sqrt{2} a^{3} \cos\left(d x + c\right)^{2} - {\left(\sqrt{2} a^{3} \cos\left(d x + c\right)^{4} - 4 \, \sqrt{2} a^{3} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + 4 \, {\left(315 \, a^{3} \cos\left(d x + c\right)^{4} - 1722 \, a^{3} \cos\left(d x + c\right)^{2} + 896 \, a^{3} + 6 \, {\left(175 \, a^{3} \cos\left(d x + c\right)^{2} - 192 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{8192 \, {\left(3 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/8192*(315*(3*sqrt(2)*a^3*cos(d*x + c)^4 - 4*sqrt(2)*a^3*cos(d*x + c)^2 - (sqrt(2)*a^3*cos(d*x + c)^4 - 4*sqrt(2)*a^3*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + 4*(315*a^3*cos(d*x + c)^4 - 1722*a^3*cos(d*x + c)^2 + 896*a^3 + 6*(175*a^3*cos(d*x + c)^2 - 192*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a))/(3*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 - (d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2)*sin(d*x + c))","A",0
155,1,346,0,1.351898," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{3465 \, {\left(3 \, \sqrt{2} a^{3} \cos\left(d x + c\right)^{5} - 4 \, \sqrt{2} a^{3} \cos\left(d x + c\right)^{3} - {\left(\sqrt{2} a^{3} \cos\left(d x + c\right)^{5} - 4 \, \sqrt{2} a^{3} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sqrt{2} \cos\left(d x + c\right) - \sqrt{2} \sin\left(d x + c\right) + \sqrt{2}\right)} \sqrt{a} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(12705 \, a^{3} \cos\left(d x + c\right)^{4} - 25212 \, a^{3} \cos\left(d x + c\right)^{2} + 3920 \, a^{3} - 77 \, {\left(45 \, a^{3} \cos\left(d x + c\right)^{4} - 276 \, a^{3} \cos\left(d x + c\right)^{2} + 80 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{80640 \, {\left(3 \, d \cos\left(d x + c\right)^{5} - 4 \, d \cos\left(d x + c\right)^{3} - {\left(d \cos\left(d x + c\right)^{5} - 4 \, d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/80640*(3465*(3*sqrt(2)*a^3*cos(d*x + c)^5 - 4*sqrt(2)*a^3*cos(d*x + c)^3 - (sqrt(2)*a^3*cos(d*x + c)^5 - 4*sqrt(2)*a^3*cos(d*x + c)^3)*sin(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(a*sin(d*x + c) + a)*(sqrt(2)*cos(d*x + c) - sqrt(2)*sin(d*x + c) + sqrt(2))*sqrt(a) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(12705*a^3*cos(d*x + c)^4 - 25212*a^3*cos(d*x + c)^2 + 3920*a^3 - 77*(45*a^3*cos(d*x + c)^4 - 276*a^3*cos(d*x + c)^2 + 80*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a))/(3*d*cos(d*x + c)^5 - 4*d*cos(d*x + c)^3 - (d*cos(d*x + c)^5 - 4*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
156,1,82,0,1.283612," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, \cos\left(d x + c\right)^{6} + 28 \, \cos\left(d x + c\right)^{4} + 64 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(63 \, \cos\left(d x + c\right)^{4} + 80 \, \cos\left(d x + c\right)^{2} + 128\right)} \sin\left(d x + c\right) + 512\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3003 \, a d}"," ",0,"2/3003*(231*cos(d*x + c)^6 + 28*cos(d*x + c)^4 + 64*cos(d*x + c)^2 + 4*(63*cos(d*x + c)^4 + 80*cos(d*x + c)^2 + 128)*sin(d*x + c) + 512)*sqrt(a*sin(d*x + c) + a)/(a*d)","A",0
157,1,155,0,1.540031," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, \cos\left(d x + c\right)^{6} - 7 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{4} - 16 \, \cos\left(d x + c\right)^{3} + 32 \, \cos\left(d x + c\right)^{2} + {\left(63 \, \cos\left(d x + c\right)^{5} + 70 \, \cos\left(d x + c\right)^{4} + 80 \, \cos\left(d x + c\right)^{3} + 96 \, \cos\left(d x + c\right)^{2} + 128 \, \cos\left(d x + c\right) + 256\right)} \sin\left(d x + c\right) - 128 \, \cos\left(d x + c\right) - 256\right)} \sqrt{a \sin\left(d x + c\right) + a}}{693 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"2/693*(63*cos(d*x + c)^6 - 7*cos(d*x + c)^5 + 10*cos(d*x + c)^4 - 16*cos(d*x + c)^3 + 32*cos(d*x + c)^2 + (63*cos(d*x + c)^5 + 70*cos(d*x + c)^4 + 80*cos(d*x + c)^3 + 96*cos(d*x + c)^2 + 128*cos(d*x + c) + 256)*sin(d*x + c) - 128*cos(d*x + c) - 256)*sqrt(a*sin(d*x + c) + a)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
158,1,62,0,1.436833," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, \cos\left(d x + c\right)^{4} + 8 \, \cos\left(d x + c\right)^{2} + 8 \, {\left(5 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 64\right)} \sqrt{a \sin\left(d x + c\right) + a}}{315 \, a d}"," ",0,"2/315*(35*cos(d*x + c)^4 + 8*cos(d*x + c)^2 + 8*(5*cos(d*x + c)^2 + 8)*sin(d*x + c) + 64)*sqrt(a*sin(d*x + c) + a)/(a*d)","A",0
159,1,115,0,1.368073," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + {\left(5 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 8 \, \cos\left(d x + c\right) + 16\right)} \sin\left(d x + c\right) - 8 \, \cos\left(d x + c\right) - 16\right)} \sqrt{a \sin\left(d x + c\right) + a}}{35 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"2/35*(5*cos(d*x + c)^4 - cos(d*x + c)^3 + 2*cos(d*x + c)^2 + (5*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 8*cos(d*x + c) + 16)*sin(d*x + c) - 8*cos(d*x + c) - 16)*sqrt(a*sin(d*x + c) + a)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","B",0
160,1,40,0,1.267910," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right) + 4\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15 \, a d}"," ",0,"2/15*(3*cos(d*x + c)^2 + 4*sin(d*x + c) + 4)*sqrt(a*sin(d*x + c) + a)/(a*d)","A",0
161,1,71,0,1.442089," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"2/3*(cos(d*x + c)^2 + (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)*sqrt(a*sin(d*x + c) + a)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","B",0
162,1,20,0,1.347204," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\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
163,1,90,0,1.471700," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} {\left(a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a}}{\sqrt{a}} + \sin\left(d x + c\right) + 3}{\sin\left(d x + c\right) - 1}\right)}{\sqrt{a}} - 4 \, \sqrt{a \sin\left(d x + c\right) + a}}{4 \, {\left(a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"1/4*(sqrt(2)*(a*sin(d*x + c) + a)*log(-(2*sqrt(2)*sqrt(a*sin(d*x + c) + a)/sqrt(a) + sin(d*x + c) + 3)/(sin(d*x + c) - 1))/sqrt(a) - 4*sqrt(a*sin(d*x + c) + a))/(a*d*sin(d*x + c) + a*d)","A",0
164,1,200,0,1.774222," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right) \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(3 \, \sin\left(d x + c\right) + 1\right)}}{16 \, {\left(a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)}}"," ",0,"1/16*(3*sqrt(2)*(cos(d*x + c)*sin(d*x + c) + cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*sqrt(a*sin(d*x + c) + a)*(3*sin(d*x + c) + 1))/(a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))","B",0
165,1,145,0,1.594567," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, {\left(15 \, \cos\left(d x + c\right)^{2} - 10 \, \sin\left(d x + c\right) - 2\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(a d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/96*(15*sqrt(2)*(cos(d*x + c)^2*sin(d*x + c) + cos(d*x + c)^2)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*(15*cos(d*x + c)^2 - 10*sin(d*x + c) - 2)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^2*sin(d*x + c) + a*d*cos(d*x + c)^2)","A",0
166,1,230,0,1.582345," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(35 \, \cos\left(d x + c\right)^{2} + 7 \, {\left(15 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 8\right)} \sqrt{a \sin\left(d x + c\right) + a}}{768 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/768*(105*sqrt(2)*(cos(d*x + c)^3*sin(d*x + c) + cos(d*x + c)^3)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(35*cos(d*x + c)^2 + 7*(15*cos(d*x + c)^2 + 8)*sin(d*x + c) + 8)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
167,1,167,0,0.930906," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{315 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, {\left(315 \, \cos\left(d x + c\right)^{4} - 42 \, \cos\left(d x + c\right)^{2} - 6 \, {\left(35 \, \cos\left(d x + c\right)^{2} + 24\right)} \sin\left(d x + c\right) - 16\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2560 \, {\left(a d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/2560*(315*sqrt(2)*(cos(d*x + c)^4*sin(d*x + c) + cos(d*x + c)^4)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*(315*cos(d*x + c)^4 - 42*cos(d*x + c)^2 - 6*(35*cos(d*x + c)^2 + 24)*sin(d*x + c) - 16)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^4*sin(d*x + c) + a*d*cos(d*x + c)^4)","A",0
168,1,250,0,1.386423," ","integrate(sec(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3465 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{5}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(1155 \, \cos\left(d x + c\right)^{4} + 264 \, \cos\left(d x + c\right)^{2} + 11 \, {\left(315 \, \cos\left(d x + c\right)^{4} + 168 \, \cos\left(d x + c\right)^{2} + 128\right)} \sin\left(d x + c\right) + 128\right)} \sqrt{a \sin\left(d x + c\right) + a}}{30720 \, {\left(a d \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"1/30720*(3465*sqrt(2)*(cos(d*x + c)^5*sin(d*x + c) + cos(d*x + c)^5)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(1155*cos(d*x + c)^4 + 264*cos(d*x + c)^2 + 11*(315*cos(d*x + c)^4 + 168*cos(d*x + c)^2 + 128)*sin(d*x + c) + 128)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^5*sin(d*x + c) + a*d*cos(d*x + c)^5)","A",0
169,1,72,0,1.485495," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(245 \, \cos\left(d x + c\right)^{4} + 32 \, \cos\left(d x + c\right)^{2} - {\left(105 \, \cos\left(d x + c\right)^{4} - 160 \, \cos\left(d x + c\right)^{2} - 256\right)} \sin\left(d x + c\right) + 256\right)} \sqrt{a \sin\left(d x + c\right) + a}}{1155 \, a^{2} d}"," ",0,"2/1155*(245*cos(d*x + c)^4 + 32*cos(d*x + c)^2 - (105*cos(d*x + c)^4 - 160*cos(d*x + c)^2 - 256)*sin(d*x + c) + 256)*sqrt(a*sin(d*x + c) + a)/(a^2*d)","A",0
170,1,142,0,1.200857," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, \cos\left(d x + c\right)^{5} + 17 \, \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} - {\left(7 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{3} - 12 \, \cos\left(d x + c\right)^{2} - 16 \, \cos\left(d x + c\right) - 32\right)} \sin\left(d x + c\right) - 16 \, \cos\left(d x + c\right) - 32\right)} \sqrt{a \sin\left(d x + c\right) + a}}{63 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"2/63*(7*cos(d*x + c)^5 + 17*cos(d*x + c)^4 - 2*cos(d*x + c)^3 + 4*cos(d*x + c)^2 - (7*cos(d*x + c)^4 - 10*cos(d*x + c)^3 - 12*cos(d*x + c)^2 - 16*cos(d*x + c) - 32)*sin(d*x + c) - 16*cos(d*x + c) - 32)*sqrt(a*sin(d*x + c) + a)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","B",0
171,1,52,0,1.466386," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(39 \, \cos\left(d x + c\right)^{2} - {\left(15 \, \cos\left(d x + c\right)^{2} - 32\right)} \sin\left(d x + c\right) + 32\right)} \sqrt{a \sin\left(d x + c\right) + a}}{105 \, a^{2} d}"," ",0,"2/105*(39*cos(d*x + c)^2 - (15*cos(d*x + c)^2 - 32)*sin(d*x + c) + 32)*sqrt(a*sin(d*x + c) + a)/(a^2*d)","A",0
172,1,98,0,1.108029," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 4\right)} \sqrt{a \sin\left(d x + c\right) + a}}{5 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"2/5*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 - (cos(d*x + c)^2 - 2*cos(d*x + c) - 4)*sin(d*x + c) - 2*cos(d*x + c) - 4)*sqrt(a*sin(d*x + c) + a)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","B",0
173,1,28,0,1.354927," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sin\left(d x + c\right) - 5\right)}}{3 \, a^{2} d}"," ",0,"-2/3*sqrt(a*sin(d*x + c) + a)*(sin(d*x + c) - 5)/(a^2*d)","A",0
174,1,196,0,1.242697," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + 2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"(sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + 2*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1))/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","B",0
175,1,33,0,0.999303," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a}}{a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"-2*sqrt(a*sin(d*x + c) + a)/(a^2*d*sin(d*x + c) + a^2*d)","A",0
176,1,132,0,1.584623," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(3 \, \sin\left(d x + c\right) + 5\right)}}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - 2 \, a^{2} d \sin\left(d x + c\right) - 2 \, a^{2} d\right)}}"," ",0,"1/24*(3*sqrt(2)*(cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + 4*sqrt(a*sin(d*x + c) + a)*(3*sin(d*x + c) + 5))/(a^2*d*cos(d*x + c)^2 - 2*a^2*d*sin(d*x + c) - 2*a^2*d)","A",0
177,1,240,0,1.115570," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(15 \, \cos\left(d x + c\right)^{2} - 20 \, \sin\left(d x + c\right) - 12\right)} \sqrt{a \sin\left(d x + c\right) + a}}{128 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"1/128*(15*sqrt(2)*(cos(d*x + c)^3 - 2*cos(d*x + c)*sin(d*x + c) - 2*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(15*cos(d*x + c)^2 - 20*sin(d*x + c) - 12)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","B",0
178,1,187,0,1.150251," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + 4 \, {\left(175 \, \cos\left(d x + c\right)^{2} + 21 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 36\right)} \sqrt{a \sin\left(d x + c\right) + a}}{960 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/960*(105*sqrt(2)*(cos(d*x + c)^4 - 2*cos(d*x + c)^2*sin(d*x + c) - 2*cos(d*x + c)^2)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + 4*(175*cos(d*x + c)^2 + 21*(5*cos(d*x + c)^2 - 4)*sin(d*x + c) - 36)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^2)","A",0
179,1,270,0,1.153770," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{315 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(315 \, \cos\left(d x + c\right)^{4} - 252 \, \cos\left(d x + c\right)^{2} - 12 \, {\left(35 \, \cos\left(d x + c\right)^{2} + 16\right)} \sin\left(d x + c\right) - 64\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3072 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/3072*(315*sqrt(2)*(cos(d*x + c)^5 - 2*cos(d*x + c)^3*sin(d*x + c) - 2*cos(d*x + c)^3)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(315*cos(d*x + c)^4 - 252*cos(d*x + c)^2 - 12*(35*cos(d*x + c)^2 + 16)*sin(d*x + c) - 64)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
180,1,207,0,1.572101," ","integrate(sec(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3465 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{6} - 2 \, \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) + 4 \, {\left(5775 \, \cos\left(d x + c\right)^{4} - 1188 \, \cos\left(d x + c\right)^{2} + 11 \, {\left(315 \, \cos\left(d x + c\right)^{4} - 252 \, \cos\left(d x + c\right)^{2} - 160\right)} \sin\left(d x + c\right) - 480\right)} \sqrt{a \sin\left(d x + c\right) + a}}{35840 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 2 \, a^{2} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/35840*(3465*sqrt(2)*(cos(d*x + c)^6 - 2*cos(d*x + c)^4*sin(d*x + c) - 2*cos(d*x + c)^4)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) + 4*(5775*cos(d*x + c)^4 - 1188*cos(d*x + c)^2 + 11*(315*cos(d*x + c)^4 - 252*cos(d*x + c)^2 - 160)*sin(d*x + c) - 480)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^6 - 2*a^2*d*cos(d*x + c)^4*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^4)","A",0
181,1,290,0,1.233485," ","integrate(sec(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{45045 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{7} - 2 \, \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{5}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(45045 \, \cos\left(d x + c\right)^{6} - 36036 \, \cos\left(d x + c\right)^{4} - 9152 \, \cos\left(d x + c\right)^{2} - 156 \, {\left(385 \, \cos\left(d x + c\right)^{4} + 176 \, \cos\left(d x + c\right)^{2} + 128\right)} \sin\left(d x + c\right) - 4608\right)} \sqrt{a \sin\left(d x + c\right) + a}}{491520 \, {\left(a^{2} d \cos\left(d x + c\right)^{7} - 2 \, a^{2} d \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"1/491520*(45045*sqrt(2)*(cos(d*x + c)^7 - 2*cos(d*x + c)^5*sin(d*x + c) - 2*cos(d*x + c)^5)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(45045*cos(d*x + c)^6 - 36036*cos(d*x + c)^4 - 9152*cos(d*x + c)^2 - 156*(385*cos(d*x + c)^4 + 176*cos(d*x + c)^2 + 128)*sin(d*x + c) - 4608)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^7 - 2*a^2*d*cos(d*x + c)^5*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^5)","A",0
182,1,201,0,1.231611," ","integrate(cos(d*x+c)^10/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(143 \, \cos\left(d x + c\right)^{8} - 341 \, \cos\left(d x + c\right)^{7} - 736 \, \cos\left(d x + c\right)^{6} + 28 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{4} + 64 \, \cos\left(d x + c\right)^{3} - 128 \, \cos\left(d x + c\right)^{2} + {\left(143 \, \cos\left(d x + c\right)^{7} + 484 \, \cos\left(d x + c\right)^{6} - 252 \, \cos\left(d x + c\right)^{5} - 280 \, \cos\left(d x + c\right)^{4} - 320 \, \cos\left(d x + c\right)^{3} - 384 \, \cos\left(d x + c\right)^{2} - 512 \, \cos\left(d x + c\right) - 1024\right)} \sin\left(d x + c\right) + 512 \, \cos\left(d x + c\right) + 1024\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2145 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-2/2145*(143*cos(d*x + c)^8 - 341*cos(d*x + c)^7 - 736*cos(d*x + c)^6 + 28*cos(d*x + c)^5 - 40*cos(d*x + c)^4 + 64*cos(d*x + c)^3 - 128*cos(d*x + c)^2 + (143*cos(d*x + c)^7 + 484*cos(d*x + c)^6 - 252*cos(d*x + c)^5 - 280*cos(d*x + c)^4 - 320*cos(d*x + c)^3 - 384*cos(d*x + c)^2 - 512*cos(d*x + c) - 1024)*sin(d*x + c) + 512*cos(d*x + c) + 1024)*sqrt(a*sin(d*x + c) + a)/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","B",0
183,1,82,0,1.314949," ","integrate(cos(d*x+c)^9/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(1155 \, \cos\left(d x + c\right)^{6} - 6230 \, \cos\left(d x + c\right)^{4} - 512 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(1995 \, \cos\left(d x + c\right)^{4} - 1280 \, \cos\left(d x + c\right)^{2} - 2048\right)} \sin\left(d x + c\right) - 4096\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15015 \, a^{3} d}"," ",0,"-2/15015*(1155*cos(d*x + c)^6 - 6230*cos(d*x + c)^4 - 512*cos(d*x + c)^2 + 2*(1995*cos(d*x + c)^4 - 1280*cos(d*x + c)^2 - 2048)*sin(d*x + c) - 4096)*sqrt(a*sin(d*x + c) + a)/(a^3*d)","A",0
184,1,161,0,1.212927," ","integrate(cos(d*x+c)^8/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{6} - 23 \, \cos\left(d x + c\right)^{5} - 52 \, \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} - 8 \, \cos\left(d x + c\right)^{2} + {\left(9 \, \cos\left(d x + c\right)^{5} + 32 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{3} - 24 \, \cos\left(d x + c\right)^{2} - 32 \, \cos\left(d x + c\right) - 64\right)} \sin\left(d x + c\right) + 32 \, \cos\left(d x + c\right) + 64\right)} \sqrt{a \sin\left(d x + c\right) + a}}{99 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-2/99*(9*cos(d*x + c)^6 - 23*cos(d*x + c)^5 - 52*cos(d*x + c)^4 + 4*cos(d*x + c)^3 - 8*cos(d*x + c)^2 + (9*cos(d*x + c)^5 + 32*cos(d*x + c)^4 - 20*cos(d*x + c)^3 - 24*cos(d*x + c)^2 - 32*cos(d*x + c) - 64)*sin(d*x + c) + 32*cos(d*x + c) + 64)*sqrt(a*sin(d*x + c) + a)/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","B",0
185,1,62,0,1.399611," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, \cos\left(d x + c\right)^{4} - 226 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(65 \, \cos\left(d x + c\right)^{2} - 64\right)} \sin\left(d x + c\right) - 128\right)} \sqrt{a \sin\left(d x + c\right) + a}}{315 \, a^{3} d}"," ",0,"-2/315*(35*cos(d*x + c)^4 - 226*cos(d*x + c)^2 + 2*(65*cos(d*x + c)^2 - 64)*sin(d*x + c) - 128)*sqrt(a*sin(d*x + c) + a)/(a^3*d)","A",0
186,1,117,0,1.285834," ","integrate(cos(d*x+c)^6/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{3} - 8 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right) - 8\right)} \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right) + 8\right)} \sqrt{a \sin\left(d x + c\right) + a}}{7 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-2/7*(cos(d*x + c)^4 - 3*cos(d*x + c)^3 - 8*cos(d*x + c)^2 + (cos(d*x + c)^3 + 4*cos(d*x + c)^2 - 4*cos(d*x + c) - 8)*sin(d*x + c) + 4*cos(d*x + c) + 8)*sqrt(a*sin(d*x + c) + a)/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","B",0
187,1,40,0,1.221770," ","integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 14 \, \sin\left(d x + c\right) - 46\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15 \, a^{3} d}"," ",0,"-2/15*(3*cos(d*x + c)^2 + 14*sin(d*x + c) - 46)*sqrt(a*sin(d*x + c) + a)/(a^3*d)","A",0
188,1,215,0,1.438866," ","integrate(cos(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\frac{3 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right) - 7 \, \cos\left(d x + c\right) - 8\right)} \sqrt{a \sin\left(d x + c\right) + a}\right)}}{3 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"2/3*(3*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - (cos(d*x + c)^2 + (cos(d*x + c) + 8)*sin(d*x + c) - 7*cos(d*x + c) - 8)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","B",0
189,1,41,0,1.308688," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\sin\left(d x + c\right) + 3\right)}}{a^{3} d \sin\left(d x + c\right) + a^{3} d}"," ",0,"-2*sqrt(a*sin(d*x + c) + a)*(sin(d*x + c) + 3)/(a^3*d*sin(d*x + c) + a^3*d)","A",0
190,1,252,0,1.073008," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} {\left(a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) + 2 \, a\right)} \sin\left(d x + c\right) - 2 \, a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right) + 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*(sqrt(2)*(a*cos(d*x + c)^2 - a*cos(d*x + c) - (a*cos(d*x + c) + 2*a)*sin(d*x + c) - 2*a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + 4*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1))/(a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d - (a^3*d*cos(d*x + c) + 2*a^3*d)*sin(d*x + c))","B",0
191,1,48,0,1.181991," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \sin\left(d x + c\right) + a}}{3 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"2/3*sqrt(a*sin(d*x + c) + a)/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","B",0
192,1,169,0,1.445943," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, {\left(15 \, \cos\left(d x + c\right)^{2} - 40 \, \sin\left(d x + c\right) - 52\right)} \sqrt{a \sin\left(d x + c\right) + a}}{240 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{2} - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/240*(15*sqrt(2)*(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*(15*cos(d*x + c)^2 - 40*sin(d*x + c) - 52)*sqrt(a*sin(d*x + c) + a))/(3*a^3*d*cos(d*x + c)^2 - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 4*a^3*d)*sin(d*x + c))","A",0
193,1,280,0,1.569768," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} {\left(3 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{3} - 4 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 4 \, \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(245 \, \cos\left(d x + c\right)^{2} + 7 \, {\left(15 \, \cos\left(d x + c\right)^{2} - 32\right)} \sin\left(d x + c\right) - 160\right)} \sqrt{a \sin\left(d x + c\right) + a}}{1536 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/1536*(105*sqrt(2)*(3*cos(d*x + c)^3 + (cos(d*x + c)^3 - 4*cos(d*x + c))*sin(d*x + c) - 4*cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(245*cos(d*x + c)^2 + 7*(15*cos(d*x + c)^2 - 32)*sin(d*x + c) - 160)*sqrt(a*sin(d*x + c) + a))/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
194,1,225,0,1.467230," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{315 \, \sqrt{2} {\left(3 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \sin\left(d x + c\right) + 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} + 3 \, a}{\sin\left(d x + c\right) - 1}\right) - 4 \, {\left(315 \, \cos\left(d x + c\right)^{4} - 1092 \, \cos\left(d x + c\right)^{2} - 120 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 3\right)} \sin\left(d x + c\right) + 200\right)} \sqrt{a \sin\left(d x + c\right) + a}}{4480 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{4} - 4 \, a^{3} d \cos\left(d x + c\right)^{2} + {\left(a^{3} d \cos\left(d x + c\right)^{4} - 4 \, a^{3} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4480*(315*sqrt(2)*(3*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + (cos(d*x + c)^4 - 4*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a)*log(-(a*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a) + 3*a)/(sin(d*x + c) - 1)) - 4*(315*cos(d*x + c)^4 - 1092*cos(d*x + c)^2 - 120*(7*cos(d*x + c)^2 - 3)*sin(d*x + c) + 200)*sqrt(a*sin(d*x + c) + a))/(3*a^3*d*cos(d*x + c)^4 - 4*a^3*d*cos(d*x + c)^2 + (a^3*d*cos(d*x + c)^4 - 4*a^3*d*cos(d*x + c)^2)*sin(d*x + c))","A",0
195,1,308,0,0.965708," ","integrate(sec(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3465 \, \sqrt{2} {\left(3 \, \cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)} + 3 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + 4 \, {\left(8085 \, \cos\left(d x + c\right)^{4} - 5280 \, \cos\left(d x + c\right)^{2} + 11 \, {\left(315 \, \cos\left(d x + c\right)^{4} - 672 \, \cos\left(d x + c\right)^{2} - 256\right)} \sin\left(d x + c\right) - 1280\right)} \sqrt{a \sin\left(d x + c\right) + a}}{49152 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/49152*(3465*sqrt(2)*(3*cos(d*x + c)^5 - 4*cos(d*x + c)^3 + (cos(d*x + c)^5 - 4*cos(d*x + c)^3)*sin(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - sin(d*x + c) + 1) + 3*a*cos(d*x + c) - (a*cos(d*x + c) - 2*a)*sin(d*x + c) + 2*a)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + 4*(8085*cos(d*x + c)^4 - 5280*cos(d*x + c)^2 + 11*(315*cos(d*x + c)^4 - 672*cos(d*x + c)^2 - 256)*sin(d*x + c) - 1280)*sqrt(a*sin(d*x + c) + a))/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
196,0,0,0,1.447157," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a e^{3} \cos\left(d x + c\right)^{3}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*e^3*cos(d*x + c)^3*sin(d*x + c) + a*e^3*cos(d*x + c)^3)*sqrt(e*cos(d*x + c)), x)","F",0
197,0,0,0,1.327818," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a e^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*e^2*cos(d*x + c)^2*sin(d*x + c) + a*e^2*cos(d*x + c)^2)*sqrt(e*cos(d*x + c)), x)","F",0
198,0,0,0,1.361475," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e \cos\left(d x + c\right) \sin\left(d x + c\right) + a e \cos\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*e*cos(d*x + c)*sin(d*x + c) + a*e*cos(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
199,0,0,0,1.688790," ","integrate((a+a*sin(d*x+c))*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a), x)","F",0
200,0,0,0,1.357830," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)/(e*cos(d*x + c)), x)","F",0
201,0,0,0,1.367555," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)/(e^2*cos(d*x + c)^2), x)","F",0
202,0,0,0,1.376340," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)/(e^3*cos(d*x + c)^3), x)","F",0
203,0,0,0,1.394048," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}}{e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)/(e^4*cos(d*x + c)^4), x)","F",0
204,0,0,0,1.338298," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} e^{3} \cos\left(d x + c\right)^{5} - 2 \, a^{2} e^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} e^{3} \cos\left(d x + c\right)^{3}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(a^2*e^3*cos(d*x + c)^5 - 2*a^2*e^3*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*e^3*cos(d*x + c)^3)*sqrt(e*cos(d*x + c)), x)","F",0
205,0,0,0,1.393331," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} e^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} e^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, a^{2} e^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(a^2*e^2*cos(d*x + c)^4 - 2*a^2*e^2*cos(d*x + c)^2*sin(d*x + c) - 2*a^2*e^2*cos(d*x + c)^2)*sqrt(e*cos(d*x + c)), x)","F",0
206,0,0,0,1.480969," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} e \cos\left(d x + c\right)^{3} - 2 \, a^{2} e \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} e \cos\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(a^2*e*cos(d*x + c)^3 - 2*a^2*e*cos(d*x + c)*sin(d*x + c) - 2*a^2*e*cos(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
207,0,0,0,1.504013," ","integrate((a+a*sin(d*x+c))^2*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*sqrt(e*cos(d*x + c)), x)","F",0
208,0,0,0,1.266726," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*sqrt(e*cos(d*x + c))/(e*cos(d*x + c)), x)","F",0
209,0,0,0,1.233058," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*sqrt(e*cos(d*x + c))/(e^2*cos(d*x + c)^2), x)","F",0
210,0,0,0,1.573925," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*sqrt(e*cos(d*x + c))/(e^3*cos(d*x + c)^3), x)","F",0
211,0,0,0,1.426649," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*sqrt(e*cos(d*x + c))/(e^4*cos(d*x + c)^4), x)","F",0
212,0,0,0,1.423545," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{5} \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*sqrt(e*cos(d*x + c))/(e^5*cos(d*x + c)^5), x)","F",0
213,0,0,0,1.432282," ","integrate((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{6} \cos\left(d x + c\right)^{6}}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*sqrt(e*cos(d*x + c))/(e^6*cos(d*x + c)^6), x)","F",0
214,0,0,0,1.565443," ","integrate((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} e^{3} \cos\left(d x + c\right)^{5} - 4 \, a^{3} e^{3} \cos\left(d x + c\right)^{3} + {\left(a^{3} e^{3} \cos\left(d x + c\right)^{5} - 4 \, a^{3} e^{3} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a^3*e^3*cos(d*x + c)^5 - 4*a^3*e^3*cos(d*x + c)^3 + (a^3*e^3*cos(d*x + c)^5 - 4*a^3*e^3*cos(d*x + c)^3)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
215,0,0,0,1.328987," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} e^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{3} e^{2} \cos\left(d x + c\right)^{2} + {\left(a^{3} e^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{3} e^{2} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a^3*e^2*cos(d*x + c)^4 - 4*a^3*e^2*cos(d*x + c)^2 + (a^3*e^2*cos(d*x + c)^4 - 4*a^3*e^2*cos(d*x + c)^2)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
216,0,0,0,1.142658," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} e \cos\left(d x + c\right)^{3} - 4 \, a^{3} e \cos\left(d x + c\right) + {\left(a^{3} e \cos\left(d x + c\right)^{3} - 4 \, a^{3} e \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a^3*e*cos(d*x + c)^3 - 4*a^3*e*cos(d*x + c) + (a^3*e*cos(d*x + c)^3 - 4*a^3*e*cos(d*x + c))*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
217,0,0,0,1.253163," ","integrate((a+a*sin(d*x+c))^3*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
218,0,0,0,1.192534," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e*cos(d*x + c)), x)","F",0
219,0,0,0,1.192050," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^2*cos(d*x + c)^2), x)","F",0
220,0,0,0,1.168629," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^3*cos(d*x + c)^3), x)","F",0
221,0,0,0,1.392810," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^4*cos(d*x + c)^4), x)","F",0
222,0,0,0,1.282744," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{5} \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^5*cos(d*x + c)^5), x)","F",0
223,0,0,0,1.073922," ","integrate((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{6} \cos\left(d x + c\right)^{6}}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^6*cos(d*x + c)^6), x)","F",0
224,0,0,0,1.479632," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} e \cos\left(d x + c\right)^{5} - 8 \, a^{4} e \cos\left(d x + c\right)^{3} + 8 \, a^{4} e \cos\left(d x + c\right) - 4 \, {\left(a^{4} e \cos\left(d x + c\right)^{3} - 2 \, a^{4} e \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^4*e*cos(d*x + c)^5 - 8*a^4*e*cos(d*x + c)^3 + 8*a^4*e*cos(d*x + c) - 4*(a^4*e*cos(d*x + c)^3 - 2*a^4*e*cos(d*x + c))*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
225,0,0,0,1.479884," ","integrate((a+a*sin(d*x+c))^4*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
226,0,0,0,1.485964," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e*cos(d*x + c)), x)","F",0
227,0,0,0,1.482273," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^2*cos(d*x + c)^2), x)","F",0
228,0,0,0,1.490570," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^3*cos(d*x + c)^3), x)","F",0
229,0,0,0,1.576562," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^4*cos(d*x + c)^4), x)","F",0
230,0,0,0,0.975679," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{5} \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^5*cos(d*x + c)^5), x)","F",0
231,0,0,0,1.323130," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{6} \cos\left(d x + c\right)^{6}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^6*cos(d*x + c)^6), x)","F",0
232,0,0,0,1.443094," ","integrate((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{7} \cos\left(d x + c\right)^{7}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^7*cos(d*x + c)^7), x)","F",0
233,0,0,0,1.306974," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{5} \cos\left(d x + c\right)^{5}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^5*cos(d*x + c)^5/(a*sin(d*x + c) + a), x)","F",0
234,0,0,0,1.358587," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{4} \cos\left(d x + c\right)^{4}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^4*cos(d*x + c)^4/(a*sin(d*x + c) + a), x)","F",0
235,0,0,0,1.461166," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{3} \cos\left(d x + c\right)^{3}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^3*cos(d*x + c)^3/(a*sin(d*x + c) + a), x)","F",0
236,0,0,0,1.245611," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{2} \cos\left(d x + c\right)^{2}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^2*cos(d*x + c)^2/(a*sin(d*x + c) + a), x)","F",0
237,0,0,0,1.249084," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e \cos\left(d x + c\right)}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e*cos(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
238,0,0,0,1.163632," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))/(a*sin(d*x + c) + a), x)","F",0
239,0,0,0,1.346857," ","integrate(1/(a+a*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)}}{a e \cos\left(d x + c\right) \sin\left(d x + c\right) + a e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))/(a*e*cos(d*x + c)*sin(d*x + c) + a*e*cos(d*x + c)), x)","F",0
240,0,0,0,1.408364," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)}}{a e^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))/(a*e^2*cos(d*x + c)^2*sin(d*x + c) + a*e^2*cos(d*x + c)^2), x)","F",0
241,0,0,0,1.225451," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)}}{a e^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))/(a*e^3*cos(d*x + c)^3*sin(d*x + c) + a*e^3*cos(d*x + c)^3), x)","F",0
242,0,0,0,1.286833," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)}}{a e^{4} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + a e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))/(a*e^4*cos(d*x + c)^4*sin(d*x + c) + a*e^4*cos(d*x + c)^4), x)","F",0
243,0,0,0,1.383482," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{5} \cos\left(d x + c\right)^{5}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^5*cos(d*x + c)^5/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
244,0,0,0,1.367512," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{4} \cos\left(d x + c\right)^{4}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^4*cos(d*x + c)^4/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
245,0,0,0,1.474352," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{3} \cos\left(d x + c\right)^{3}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^3*cos(d*x + c)^3/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
246,0,0,0,1.152089," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{2} \cos\left(d x + c\right)^{2}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^2*cos(d*x + c)^2/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
247,0,0,0,1.293352," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e \cos\left(d x + c\right)}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e*cos(d*x + c)/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
248,0,0,0,1.375115," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
249,0,0,0,1.415166," ","integrate(1/(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)}}{a^{2} e \cos\left(d x + c\right)^{3} - 2 \, a^{2} e \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))/(a^2*e*cos(d*x + c)^3 - 2*a^2*e*cos(d*x + c)*sin(d*x + c) - 2*a^2*e*cos(d*x + c)), x)","F",0
250,0,0,0,1.167302," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)}}{a^{2} e^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} e^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, a^{2} e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))/(a^2*e^2*cos(d*x + c)^4 - 2*a^2*e^2*cos(d*x + c)^2*sin(d*x + c) - 2*a^2*e^2*cos(d*x + c)^2), x)","F",0
251,0,0,0,1.447593," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)}}{a^{2} e^{3} \cos\left(d x + c\right)^{5} - 2 \, a^{2} e^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))/(a^2*e^3*cos(d*x + c)^5 - 2*a^2*e^3*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*e^3*cos(d*x + c)^3), x)","F",0
252,0,0,0,0.874077," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)}}{a^{2} e^{4} \cos\left(d x + c\right)^{6} - 2 \, a^{2} e^{4} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, a^{2} e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))/(a^2*e^4*cos(d*x + c)^6 - 2*a^2*e^4*cos(d*x + c)^4*sin(d*x + c) - 2*a^2*e^4*cos(d*x + c)^4), x)","F",0
253,0,0,0,1.328677," ","integrate((e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{7} \cos\left(d x + c\right)^{7}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^7*cos(d*x + c)^7/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
254,0,0,0,1.521799," ","integrate((e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{6} \cos\left(d x + c\right)^{6}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^6*cos(d*x + c)^6/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
255,0,0,0,1.296456," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{5} \cos\left(d x + c\right)^{5}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^5*cos(d*x + c)^5/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
256,0,0,0,0.958654," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{4} \cos\left(d x + c\right)^{4}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^4*cos(d*x + c)^4/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
257,0,0,0,1.009804," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{3} \cos\left(d x + c\right)^{3}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^3*cos(d*x + c)^3/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
258,0,0,0,1.389387," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e^{2} \cos\left(d x + c\right)^{2}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e^2*cos(d*x + c)^2/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
259,0,0,0,0.881695," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)} e \cos\left(d x + c\right)}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))*e*cos(d*x + c)/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
260,0,0,0,1.330814," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
261,0,0,0,1.390895," ","integrate(1/(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)}}{3 \, a^{3} e \cos\left(d x + c\right)^{3} - 4 \, a^{3} e \cos\left(d x + c\right) + {\left(a^{3} e \cos\left(d x + c\right)^{3} - 4 \, a^{3} e \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))/(3*a^3*e*cos(d*x + c)^3 - 4*a^3*e*cos(d*x + c) + (a^3*e*cos(d*x + c)^3 - 4*a^3*e*cos(d*x + c))*sin(d*x + c)), x)","F",0
262,0,0,0,1.383125," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e \cos\left(d x + c\right)}}{3 \, a^{3} e^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{3} e^{2} \cos\left(d x + c\right)^{2} + {\left(a^{3} e^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{3} e^{2} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(e*cos(d*x + c))/(3*a^3*e^2*cos(d*x + c)^4 - 4*a^3*e^2*cos(d*x + c)^2 + (a^3*e^2*cos(d*x + c)^4 - 4*a^3*e^2*cos(d*x + c)^2)*sin(d*x + c)), x)","F",0
263,0,0,0,1.256280," ","integrate((e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{7} \cos\left(d x + c\right)^{7}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^7*cos(d*x + c)^7/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
264,0,0,0,1.373364," ","integrate((e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{6} \cos\left(d x + c\right)^{6}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^6*cos(d*x + c)^6/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
265,0,0,0,1.220499," ","integrate((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{5} \cos\left(d x + c\right)^{5}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^5*cos(d*x + c)^5/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
266,0,0,0,1.395449," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{4} \cos\left(d x + c\right)^{4}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^4*cos(d*x + c)^4/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
267,0,0,0,1.289313," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{3} \cos\left(d x + c\right)^{3}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^3*cos(d*x + c)^3/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
268,0,0,0,1.471127," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e^{2} \cos\left(d x + c\right)^{2}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e^2*cos(d*x + c)^2/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
269,0,0,0,1.053515," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} e \cos\left(d x + c\right)}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*e*cos(d*x + c)/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
270,0,0,0,1.299589," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
271,0,0,0,1.414663," ","integrate(1/(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)}}{a^{4} e \cos\left(d x + c\right)^{5} - 8 \, a^{4} e \cos\left(d x + c\right)^{3} + 8 \, a^{4} e \cos\left(d x + c\right) - 4 \, {\left(a^{4} e \cos\left(d x + c\right)^{3} - 2 \, a^{4} e \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))/(a^4*e*cos(d*x + c)^5 - 8*a^4*e*cos(d*x + c)^3 + 8*a^4*e*cos(d*x + c) - 4*(a^4*e*cos(d*x + c)^3 - 2*a^4*e*cos(d*x + c))*sin(d*x + c)), x)","F",0
272,0,0,0,1.328996," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)}}{a^{4} e^{2} \cos\left(d x + c\right)^{6} - 8 \, a^{4} e^{2} \cos\left(d x + c\right)^{4} + 8 \, a^{4} e^{2} \cos\left(d x + c\right)^{2} - 4 \, {\left(a^{4} e^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{4} e^{2} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))/(a^4*e^2*cos(d*x + c)^6 - 8*a^4*e^2*cos(d*x + c)^4 + 8*a^4*e^2*cos(d*x + c)^2 - 4*(a^4*e^2*cos(d*x + c)^4 - 2*a^4*e^2*cos(d*x + c)^2)*sin(d*x + c)), x)","F",0
273,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,1,38,0,0.843247," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{d e^{2} \cos\left(d x + c\right)}"," ",0,"2*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*e^2*cos(d*x + c))","A",0
277,1,48,0,1.678098," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a} {\left(2 \, \sin\left(d x + c\right) - 1\right)}}{3 \, d e^{3} \cos\left(d x + c\right)^{2}}"," ",0,"2/3*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)*(2*sin(d*x + c) - 1)/(d*e^3*cos(d*x + c)^2)","A",0
278,1,58,0,0.943288," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(8 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right) - 1\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15 \, d e^{4} \cos\left(d x + c\right)^{3}}"," ",0,"2/15*sqrt(e*cos(d*x + c))*(8*cos(d*x + c)^2 + 4*sin(d*x + c) - 1)*sqrt(a*sin(d*x + c) + a)/(d*e^4*cos(d*x + c)^3)","A",0
279,1,70,0,1.327527," ","integrate((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(8 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(8 \, \cos\left(d x + c\right)^{2} + 3\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a \sin\left(d x + c\right) + a}}{35 \, d e^{5} \cos\left(d x + c\right)^{4}}"," ",0,"-2/35*sqrt(e*cos(d*x + c))*(8*cos(d*x + c)^2 - 2*(8*cos(d*x + c)^2 + 3)*sin(d*x + c) + 1)*sqrt(a*sin(d*x + c) + a)/(d*e^5*cos(d*x + c)^4)","A",0
280,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,1,45,0,1.245879," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a} a}{3 \, {\left(d e^{3} \sin\left(d x + c\right) - d e^{3}\right)}}"," ",0,"-2/3*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)*a/(d*e^3*sin(d*x + c) - d*e^3)","A",0
286,1,69,0,1.448536," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(2 \, a \sin\left(d x + c\right) - 3 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{5 \, {\left(d e^{4} \cos\left(d x + c\right) \sin\left(d x + c\right) - d e^{4} \cos\left(d x + c\right)\right)}}"," ",0,"2/5*sqrt(e*cos(d*x + c))*(2*a*sin(d*x + c) - 3*a)*sqrt(a*sin(d*x + c) + a)/(d*e^4*cos(d*x + c)*sin(d*x + c) - d*e^4*cos(d*x + c))","A",0
287,1,84,0,1.569741," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a \cos\left(d x + c\right)^{2} + 12 \, a \sin\left(d x + c\right) - 9 \, a\right)} \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{21 \, {\left(d e^{5} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d e^{5} \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-2/21*(8*a*cos(d*x + c)^2 + 12*a*sin(d*x + c) - 9*a)*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*e^5*cos(d*x + c)^2*sin(d*x + c) - d*e^5*cos(d*x + c)^2)","A",0
288,1,98,0,1.127564," ","integrate((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(24 \, a \cos\left(d x + c\right)^{2} - 2 \, {\left(8 \, a \cos\left(d x + c\right)^{2} - 5 \, a\right)} \sin\left(d x + c\right) - 5 \, a\right)} \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{45 \, {\left(d e^{6} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - d e^{6} \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-2/45*(24*a*cos(d*x + c)^2 - 2*(8*a*cos(d*x + c)^2 - 5*a)*sin(d*x + c) - 5*a)*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*e^6*cos(d*x + c)^3*sin(d*x + c) - d*e^6*cos(d*x + c)^3)","A",0
289,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,1,107,0,1.632823," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2} \sin\left(d x + c\right) + a^{2}\right)} \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{5 \, {\left(d e^{4} \cos\left(d x + c\right)^{2} - d e^{4} \cos\left(d x + c\right) - 2 \, d e^{4} + {\left(d e^{4} \cos\left(d x + c\right) + 2 \, d e^{4}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-2/5*(a^2*cos(d*x + c) + a^2*sin(d*x + c) + a^2)*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*e^4*cos(d*x + c)^2 - d*e^4*cos(d*x + c) - 2*d*e^4 + (d*e^4*cos(d*x + c) + 2*d*e^4)*sin(d*x + c))","B",0
295,1,75,0,1.564448," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} \sin\left(d x + c\right) - 5 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{21 \, {\left(d e^{5} \cos\left(d x + c\right)^{2} + 2 \, d e^{5} \sin\left(d x + c\right) - 2 \, d e^{5}\right)}}"," ",0,"2/21*(2*a^2*sin(d*x + c) - 5*a^2)*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*e^5*cos(d*x + c)^2 + 2*d*e^5*sin(d*x + c) - 2*d*e^5)","A",0
296,1,100,0,1.527625," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{2} + 20 \, a^{2} \sin\left(d x + c\right) - 25 \, a^{2}\right)} \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{45 \, {\left(d e^{6} \cos\left(d x + c\right)^{3} + 2 \, d e^{6} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, d e^{6} \cos\left(d x + c\right)\right)}}"," ",0,"2/45*(8*a^2*cos(d*x + c)^2 + 20*a^2*sin(d*x + c) - 25*a^2)*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*e^6*cos(d*x + c)^3 + 2*d*e^6*cos(d*x + c)*sin(d*x + c) - 2*d*e^6*cos(d*x + c))","A",0
297,1,120,0,1.578770," ","integrate((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(40 \, a^{2} \cos\left(d x + c\right)^{2} - 35 \, a^{2} - 2 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{2} - 21 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{77 \, {\left(d e^{7} \cos\left(d x + c\right)^{4} + 2 \, d e^{7} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, d e^{7} \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-2/77*(40*a^2*cos(d*x + c)^2 - 35*a^2 - 2*(8*a^2*cos(d*x + c)^2 - 21*a^2)*sin(d*x + c))*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*e^7*cos(d*x + c)^4 + 2*d*e^7*cos(d*x + c)^2*sin(d*x + c) - 2*d*e^7*cos(d*x + c)^2)","A",0
298,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,1,41,0,1.902986," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{a d e \sin\left(d x + c\right) + a d e}"," ",0,"-2*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(a*d*e*sin(d*x + c) + a*d*e)","A",0
302,1,67,0,1.802246," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a} {\left(2 \, \sin\left(d x + c\right) + 1\right)}}{3 \, {\left(a d e^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + a d e^{2} \cos\left(d x + c\right)\right)}}"," ",0,"2/3*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)*(2*sin(d*x + c) + 1)/(a*d*e^2*cos(d*x + c)*sin(d*x + c) + a*d*e^2*cos(d*x + c))","A",0
303,1,81,0,1.475434," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(8 \, \cos\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) - 1\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15 \, {\left(a d e^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a d e^{3} \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-2/15*sqrt(e*cos(d*x + c))*(8*cos(d*x + c)^2 - 4*sin(d*x + c) - 1)*sqrt(a*sin(d*x + c) + a)/(a*d*e^3*cos(d*x + c)^2*sin(d*x + c) + a*d*e^3*cos(d*x + c)^2)","A",0
304,1,93,0,1.533380," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(8 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, \cos\left(d x + c\right)^{2} + 3\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a \sin\left(d x + c\right) + a}}{35 \, {\left(a d e^{4} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d e^{4} \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/35*sqrt(e*cos(d*x + c))*(8*cos(d*x + c)^2 + 2*(8*cos(d*x + c)^2 + 3)*sin(d*x + c) + 1)*sqrt(a*sin(d*x + c) + a)/(a*d*e^4*cos(d*x + c)^3*sin(d*x + c) + a*d*e^4*cos(d*x + c)^3)","A",0
305,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,1,100,0,1.641814," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \cos\left(d x + c\right) - 2 \, a^{2} d - {\left(a^{2} d \cos\left(d x + c\right) + 2 \, a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"2/3*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/(a^2*d*cos(d*x + c)^2 - a^2*d*cos(d*x + c) - 2*a^2*d - (a^2*d*cos(d*x + c) + 2*a^2*d)*sin(d*x + c))","B",0
309,1,71,0,1.787723," ","integrate(1/(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a} {\left(2 \, \sin\left(d x + c\right) + 3\right)}}{5 \, {\left(a^{2} d e \cos\left(d x + c\right)^{2} - 2 \, a^{2} d e \sin\left(d x + c\right) - 2 \, a^{2} d e\right)}}"," ",0,"2/5*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)*(2*sin(d*x + c) + 3)/(a^2*d*e*cos(d*x + c)^2 - 2*a^2*d*e*sin(d*x + c) - 2*a^2*d*e)","A",0
310,1,99,0,1.300757," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(8 \, \cos\left(d x + c\right)^{2} - 12 \, \sin\left(d x + c\right) - 9\right)} \sqrt{a \sin\left(d x + c\right) + a}}{21 \, {\left(a^{2} d e^{2} \cos\left(d x + c\right)^{3} - 2 \, a^{2} d e^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d e^{2} \cos\left(d x + c\right)\right)}}"," ",0,"2/21*sqrt(e*cos(d*x + c))*(8*cos(d*x + c)^2 - 12*sin(d*x + c) - 9)*sqrt(a*sin(d*x + c) + a)/(a^2*d*e^2*cos(d*x + c)^3 - 2*a^2*d*e^2*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*e^2*cos(d*x + c))","A",0
311,1,115,0,1.796737," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(24 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) - 5\right)} \sqrt{a \sin\left(d x + c\right) + a}}{45 \, {\left(a^{2} d e^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{2} d e^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, a^{2} d e^{3} \cos\left(d x + c\right)^{2}\right)}}"," ",0,"2/45*sqrt(e*cos(d*x + c))*(24*cos(d*x + c)^2 + 2*(8*cos(d*x + c)^2 - 5)*sin(d*x + c) - 5)*sqrt(a*sin(d*x + c) + a)/(a^2*d*e^3*cos(d*x + c)^4 - 2*a^2*d*e^3*cos(d*x + c)^2*sin(d*x + c) - 2*a^2*d*e^3*cos(d*x + c)^2)","A",0
312,1,125,0,1.401200," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, \cos\left(d x + c\right)^{4} - 144 \, \cos\left(d x + c\right)^{2} - 8 \, {\left(24 \, \cos\left(d x + c\right)^{2} + 7\right)} \sin\left(d x + c\right) - 21\right)} \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{385 \, {\left(a^{2} d e^{4} \cos\left(d x + c\right)^{5} - 2 \, a^{2} d e^{4} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d e^{4} \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/385*(128*cos(d*x + c)^4 - 144*cos(d*x + c)^2 - 8*(24*cos(d*x + c)^2 + 7)*sin(d*x + c) - 21)*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(a^2*d*e^4*cos(d*x + c)^5 - 2*a^2*d*e^4*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*e^4*cos(d*x + c)^3)","A",0
313,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,1,70,0,1.633495," ","integrate((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a} {\left(e \sin\left(d x + c\right) - e\right)}}{5 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"-2/5*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)*(e*sin(d*x + c) - e)/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","B",0
317,1,148,0,1.835010," ","integrate((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(2 \, \cos\left(d x + c\right)^{2} + {\left(2 \, \cos\left(d x + c\right) - 3\right)} \sin\left(d x + c\right) + 5 \, \cos\left(d x + c\right) + 3\right)} \sqrt{a \sin\left(d x + c\right) + a}}{21 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"2/21*sqrt(e*cos(d*x + c))*(2*cos(d*x + c)^2 + (2*cos(d*x + c) - 3)*sin(d*x + c) + 5*cos(d*x + c) + 3)*sqrt(a*sin(d*x + c) + a)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
318,1,98,0,1.143729," ","integrate(1/(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(8 \, \cos\left(d x + c\right)^{2} - 20 \, \sin\left(d x + c\right) - 25\right)} \sqrt{a \sin\left(d x + c\right) + a}}{45 \, {\left(3 \, a^{3} d e \cos\left(d x + c\right)^{2} - 4 \, a^{3} d e + {\left(a^{3} d e \cos\left(d x + c\right)^{2} - 4 \, a^{3} d e\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-2/45*sqrt(e*cos(d*x + c))*(8*cos(d*x + c)^2 - 20*sin(d*x + c) - 25)*sqrt(a*sin(d*x + c) + a)/(3*a^3*d*e*cos(d*x + c)^2 - 4*a^3*d*e + (a^3*d*e*cos(d*x + c)^2 - 4*a^3*d*e)*sin(d*x + c))","A",0
319,1,130,0,0.745682," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{e \cos\left(d x + c\right)} {\left(40 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, \cos\left(d x + c\right)^{2} - 21\right)} \sin\left(d x + c\right) - 35\right)} \sqrt{a \sin\left(d x + c\right) + a}}{77 \, {\left(3 \, a^{3} d e^{2} \cos\left(d x + c\right)^{3} - 4 \, a^{3} d e^{2} \cos\left(d x + c\right) + {\left(a^{3} d e^{2} \cos\left(d x + c\right)^{3} - 4 \, a^{3} d e^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"2/77*sqrt(e*cos(d*x + c))*(40*cos(d*x + c)^2 + 2*(8*cos(d*x + c)^2 - 21)*sin(d*x + c) - 35)*sqrt(a*sin(d*x + c) + a)/(3*a^3*d*e^2*cos(d*x + c)^3 - 4*a^3*d*e^2*cos(d*x + c) + (a^3*d*e^2*cos(d*x + c)^3 - 4*a^3*d*e^2*cos(d*x + c))*sin(d*x + c))","A",0
320,1,144,0,0.922635," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, \cos\left(d x + c\right)^{4} - 400 \, \cos\left(d x + c\right)^{2} - 40 \, {\left(8 \, \cos\left(d x + c\right)^{2} - 3\right)} \sin\left(d x + c\right) + 75\right)} \sqrt{e \cos\left(d x + c\right)} \sqrt{a \sin\left(d x + c\right) + a}}{585 \, {\left(3 \, a^{3} d e^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} d e^{3} \cos\left(d x + c\right)^{2} + {\left(a^{3} d e^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} d e^{3} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-2/585*(128*cos(d*x + c)^4 - 400*cos(d*x + c)^2 - 40*(8*cos(d*x + c)^2 - 3)*sin(d*x + c) + 75)*sqrt(e*cos(d*x + c))*sqrt(a*sin(d*x + c) + a)/(3*a^3*d*e^3*cos(d*x + c)^4 - 4*a^3*d*e^3*cos(d*x + c)^2 + (a^3*d*e^3*cos(d*x + c)^4 - 4*a^3*d*e^3*cos(d*x + c)^2)*sin(d*x + c))","A",0
321,0,0,0,1.374953," ","integrate((e*cos(d*x+c))^(7/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{\frac{1}{3}} e^{2} \cos\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral((e*cos(d*x + c))^(1/3)*e^2*cos(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
322,0,0,0,1.616855," ","integrate((e*cos(d*x+c))^(5/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{\frac{2}{3}} e \cos\left(d x + c\right)}{\sqrt{a \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral((e*cos(d*x + c))^(2/3)*e*cos(d*x + c)/sqrt(a*sin(d*x + c) + a), x)","F",0
323,0,0,0,3.282502," ","integrate((e*cos(d*x+c))^(2/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{\frac{2}{3}}}{\sqrt{a \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral((e*cos(d*x + c))^(2/3)/sqrt(a*sin(d*x + c) + a), x)","F",0
324,0,0,0,1.069140," ","integrate((e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{\frac{1}{3}}}{\sqrt{a \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral((e*cos(d*x + c))^(1/3)/sqrt(a*sin(d*x + c) + a), x)","F",0
325,0,0,0,1.036894," ","integrate(1/(e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{\frac{2}{3}} \sqrt{a \sin\left(d x + c\right) + a}}{a e \cos\left(d x + c\right) \sin\left(d x + c\right) + a e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((e*cos(d*x + c))^(2/3)*sqrt(a*sin(d*x + c) + a)/(a*e*cos(d*x + c)*sin(d*x + c) + a*e*cos(d*x + c)), x)","F",0
326,0,0,0,1.005175," ","integrate(1/(e*cos(d*x+c))^(4/3)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{\frac{2}{3}} \sqrt{a \sin\left(d x + c\right) + a}}{a e^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((e*cos(d*x + c))^(2/3)*sqrt(a*sin(d*x + c) + a)/(a*e^2*cos(d*x + c)^2*sin(d*x + c) + a*e^2*cos(d*x + c)^2), x)","F",0
327,0,0,0,1.107031," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{8} \cos\left(d x + c\right)^{8} - 32 \, a^{8} \cos\left(d x + c\right)^{6} + 160 \, a^{8} \cos\left(d x + c\right)^{4} - 256 \, a^{8} \cos\left(d x + c\right)^{2} + 128 \, a^{8} - 8 \, {\left(a^{8} \cos\left(d x + c\right)^{6} - 10 \, a^{8} \cos\left(d x + c\right)^{4} + 24 \, a^{8} \cos\left(d x + c\right)^{2} - 16 \, a^{8}\right)} \sin\left(d x + c\right)\right)} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral((a^8*cos(d*x + c)^8 - 32*a^8*cos(d*x + c)^6 + 160*a^8*cos(d*x + c)^4 - 256*a^8*cos(d*x + c)^2 + 128*a^8 - 8*(a^8*cos(d*x + c)^6 - 10*a^8*cos(d*x + c)^4 + 24*a^8*cos(d*x + c)^2 - 16*a^8)*sin(d*x + c))*(e*cos(d*x + c))^p, x)","F",0
328,0,0,0,0.855371," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*(e*cos(d*x + c))^p, x)","F",0
329,0,0,0,0.818526," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*(e*cos(d*x + c))^p, x)","F",0
330,0,0,0,0.981653," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
331,0,0,0,0.860503," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((e*cos(d*x + c))^p/(a*sin(d*x + c) + a), x)","F",0
332,0,0,0,1.041055," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(e*cos(d*x + c))^p/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
333,0,0,0,0.945064," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(e*cos(d*x + c))^p/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
334,0,0,0,0.965395," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{a^{8} \cos\left(d x + c\right)^{8} - 32 \, a^{8} \cos\left(d x + c\right)^{6} + 160 \, a^{8} \cos\left(d x + c\right)^{4} - 256 \, a^{8} \cos\left(d x + c\right)^{2} + 128 \, a^{8} - 8 \, {\left(a^{8} \cos\left(d x + c\right)^{6} - 10 \, a^{8} \cos\left(d x + c\right)^{4} + 24 \, a^{8} \cos\left(d x + c\right)^{2} - 16 \, a^{8}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral((e*cos(d*x + c))^p/(a^8*cos(d*x + c)^8 - 32*a^8*cos(d*x + c)^6 + 160*a^8*cos(d*x + c)^4 - 256*a^8*cos(d*x + c)^2 + 128*a^8 - 8*(a^8*cos(d*x + c)^6 - 10*a^8*cos(d*x + c)^4 + 24*a^8*cos(d*x + c)^2 - 16*a^8)*sin(d*x + c)), x)","F",0
335,0,0,0,0.935632," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
336,0,0,0,0.947130," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \sqrt{a \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2)*sqrt(a*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
337,0,0,0,0.721086," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^(3/2)*(e*cos(d*x + c))^p, x)","F",0
338,0,0,0,0.835794," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(sqrt(a*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
339,0,0,0,0.956826," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{\sqrt{a \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral((e*cos(d*x + c))^p/sqrt(a*sin(d*x + c) + a), x)","F",0
340,0,0,0,0.633040," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(d*x + c) + a)*(e*cos(d*x + c))^p/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
341,0,0,0,0.899773," ","integrate((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(a*sin(d*x + c) + a)*(e*cos(d*x + c))^p/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
342,0,0,0,0.951100," ","integrate((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{p} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^p*(a*sin(d*x + c) + a)^m, x)","F",0
343,1,153,0,0.760719," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left({\left(m^{3} + 9 \, m^{2} + 20 \, m\right)} \cos\left(d x + c\right)^{6} + 12 \, {\left(m^{2} + 3 \, m\right)} \cos\left(d x + c\right)^{4} + 96 \, m \cos\left(d x + c\right)^{2} + {\left({\left(m^{3} + 15 \, m^{2} + 74 \, m + 120\right)} \cos\left(d x + c\right)^{6} + 12 \, {\left(m^{2} + 7 \, m + 12\right)} \cos\left(d x + c\right)^{4} + 96 \, {\left(m + 2\right)} \cos\left(d x + c\right)^{2} + 384\right)} \sin\left(d x + c\right) + 384\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{4} + 22 \, d m^{3} + 179 \, d m^{2} + 638 \, d m + 840 \, d}"," ",0,"((m^3 + 9*m^2 + 20*m)*cos(d*x + c)^6 + 12*(m^2 + 3*m)*cos(d*x + c)^4 + 96*m*cos(d*x + c)^2 + ((m^3 + 15*m^2 + 74*m + 120)*cos(d*x + c)^6 + 12*(m^2 + 7*m + 12)*cos(d*x + c)^4 + 96*(m + 2)*cos(d*x + c)^2 + 384)*sin(d*x + c) + 384)*(a*sin(d*x + c) + a)^m/(d*m^4 + 22*d*m^3 + 179*d*m^2 + 638*d*m + 840*d)","A",0
344,1,102,0,0.864207," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left({\left(m^{2} + 3 \, m\right)} \cos\left(d x + c\right)^{4} + 8 \, m \cos\left(d x + c\right)^{2} + {\left({\left(m^{2} + 7 \, m + 12\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(m + 2\right)} \cos\left(d x + c\right)^{2} + 32\right)} \sin\left(d x + c\right) + 32\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{3} + 12 \, d m^{2} + 47 \, d m + 60 \, d}"," ",0,"((m^2 + 3*m)*cos(d*x + c)^4 + 8*m*cos(d*x + c)^2 + ((m^2 + 7*m + 12)*cos(d*x + c)^4 + 8*(m + 2)*cos(d*x + c)^2 + 32)*sin(d*x + c) + 32)*(a*sin(d*x + c) + a)^m/(d*m^3 + 12*d*m^2 + 47*d*m + 60*d)","A",0
345,1,61,0,0.886840," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left(m \cos\left(d x + c\right)^{2} + {\left({\left(m + 2\right)} \cos\left(d x + c\right)^{2} + 4\right)} \sin\left(d x + c\right) + 4\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{2} + 5 \, d m + 6 \, d}"," ",0,"(m*cos(d*x + c)^2 + ((m + 2)*cos(d*x + c)^2 + 4)*sin(d*x + c) + 4)*(a*sin(d*x + c) + a)^m/(d*m^2 + 5*d*m + 6*d)","A",0
346,1,28,0,0.982298," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m} {\left(\sin\left(d x + c\right) + 1\right)}}{d m + d}"," ",0,"(a*sin(d*x + c) + a)^m*(sin(d*x + c) + 1)/(d*m + d)","A",0
347,0,0,0,0.936594," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right), x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*sec(d*x + c), x)","F",0
348,0,0,0,0.763074," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*sec(d*x + c)^3, x)","F",0
349,0,0,0,1.002896," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{5}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*sec(d*x + c)^5, x)","F",0
350,0,0,0,1.050238," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{4}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*cos(d*x + c)^4, x)","F",0
351,0,0,0,0.903310," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*cos(d*x + c)^2, x)","F",0
352,0,0,0,0.988820," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*sec(d*x + c)^2, x)","F",0
353,0,0,0,0.977845," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*sec(d*x + c)^4, x)","F",0
354,0,0,0,0.985198," ","integrate((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m} e^{2} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^m*e^2*cos(d*x + c)^2, x)","F",0
355,0,0,0,0.835993," ","integrate((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m} e \cos\left(d x + c\right), x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^m*e*cos(d*x + c), x)","F",0
356,0,0,0,0.944059," ","integrate((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^m, x)","F",0
357,0,0,0,0.943452," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^m/(e*cos(d*x + c)), x)","F",0
358,0,0,0,1.016457," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^m/(e^2*cos(d*x + c)^2), x)","F",0
359,0,0,0,0.959043," ","integrate((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(a*sin(d*x + c) + a)^m/(e^3*cos(d*x + c)^3), x)","F",0
360,1,104,0,0.961098," ","integrate((e*cos(d*x+c))^(-4-m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","-\frac{{\left(6 \, m \cos\left(d x + c\right)^{3} - {\left(m^{3} - m\right)} \cos\left(d x + c\right) - 3 \, {\left(2 \, \cos\left(d x + c\right)^{3} - {\left(m^{2} - 1\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \left(e \cos\left(d x + c\right)\right)^{-m - 4} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{4} - 10 \, d m^{2} + 9 \, d}"," ",0,"-(6*m*cos(d*x + c)^3 - (m^3 - m)*cos(d*x + c) - 3*(2*cos(d*x + c)^3 - (m^2 - 1)*cos(d*x + c))*sin(d*x + c))*(e*cos(d*x + c))^(-m - 4)*(a*sin(d*x + c) + a)^m/(d*m^4 - 10*d*m^2 + 9*d)","A",0
361,1,75,0,0.922199," ","integrate((e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left(m^{2} \cos\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{3} - 2 \, m \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \left(e \cos\left(d x + c\right)\right)^{-m - 3} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{3} - 4 \, d m}"," ",0,"(m^2*cos(d*x + c) - 2*cos(d*x + c)^3 - 2*m*cos(d*x + c)*sin(d*x + c))*(e*cos(d*x + c))^(-m - 3)*(a*sin(d*x + c) + a)^m/(d*m^3 - 4*d*m)","A",0
362,1,61,0,0.994411," ","integrate((e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left(m \cos\left(d x + c\right) - \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \left(e \cos\left(d x + c\right)\right)^{-m - 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{2} - d}"," ",0,"(m*cos(d*x + c) - cos(d*x + c)*sin(d*x + c))*(e*cos(d*x + c))^(-m - 2)*(a*sin(d*x + c) + a)^m/(d*m^2 - d)","A",0
363,1,39,0,0.784795," ","integrate((e*cos(d*x+c))^(-1-m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{\left(e \cos\left(d x + c\right)\right)^{-m - 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)}{d m}"," ",0,"(e*cos(d*x + c))^(-m - 1)*(a*sin(d*x + c) + a)^m*cos(d*x + c)/(d*m)","A",0
364,0,0,0,0.927476," ","integrate((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{m}}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^m, x)","F",0
365,0,0,0,0.948382," ","integrate((e*cos(d*x+c))^(1-m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-m + 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-m + 1)*(a*sin(d*x + c) + a)^m, x)","F",0
366,0,0,0,0.947257," ","integrate((e*cos(d*x+c))^(2-m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-m + 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-m + 2)*(a*sin(d*x + c) + a)^m, x)","F",0
367,1,314,0,0.916732," ","integrate((e*cos(d*x+c))^(5-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","-\frac{{\left({\left(m^{2} - 7 \, m + 12\right)} \cos\left(d x + c\right)^{3} - {\left(m^{2} - 11 \, m + 24\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(m^{2} - 9 \, m + 22\right)} \cos\left(d x + c\right) - {\left({\left(m^{2} - 7 \, m + 12\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(m^{2} - 9 \, m + 18\right)} \cos\left(d x + c\right) - 8\right)} \sin\left(d x + c\right) - 8\right)} \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 5} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{4 \, d m^{3} - {\left(d m^{3} - 12 \, d m^{2} + 47 \, d m - 60 \, d\right)} \cos\left(d x + c\right)^{3} - 48 \, d m^{2} - 3 \, {\left(d m^{3} - 12 \, d m^{2} + 47 \, d m - 60 \, d\right)} \cos\left(d x + c\right)^{2} + 188 \, d m + 2 \, {\left(d m^{3} - 12 \, d m^{2} + 47 \, d m - 60 \, d\right)} \cos\left(d x + c\right) + {\left(4 \, d m^{3} - 48 \, d m^{2} - {\left(d m^{3} - 12 \, d m^{2} + 47 \, d m - 60 \, d\right)} \cos\left(d x + c\right)^{2} + 188 \, d m + 2 \, {\left(d m^{3} - 12 \, d m^{2} + 47 \, d m - 60 \, d\right)} \cos\left(d x + c\right) - 240 \, d\right)} \sin\left(d x + c\right) - 240 \, d}"," ",0,"-((m^2 - 7*m + 12)*cos(d*x + c)^3 - (m^2 - 11*m + 24)*cos(d*x + c)^2 - 2*(m^2 - 9*m + 22)*cos(d*x + c) - ((m^2 - 7*m + 12)*cos(d*x + c)^2 + 2*(m^2 - 9*m + 18)*cos(d*x + c) - 8)*sin(d*x + c) - 8)*(e*cos(d*x + c))^(-2*m + 5)*(a*sin(d*x + c) + a)^m/(4*d*m^3 - (d*m^3 - 12*d*m^2 + 47*d*m - 60*d)*cos(d*x + c)^3 - 48*d*m^2 - 3*(d*m^3 - 12*d*m^2 + 47*d*m - 60*d)*cos(d*x + c)^2 + 188*d*m + 2*(d*m^3 - 12*d*m^2 + 47*d*m - 60*d)*cos(d*x + c) + (4*d*m^3 - 48*d*m^2 - (d*m^3 - 12*d*m^2 + 47*d*m - 60*d)*cos(d*x + c)^2 + 188*d*m + 2*(d*m^3 - 12*d*m^2 + 47*d*m - 60*d)*cos(d*x + c) - 240*d)*sin(d*x + c) - 240*d)","B",0
368,1,170,0,1.107704," ","integrate((e*cos(d*x+c))^(3-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left({\left(m - 2\right)} \cos\left(d x + c\right)^{2} + {\left(m - 4\right)} \cos\left(d x + c\right) + {\left({\left(m - 2\right)} \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - 2\right)} \left(e \cos\left(d x + c\right)\right)^{-2 \, m + 3} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{2 \, d m^{2} - {\left(d m^{2} - 5 \, d m + 6 \, d\right)} \cos\left(d x + c\right)^{2} - 10 \, d m + {\left(d m^{2} - 5 \, d m + 6 \, d\right)} \cos\left(d x + c\right) + {\left(2 \, d m^{2} - 10 \, d m + {\left(d m^{2} - 5 \, d m + 6 \, d\right)} \cos\left(d x + c\right) + 12 \, d\right)} \sin\left(d x + c\right) + 12 \, d}"," ",0,"((m - 2)*cos(d*x + c)^2 + (m - 4)*cos(d*x + c) + ((m - 2)*cos(d*x + c) + 2)*sin(d*x + c) - 2)*(e*cos(d*x + c))^(-2*m + 3)*(a*sin(d*x + c) + a)^m/(2*d*m^2 - (d*m^2 - 5*d*m + 6*d)*cos(d*x + c)^2 - 10*d*m + (d*m^2 - 5*d*m + 6*d)*cos(d*x + c) + (2*d*m^2 - 10*d*m + (d*m^2 - 5*d*m + 6*d)*cos(d*x + c) + 12*d)*sin(d*x + c) + 12*d)","A",0
369,1,80,0,0.906102," ","integrate((e*cos(d*x+c))^(1-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{\left(e \cos\left(d x + c\right)\right)^{-2 \, m + 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{d m + {\left(d m - d\right)} \cos\left(d x + c\right) + {\left(d m - d\right)} \sin\left(d x + c\right) - d}"," ",0,"(e*cos(d*x + c))^(-2*m + 1)*(a*sin(d*x + c) + a)^m*(cos(d*x + c) - sin(d*x + c) + 1)/(d*m + (d*m - d)*cos(d*x + c) + (d*m - d)*sin(d*x + c) - d)","A",0
370,0,0,0,0.934547," ","integrate((e*cos(d*x+c))^(-1-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-2 \, m - 1} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-2*m - 1)*(a*sin(d*x + c) + a)^m, x)","F",0
371,0,0,0,0.895576," ","integrate((e*cos(d*x+c))^(-3-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-2 \, m - 3} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-2*m - 3)*(a*sin(d*x + c) + a)^m, x)","F",0
372,0,0,0,0.755084," ","integrate((e*cos(d*x+c))^(4-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-2 \, m + 4} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-2*m + 4)*(a*sin(d*x + c) + a)^m, x)","F",0
373,0,0,0,0.936499," ","integrate((e*cos(d*x+c))^(2-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-2 \, m + 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-2*m + 2)*(a*sin(d*x + c) + a)^m, x)","F",0
374,0,0,0,1.055440," ","integrate((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^(2*m)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{2 \, m}}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m/(e*cos(d*x + c))^(2*m), x)","F",0
375,0,0,0,0.804357," ","integrate((e*cos(d*x+c))^(-2-2*m)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-2 \, m - 2} {\left(a \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-2*m - 2)*(a*sin(d*x + c) + a)^m, x)","F",0
376,1,51,0,0.865971," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{5 \, b \cos\left(d x + c\right)^{6} - 2 \, {\left(3 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(5*b*cos(d*x + c)^6 - 2*(3*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c))/d","A",0
377,1,39,0,0.954440," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, b \cos\left(d x + c\right)^{4} - 4 \, {\left(a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*b*cos(d*x + c)^4 - 4*(a*cos(d*x + c)^2 + 2*a)*sin(d*x + c))/d","A",0
378,1,25,0,0.907917," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(b*cos(d*x + c)^2 - 2*a*sin(d*x + c))/d","A",0
379,1,37,0,0.955563," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\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
380,1,67,0,0.962422," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, a \sin\left(d x + c\right) + 2 \, b}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(a*cos(d*x + c)^2*log(sin(d*x + c) + 1) - a*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*a*sin(d*x + c) + 2*b)/(d*cos(d*x + c)^2)","A",0
381,1,82,0,0.900177," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right) + 4 \, b}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(3*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(3*a*cos(d*x + c)^2 + 2*a)*sin(d*x + c) + 4*b)/(d*cos(d*x + c)^4)","A",0
382,1,51,0,0.920142," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, b \cos\left(d x + c\right)^{5} - 15 \, a d x - 5 \, {\left(2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40 \, d}"," ",0,"-1/40*(8*b*cos(d*x + c)^5 - 15*a*d*x - 5*(2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
383,1,37,0,0.925400," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b \cos\left(d x + c\right)^{3} - 3 \, a d x - 3 \, a \cos\left(d x + c\right) \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*b*cos(d*x + c)^3 - 3*a*d*x - 3*a*cos(d*x + c)*sin(d*x + c))/d","A",0
384,1,22,0,1.046288," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \sin\left(d x + c\right) + b}{d \cos\left(d x + c\right)}"," ",0,"(a*sin(d*x + c) + b)/(d*cos(d*x + c))","A",0
385,1,35,0,0.943995," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) + b}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/3*((2*a*cos(d*x + c)^2 + a)*sin(d*x + c) + b)/(d*cos(d*x + c)^3)","A",0
386,1,50,0,1.112811," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(8 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} + 3 \, a\right)} \sin\left(d x + c\right) + 3 \, b}{15 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/15*((8*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 + 3*a)*sin(d*x + c) + 3*b)/(d*cos(d*x + c)^5)","A",0
387,1,87,0,1.147515," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{35 \, a b \cos\left(d x + c\right)^{6} + {\left(15 \, b^{2} \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(7 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} - 56 \, a^{2} - 8 \, b^{2}\right)} \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(35*a*b*cos(d*x + c)^6 + (15*b^2*cos(d*x + c)^6 - 3*(7*a^2 + b^2)*cos(d*x + c)^4 - 4*(7*a^2 + b^2)*cos(d*x + c)^2 - 56*a^2 - 8*b^2)*sin(d*x + c))/d","A",0
388,1,69,0,1.047360," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{15 \, a b \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, b^{2} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} - 10 \, a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(15*a*b*cos(d*x + c)^4 + 2*(3*b^2*cos(d*x + c)^4 - (5*a^2 + b^2)*cos(d*x + c)^2 - 10*a^2 - 2*b^2)*sin(d*x + c))/d","A",0
389,1,48,0,0.618528," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, a b \cos\left(d x + c\right)^{2} + {\left(b^{2} \cos\left(d x + c\right)^{2} - 3 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(3*a*b*cos(d*x + c)^2 + (b^2*cos(d*x + c)^2 - 3*a^2 - b^2)*sin(d*x + c))/d","B",0
390,1,62,0,1.091119," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\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
391,1,90,0,1.141264," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a b + 2 \, {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((a^2 - b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (a^2 - b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 4*a*b + 2*(a^2 + b^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
392,1,118,0,1.172635," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, a b + 2 \, {\left({\left(3 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*((3*a^2 - b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (3*a^2 - b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 8*a*b + 2*((3*a^2 - b^2)*cos(d*x + c)^2 + 2*a^2 + 2*b^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
393,1,108,0,0.767553," ","integrate(cos(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{768 \, a b \cos\left(d x + c\right)^{7} - 105 \, {\left(8 \, a^{2} + b^{2}\right)} d x + 7 \, {\left(48 \, b^{2} \cos\left(d x + c\right)^{7} - 8 \, {\left(8 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(8 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(8 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2688 \, d}"," ",0,"-1/2688*(768*a*b*cos(d*x + c)^7 - 105*(8*a^2 + b^2)*d*x + 7*(48*b^2*cos(d*x + c)^7 - 8*(8*a^2 + b^2)*cos(d*x + c)^5 - 10*(8*a^2 + b^2)*cos(d*x + c)^3 - 15*(8*a^2 + b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
394,1,89,0,1.180373," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{96 \, a b \cos\left(d x + c\right)^{5} - 15 \, {\left(6 \, a^{2} + b^{2}\right)} d x + 5 \, {\left(8 \, b^{2} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(6 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(96*a*b*cos(d*x + c)^5 - 15*(6*a^2 + b^2)*d*x + 5*(8*b^2*cos(d*x + c)^5 - 2*(6*a^2 + b^2)*cos(d*x + c)^3 - 3*(6*a^2 + b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
395,1,70,0,0.952655," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{16 \, a b \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} + b^{2}\right)} d x + 3 \, {\left(2 \, b^{2} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"-1/24*(16*a*b*cos(d*x + c)^3 - 3*(4*a^2 + b^2)*d*x + 3*(2*b^2*cos(d*x + c)^3 - (4*a^2 + b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
396,1,45,0,1.030009," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{b^{2} d x \cos\left(d x + c\right) - 2 \, a b - {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"-(b^2*d*x*cos(d*x + c) - 2*a*b - (a^2 + b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
397,1,52,0,0.899596," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a b + {\left({\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/3*(2*a*b + ((2*a^2 - b^2)*cos(d*x + c)^2 + a^2 + b^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
398,1,77,0,0.924881," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, a b + {\left(2 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, a^{2} + 3 \, b^{2}\right)} \sin\left(d x + c\right)}{15 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/15*(6*a*b + (2*(4*a^2 - b^2)*cos(d*x + c)^4 + (4*a^2 - b^2)*cos(d*x + c)^2 + 3*a^2 + 3*b^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
399,1,99,0,1.063761," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{30 \, a b + {\left(8 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, a^{2} + 15 \, b^{2}\right)} \sin\left(d x + c\right)}{105 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/105*(30*a*b + (8*(6*a^2 - b^2)*cos(d*x + c)^6 + 4*(6*a^2 - b^2)*cos(d*x + c)^4 + 3*(6*a^2 - b^2)*cos(d*x + c)^2 + 15*a^2 + 15*b^2)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
400,1,117,0,0.984280," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{105 \, b^{3} \cos\left(d x + c\right)^{8} - 140 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{6} - 8 \, {\left(45 \, a b^{2} \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} - 56 \, a^{3} - 24 \, a b^{2} - 4 \, {\left(7 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*b^3*cos(d*x + c)^8 - 140*(3*a^2*b + b^3)*cos(d*x + c)^6 - 8*(45*a*b^2*cos(d*x + c)^6 - 3*(7*a^3 + 3*a*b^2)*cos(d*x + c)^4 - 56*a^3 - 24*a*b^2 - 4*(7*a^3 + 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
401,1,95,0,1.162761," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, b^{3} \cos\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(9 \, a b^{2} \cos\left(d x + c\right)^{4} - 10 \, a^{3} - 6 \, a b^{2} - {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*b^3*cos(d*x + c)^6 - 15*(3*a^2*b + b^3)*cos(d*x + c)^4 - 4*(9*a*b^2*cos(d*x + c)^4 - 10*a^3 - 6*a*b^2 - (5*a^3 + 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
402,1,71,0,0.775486," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{b^{3} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(b^3*cos(d*x + c)^4 - 2*(3*a^2*b + b^3)*cos(d*x + c)^2 - 4*(a*b^2*cos(d*x + c)^2 - a^3 - a*b^2)*sin(d*x + c))/d","B",0
403,1,93,0,1.222006," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{b^{3} \cos\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*cos(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
404,1,112,0,1.063562," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} - 3 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 6 \, a^{2} b + 2 \, b^{3} + 2 \, {\left(a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((a^3 - 3*a*b^2 + 2*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (a^3 - 3*a*b^2 - 2*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 6*a^2*b + 2*b^3 + 2*(a^3 + 3*a*b^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
405,1,138,0,1.134451," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 8 \, b^{3} \cos\left(d x + c\right)^{2} + 12 \, a^{2} b + 4 \, b^{3} + 2 \, {\left(2 \, a^{3} + 6 \, a b^{2} + 3 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(3*(a^3 - a*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(a^3 - a*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 8*b^3*cos(d*x + c)^2 + 12*a^2*b + 4*b^3 + 2*(2*a^3 + 6*a*b^2 + 3*(a^3 - a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
406,1,117,0,1.013948," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{80 \, b^{3} \cos\left(d x + c\right)^{7} - 112 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{5} + 105 \, {\left(2 \, a^{3} + a b^{2}\right)} d x - 35 \, {\left(8 \, a b^{2} \cos\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{560 \, d}"," ",0,"1/560*(80*b^3*cos(d*x + c)^7 - 112*(3*a^2*b + b^3)*cos(d*x + c)^5 + 105*(2*a^3 + a*b^2)*d*x - 35*(8*a*b^2*cos(d*x + c)^5 - 2*(2*a^3 + a*b^2)*cos(d*x + c)^3 - 3*(2*a^3 + a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
407,1,98,0,1.134646," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{24 \, b^{3} \cos\left(d x + c\right)^{5} - 40 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} d x - 15 \, {\left(6 \, a b^{2} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(24*b^3*cos(d*x + c)^5 - 40*(3*a^2*b + b^3)*cos(d*x + c)^3 + 15*(4*a^3 + 3*a*b^2)*d*x - 15*(6*a*b^2*cos(d*x + c)^3 - (4*a^3 + 3*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
408,1,70,0,0.975809," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, a b^{2} d x \cos\left(d x + c\right) - b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3} - {\left(a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"-(3*a*b^2*d*x*cos(d*x + c) - b^3*cos(d*x + c)^2 - 3*a^2*b - b^3 - (a^3 + 3*a*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
409,1,77,0,0.887000," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3} - {\left(a^{3} + 3 \, a b^{2} + {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*b^3*cos(d*x + c)^2 - 3*a^2*b - b^3 - (a^3 + 3*a*b^2 + (2*a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
410,1,101,0,0.813696," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{5 \, b^{3} \cos\left(d x + c\right)^{2} - 9 \, a^{2} b - 3 \, b^{3} - {\left(2 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{3} + 9 \, a b^{2} + {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{15 \, d \cos\left(d x + c\right)^{5}}"," ",0,"-1/15*(5*b^3*cos(d*x + c)^2 - 9*a^2*b - 3*b^3 - (2*(4*a^3 - 3*a*b^2)*cos(d*x + c)^4 + 3*a^3 + 9*a*b^2 + (4*a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
411,1,124,0,1.048990," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{7 \, b^{3} \cos\left(d x + c\right)^{2} - 15 \, a^{2} b - 5 \, b^{3} - {\left(8 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{4} + 5 \, a^{3} + 15 \, a b^{2} + 3 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{35 \, d \cos\left(d x + c\right)^{7}}"," ",0,"-1/35*(7*b^3*cos(d*x + c)^2 - 15*a^2*b - 5*b^3 - (8*(2*a^3 - a*b^2)*cos(d*x + c)^6 + 4*(2*a^3 - a*b^2)*cos(d*x + c)^4 + 5*a^3 + 15*a*b^2 + 3*(2*a^3 - a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
412,1,146,0,0.717648," ","integrate(sec(d*x+c)^10*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{45 \, b^{3} \cos\left(d x + c\right)^{2} - 105 \, a^{2} b - 35 \, b^{3} - {\left(16 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + 35 \, a^{3} + 105 \, a b^{2} + 5 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{315 \, d \cos\left(d x + c\right)^{9}}"," ",0,"-1/315*(45*b^3*cos(d*x + c)^2 - 105*a^2*b - 35*b^3 - (16*(8*a^3 - 3*a*b^2)*cos(d*x + c)^8 + 8*(8*a^3 - 3*a*b^2)*cos(d*x + c)^6 + 6*(8*a^3 - 3*a*b^2)*cos(d*x + c)^4 + 35*a^3 + 105*a*b^2 + 5*(8*a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^9)","A",0
413,1,356,0,1.044915," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{4290 \, a b^{7} \cos\left(d x + c\right)^{12} - 5148 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{10} + 6435 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{8} - 8580 \, {\left(a^{7} b + 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{6} + {\left(495 \, b^{8} \cos\left(d x + c\right)^{12} - 180 \, {\left(91 \, a^{2} b^{6} + 10 \, b^{8}\right)} \cos\left(d x + c\right)^{10} + 10 \, {\left(5005 \, a^{4} b^{4} + 4186 \, a^{2} b^{6} + 229 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 3432 \, a^{8} + 13728 \, a^{6} b^{2} + 11440 \, a^{4} b^{4} + 2080 \, a^{2} b^{6} + 40 \, b^{8} - 20 \, {\left(1287 \, a^{6} b^{2} + 3575 \, a^{4} b^{4} + 1469 \, a^{2} b^{6} + 53 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(429 \, a^{8} + 1716 \, a^{6} b^{2} + 1430 \, a^{4} b^{4} + 260 \, a^{2} b^{6} + 5 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(429 \, a^{8} + 1716 \, a^{6} b^{2} + 1430 \, a^{4} b^{4} + 260 \, a^{2} b^{6} + 5 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6435 \, d}"," ",0,"1/6435*(4290*a*b^7*cos(d*x + c)^12 - 5148*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^10 + 6435*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^8 - 8580*(a^7*b + 7*a^5*b^3 + 7*a^3*b^5 + a*b^7)*cos(d*x + c)^6 + (495*b^8*cos(d*x + c)^12 - 180*(91*a^2*b^6 + 10*b^8)*cos(d*x + c)^10 + 10*(5005*a^4*b^4 + 4186*a^2*b^6 + 229*b^8)*cos(d*x + c)^8 + 3432*a^8 + 13728*a^6*b^2 + 11440*a^4*b^4 + 2080*a^2*b^6 + 40*b^8 - 20*(1287*a^6*b^2 + 3575*a^4*b^4 + 1469*a^2*b^6 + 53*b^8)*cos(d*x + c)^6 + 3*(429*a^8 + 1716*a^6*b^2 + 1430*a^4*b^4 + 260*a^2*b^6 + 5*b^8)*cos(d*x + c)^4 + 4*(429*a^8 + 1716*a^6*b^2 + 1430*a^4*b^4 + 260*a^2*b^6 + 5*b^8)*cos(d*x + c)^2)*sin(d*x + c))/d","B",0
414,1,310,0,1.215191," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{396 \, a b^{7} \cos\left(d x + c\right)^{10} - 495 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{8} + 660 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{6} - 990 \, {\left(a^{7} b + 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(45 \, b^{8} \cos\left(d x + c\right)^{10} - 10 \, {\left(154 \, a^{2} b^{6} + 17 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 330 \, a^{8} + 1848 \, a^{6} b^{2} + 1980 \, a^{4} b^{4} + 440 \, a^{2} b^{6} + 10 \, b^{8} + 10 \, {\left(495 \, a^{4} b^{4} + 418 \, a^{2} b^{6} + 23 \, b^{8}\right)} \cos\left(d x + c\right)^{6} - 12 \, {\left(231 \, a^{6} b^{2} + 660 \, a^{4} b^{4} + 275 \, a^{2} b^{6} + 10 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(165 \, a^{8} + 924 \, a^{6} b^{2} + 990 \, a^{4} b^{4} + 220 \, a^{2} b^{6} + 5 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{495 \, d}"," ",0,"1/495*(396*a*b^7*cos(d*x + c)^10 - 495*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^8 + 660*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^6 - 990*(a^7*b + 7*a^5*b^3 + 7*a^3*b^5 + a*b^7)*cos(d*x + c)^4 + (45*b^8*cos(d*x + c)^10 - 10*(154*a^2*b^6 + 17*b^8)*cos(d*x + c)^8 + 330*a^8 + 1848*a^6*b^2 + 1980*a^4*b^4 + 440*a^2*b^6 + 10*b^8 + 10*(495*a^4*b^4 + 418*a^2*b^6 + 23*b^8)*cos(d*x + c)^6 - 12*(231*a^6*b^2 + 660*a^4*b^4 + 275*a^2*b^6 + 10*b^8)*cos(d*x + c)^4 + (165*a^8 + 924*a^6*b^2 + 990*a^4*b^4 + 220*a^2*b^6 + 5*b^8)*cos(d*x + c)^2)*sin(d*x + c))/d","B",0
415,1,257,0,1.235903," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{9 \, a b^{7} \cos\left(d x + c\right)^{8} - 12 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{6} + 18 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 36 \, {\left(a^{7} b + 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(b^{8} \cos\left(d x + c\right)^{8} + 9 \, a^{8} + 84 \, a^{6} b^{2} + 126 \, a^{4} b^{4} + 36 \, a^{2} b^{6} + b^{8} - 4 \, {\left(9 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(21 \, a^{4} b^{4} + 18 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(21 \, a^{6} b^{2} + 63 \, a^{4} b^{4} + 27 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{9 \, d}"," ",0,"1/9*(9*a*b^7*cos(d*x + c)^8 - 12*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^6 + 18*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 - 36*(a^7*b + 7*a^5*b^3 + 7*a^3*b^5 + a*b^7)*cos(d*x + c)^2 + (b^8*cos(d*x + c)^8 + 9*a^8 + 84*a^6*b^2 + 126*a^4*b^4 + 36*a^2*b^6 + b^8 - 4*(9*a^2*b^6 + b^8)*cos(d*x + c)^6 + 6*(21*a^4*b^4 + 18*a^2*b^6 + b^8)*cos(d*x + c)^4 - 4*(21*a^6*b^2 + 63*a^4*b^4 + 27*a^2*b^6 + b^8)*cos(d*x + c)^2)*sin(d*x + c))/d","B",0
416,1,327,0,1.047633," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{280 \, a b^{7} \cos\left(d x + c\right)^{6} - 420 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + 840 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\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) + 2 \, {\left(15 \, b^{8} \cos\left(d x + c\right)^{6} - 2940 \, a^{6} b^{2} - 9800 \, a^{4} b^{4} - 4508 \, a^{2} b^{6} - 176 \, b^{8} - 6 \, {\left(98 \, a^{2} b^{6} + 11 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(1225 \, a^{4} b^{4} + 1078 \, a^{2} b^{6} + 61 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{210 \, d}"," ",0,"1/210*(280*a*b^7*cos(d*x + c)^6 - 420*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 + 840*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(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) + 2*(15*b^8*cos(d*x + c)^6 - 2940*a^6*b^2 - 9800*a^4*b^4 - 4508*a^2*b^6 - 176*b^8 - 6*(98*a^2*b^6 + 11*b^8)*cos(d*x + c)^4 + 2*(1225*a^4*b^4 + 1078*a^2*b^6 + 61*b^8)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
417,1,368,0,1.223487," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{120 \, a b^{7} \cos\left(d x + c\right)^{6} + 240 \, a^{7} b + 1680 \, a^{5} b^{3} + 1680 \, a^{3} b^{5} + 240 \, a b^{7} - 240 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + 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)} \cos\left(d x + c\right)^{2} \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)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 105 \, {\left(8 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, b^{8} \cos\left(d x + c\right)^{6} + 15 \, a^{8} + 420 \, a^{6} b^{2} + 1050 \, a^{4} b^{4} + 420 \, a^{2} b^{6} + 15 \, b^{8} - 8 \, {\left(35 \, a^{2} b^{6} + 4 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(525 \, a^{4} b^{4} + 490 \, a^{2} b^{6} + 29 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/60*(120*a*b^7*cos(d*x + c)^6 + 240*a^7*b + 1680*a^5*b^3 + 1680*a^3*b^5 + 240*a*b^7 - 240*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 + 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)*cos(d*x + c)^2*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)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 105*(8*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2 + 2*(6*b^8*cos(d*x + c)^6 + 15*a^8 + 420*a^6*b^2 + 1050*a^4*b^4 + 420*a^2*b^6 + 15*b^8 - 8*(35*a^2*b^6 + 4*b^8)*cos(d*x + c)^4 + 4*(525*a^4*b^4 + 490*a^2*b^6 + 29*b^8)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
418,1,366,0,1.204269," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{192 \, a b^{7} \cos\left(d x + c\right)^{6} - 96 \, a b^{7} \cos\left(d x + c\right)^{4} + 96 \, a^{7} b + 672 \, a^{5} b^{3} + 672 \, a^{3} b^{5} + 96 \, a b^{7} + 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)} \cos\left(d x + c\right)^{4} \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)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 192 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, b^{8} \cos\left(d x + c\right)^{6} + 6 \, a^{8} + 168 \, a^{6} b^{2} + 420 \, a^{4} b^{4} + 168 \, a^{2} b^{6} + 6 \, b^{8} - 16 \, {\left(42 \, a^{2} b^{6} + 5 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{8} - 28 \, a^{6} b^{2} - 350 \, a^{4} b^{4} - 252 \, a^{2} b^{6} - 13 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(192*a*b^7*cos(d*x + c)^6 - 96*a*b^7*cos(d*x + c)^4 + 96*a^7*b + 672*a^5*b^3 + 672*a^3*b^5 + 96*a*b^7 + 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)*cos(d*x + c)^4*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)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 192*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2 + 2*(8*b^8*cos(d*x + c)^6 + 6*a^8 + 168*a^6*b^2 + 420*a^4*b^4 + 168*a^2*b^6 + 6*b^8 - 16*(42*a^2*b^6 + 5*b^8)*cos(d*x + c)^4 + 3*(3*a^8 - 28*a^6*b^2 - 350*a^4*b^4 - 252*a^2*b^6 - 13*b^8)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
419,1,315,0,1.230105," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{71680 \, a b^{7} \cos\left(d x + c\right)^{9} - 92160 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{7} + 129024 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} - 215040 \, {\left(a^{7} b + 7 \, a^{5} b^{3} + 7 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{3} + 315 \, {\left(128 \, a^{8} + 896 \, a^{6} b^{2} + 1120 \, a^{4} b^{4} + 280 \, a^{2} b^{6} + 7 \, b^{8}\right)} d x + 21 \, {\left(384 \, b^{8} \cos\left(d x + c\right)^{9} - 48 \, {\left(280 \, a^{2} b^{6} + 31 \, b^{8}\right)} \cos\left(d x + c\right)^{7} + 8 \, {\left(5600 \, a^{4} b^{4} + 4760 \, a^{2} b^{6} + 263 \, b^{8}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(2688 \, a^{6} b^{2} + 7840 \, a^{4} b^{4} + 3304 \, a^{2} b^{6} + 121 \, b^{8}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(128 \, a^{8} + 896 \, a^{6} b^{2} + 1120 \, a^{4} b^{4} + 280 \, a^{2} b^{6} + 7 \, b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(71680*a*b^7*cos(d*x + c)^9 - 92160*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^7 + 129024*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^5 - 215040*(a^7*b + 7*a^5*b^3 + 7*a^3*b^5 + a*b^7)*cos(d*x + c)^3 + 315*(128*a^8 + 896*a^6*b^2 + 1120*a^4*b^4 + 280*a^2*b^6 + 7*b^8)*d*x + 21*(384*b^8*cos(d*x + c)^9 - 48*(280*a^2*b^6 + 31*b^8)*cos(d*x + c)^7 + 8*(5600*a^4*b^4 + 4760*a^2*b^6 + 263*b^8)*cos(d*x + c)^5 - 10*(2688*a^6*b^2 + 7840*a^4*b^4 + 3304*a^2*b^6 + 121*b^8)*cos(d*x + c)^3 + 15*(128*a^8 + 896*a^6*b^2 + 1120*a^4*b^4 + 280*a^2*b^6 + 7*b^8)*cos(d*x + c))*sin(d*x + c))/d","A",0
420,1,266,0,0.932049," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{384 \, a b^{7} \cos\left(d x + c\right)^{6} + 1920 \, a^{7} b + 13440 \, a^{5} b^{3} + 13440 \, a^{3} b^{5} + 1920 \, a b^{7} - 640 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 105 \, {\left(64 \, a^{6} b^{2} + 240 \, a^{4} b^{4} + 120 \, a^{2} b^{6} + 5 \, b^{8}\right)} d x \cos\left(d x + c\right) + 1920 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + 5 \, {\left(8 \, b^{8} \cos\left(d x + c\right)^{6} + 48 \, a^{8} + 1344 \, a^{6} b^{2} + 3360 \, a^{4} b^{4} + 1344 \, a^{2} b^{6} + 48 \, b^{8} - 2 \, {\left(168 \, a^{2} b^{6} + 19 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(560 \, a^{4} b^{4} + 504 \, a^{2} b^{6} + 29 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)}"," ",0,"1/240*(384*a*b^7*cos(d*x + c)^6 + 1920*a^7*b + 13440*a^5*b^3 + 13440*a^3*b^5 + 1920*a*b^7 - 640*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 - 105*(64*a^6*b^2 + 240*a^4*b^4 + 120*a^2*b^6 + 5*b^8)*d*x*cos(d*x + c) + 1920*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2 + 5*(8*b^8*cos(d*x + c)^6 + 48*a^8 + 1344*a^6*b^2 + 3360*a^4*b^4 + 1344*a^2*b^6 + 48*b^8 - 2*(168*a^2*b^6 + 19*b^8)*cos(d*x + c)^4 + 3*(560*a^4*b^4 + 504*a^2*b^6 + 29*b^8)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
421,1,268,0,0.977744," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{64 \, a b^{7} \cos\left(d x + c\right)^{6} + 64 \, a^{7} b + 448 \, a^{5} b^{3} + 448 \, a^{3} b^{5} + 64 \, a b^{7} + 105 \, {\left(16 \, a^{4} b^{4} + 16 \, a^{2} b^{6} + b^{8}\right)} d x \cos\left(d x + c\right)^{3} - 192 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 192 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, b^{8} \cos\left(d x + c\right)^{6} + 8 \, a^{8} + 224 \, a^{6} b^{2} + 560 \, a^{4} b^{4} + 224 \, a^{2} b^{6} + 8 \, b^{8} - 3 \, {\left(112 \, a^{2} b^{6} + 13 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(a^{8} - 14 \, a^{6} b^{2} - 140 \, a^{4} b^{4} - 98 \, a^{2} b^{6} - 5 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/24*(64*a*b^7*cos(d*x + c)^6 + 64*a^7*b + 448*a^5*b^3 + 448*a^3*b^5 + 64*a*b^7 + 105*(16*a^4*b^4 + 16*a^2*b^6 + b^8)*d*x*cos(d*x + c)^3 - 192*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 - 192*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2 + (6*b^8*cos(d*x + c)^6 + 8*a^8 + 224*a^6*b^2 + 560*a^4*b^4 + 224*a^2*b^6 + 8*b^8 - 3*(112*a^2*b^6 + 13*b^8)*cos(d*x + c)^4 + 16*(a^8 - 14*a^6*b^2 - 140*a^4*b^4 - 98*a^2*b^6 - 5*b^8)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
422,1,281,0,1.159980," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{240 \, a b^{7} \cos\left(d x + c\right)^{6} + 48 \, a^{7} b + 336 \, a^{5} b^{3} + 336 \, a^{3} b^{5} + 48 \, a b^{7} - 105 \, {\left(8 \, a^{2} b^{6} + b^{8}\right)} d x \cos\left(d x + c\right)^{5} + 240 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 80 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(15 \, b^{8} \cos\left(d x + c\right)^{6} + 6 \, a^{8} + 168 \, a^{6} b^{2} + 420 \, a^{4} b^{4} + 168 \, a^{2} b^{6} + 6 \, b^{8} + 4 \, {\left(4 \, a^{8} - 28 \, a^{6} b^{2} + 105 \, a^{4} b^{4} + 322 \, a^{2} b^{6} + 29 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(a^{8} - 7 \, a^{6} b^{2} - 105 \, a^{4} b^{4} - 77 \, a^{2} b^{6} - 4 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{30 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/30*(240*a*b^7*cos(d*x + c)^6 + 48*a^7*b + 336*a^5*b^3 + 336*a^3*b^5 + 48*a*b^7 - 105*(8*a^2*b^6 + b^8)*d*x*cos(d*x + c)^5 + 240*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 - 80*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2 + (15*b^8*cos(d*x + c)^6 + 6*a^8 + 168*a^6*b^2 + 420*a^4*b^4 + 168*a^2*b^6 + 6*b^8 + 4*(4*a^8 - 28*a^6*b^2 + 105*a^4*b^4 + 322*a^2*b^6 + 29*b^8)*cos(d*x + c)^4 + 8*(a^8 - 7*a^6*b^2 - 105*a^4*b^4 - 77*a^2*b^6 - 4*b^8)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
423,1,306,0,1.173492," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{105 \, b^{8} d x \cos\left(d x + c\right)^{7} - 840 \, a b^{7} \cos\left(d x + c\right)^{6} + 120 \, a^{7} b + 840 \, a^{5} b^{3} + 840 \, a^{3} b^{5} + 120 \, a b^{7} + 280 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 168 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(15 \, a^{8} + 420 \, a^{6} b^{2} + 1050 \, a^{4} b^{4} + 420 \, a^{2} b^{6} + 15 \, b^{8} + 4 \, {\left(12 \, a^{8} - 56 \, a^{6} b^{2} + 105 \, a^{4} b^{4} - 105 \, a^{2} b^{6} - 44 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(12 \, a^{8} - 56 \, a^{6} b^{2} + 105 \, a^{4} b^{4} + 630 \, a^{2} b^{6} + 61 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{8} - 14 \, a^{6} b^{2} - 280 \, a^{4} b^{4} - 210 \, a^{2} b^{6} - 11 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{105 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/105*(105*b^8*d*x*cos(d*x + c)^7 - 840*a*b^7*cos(d*x + c)^6 + 120*a^7*b + 840*a^5*b^3 + 840*a^3*b^5 + 120*a*b^7 + 280*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 - 168*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2 + (15*a^8 + 420*a^6*b^2 + 1050*a^4*b^4 + 420*a^2*b^6 + 15*b^8 + 4*(12*a^8 - 56*a^6*b^2 + 105*a^4*b^4 - 105*a^2*b^6 - 44*b^8)*cos(d*x + c)^6 + 2*(12*a^8 - 56*a^6*b^2 + 105*a^4*b^4 + 630*a^2*b^6 + 61*b^8)*cos(d*x + c)^4 + 6*(3*a^8 - 14*a^6*b^2 - 280*a^4*b^4 - 210*a^2*b^6 - 11*b^8)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
424,1,336,0,1.189229," ","integrate(sec(d*x+c)^10*(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","-\frac{840 \, a b^{7} \cos\left(d x + c\right)^{6} - 280 \, a^{7} b - 1960 \, a^{5} b^{3} - 1960 \, a^{3} b^{5} - 280 \, a b^{7} - 504 \, {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + 360 \, {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(128 \, a^{8} - 448 \, a^{6} b^{2} + 560 \, a^{4} b^{4} - 280 \, a^{2} b^{6} + 35 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 35 \, a^{8} + 980 \, a^{6} b^{2} + 2450 \, a^{4} b^{4} + 980 \, a^{2} b^{6} + 35 \, b^{8} + 4 \, {\left(16 \, a^{8} - 56 \, a^{6} b^{2} + 70 \, a^{4} b^{4} - 35 \, a^{2} b^{6} - 35 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(8 \, a^{8} - 28 \, a^{6} b^{2} + 35 \, a^{4} b^{4} + 350 \, a^{2} b^{6} + 35 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + 20 \, {\left(2 \, a^{8} - 7 \, a^{6} b^{2} - 175 \, a^{4} b^{4} - 133 \, a^{2} b^{6} - 7 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{315 \, d \cos\left(d x + c\right)^{9}}"," ",0,"-1/315*(840*a*b^7*cos(d*x + c)^6 - 280*a^7*b - 1960*a^5*b^3 - 1960*a^3*b^5 - 280*a*b^7 - 504*(7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 + 360*(7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2 - ((128*a^8 - 448*a^6*b^2 + 560*a^4*b^4 - 280*a^2*b^6 + 35*b^8)*cos(d*x + c)^8 + 35*a^8 + 980*a^6*b^2 + 2450*a^4*b^4 + 980*a^2*b^6 + 35*b^8 + 4*(16*a^8 - 56*a^6*b^2 + 70*a^4*b^4 - 35*a^2*b^6 - 35*b^8)*cos(d*x + c)^6 + 6*(8*a^8 - 28*a^6*b^2 + 35*a^4*b^4 + 350*a^2*b^6 + 35*b^8)*cos(d*x + c)^4 + 20*(2*a^8 - 7*a^6*b^2 - 175*a^4*b^4 - 133*a^2*b^6 - 7*b^8)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^9)","A",0
425,1,107,0,0.886820," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, b^{4} \cos\left(d x + c\right)^{4} - 6 \, {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{3} b + 5 \, a b^{3}\right)} \sin\left(d x + c\right)}{12 \, b^{5} d}"," ",0,"1/12*(3*b^4*cos(d*x + c)^4 - 6*(a^2*b^2 - b^4)*cos(d*x + c)^2 + 12*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a) + 4*(a*b^3*cos(d*x + c)^2 - 3*a^3*b + 5*a*b^3)*sin(d*x + c))/(b^5*d)","A",0
426,1,53,0,0.938734," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \sin\left(d x + c\right) - 2 \, {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{2 \, b^{3} d}"," ",0,"1/2*(b^2*cos(d*x + c)^2 + 2*a*b*sin(d*x + c) - 2*(a^2 - b^2)*log(b*sin(d*x + c) + a))/(b^3*d)","A",0
427,1,18,0,1.163764," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\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
428,1,62,0,0.999979," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b \log\left(b \sin\left(d x + c\right) + a\right) - {\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 \, {\left(a^{2} - b^{2}\right)} d}"," ",0,"-1/2*(2*b*log(b*sin(d*x + c) + a) - (a + b)*log(sin(d*x + c) + 1) + (a - b)*log(-sin(d*x + c) + 1))/((a^2 - b^2)*d)","A",0
429,1,153,0,1.348334," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, b^{3} \cos\left(d x + c\right)^{2} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{3} - 3 \, a b^{2} + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, a^{2} b + 2 \, b^{3} + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*b^3*cos(d*x + c)^2*log(b*sin(d*x + c) + a) + (a^3 - 3*a*b^2 - 2*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (a^3 - 3*a*b^2 + 2*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*a^2*b + 2*b^3 + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2)","A",0
430,1,253,0,1.571478," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, b^{5} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a^{4} b - 8 \, a^{2} b^{3} + 4 \, b^{5} - 8 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{5} - 4 \, a^{3} b^{2} + 2 \, a b^{4} + {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 7 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*(16*b^5*cos(d*x + c)^4*log(b*sin(d*x + c) + a) - (3*a^5 - 10*a^3*b^2 + 15*a*b^4 + 8*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) + (3*a^5 - 10*a^3*b^2 + 15*a*b^4 - 8*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*a^4*b - 8*a^2*b^3 + 4*b^5 - 8*(a^2*b^3 - b^5)*cos(d*x + c)^2 - 2*(2*a^5 - 4*a^3*b^2 + 2*a*b^4 + (3*a^5 - 10*a^3*b^2 + 7*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^4)","A",0
431,1,483,0,1.223485," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{24 \, b^{5} \cos\left(d x + c\right)^{5} - 40 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} d x + 60 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 120 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + 15 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} - 7 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, b^{6} d}, \frac{24 \, b^{5} \cos\left(d x + c\right)^{5} - 40 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} d x + 120 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 120 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + 15 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} - 7 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, b^{6} d}\right]"," ",0,"[1/120*(24*b^5*cos(d*x + c)^5 - 40*(a^2*b^3 - b^5)*cos(d*x + c)^3 + 15*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*d*x + 60*(a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 120*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c) + 15*(2*a*b^4*cos(d*x + c)^3 - (4*a^3*b^2 - 7*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^6*d), 1/120*(24*b^5*cos(d*x + c)^5 - 40*(a^2*b^3 - b^5)*cos(d*x + c)^3 + 15*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*d*x + 120*(a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 120*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c) + 15*(2*a*b^4*cos(d*x + c)^3 - (4*a^3*b^2 - 7*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^6*d)]","A",0
432,1,332,0,1.242390," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d x - 3 \, {\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)}{6 \, b^{4} d}, \frac{2 \, b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d x - 6 \, {\left(a^{2} - b^{2}\right)}^{\frac{3}{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 6 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)}{6 \, b^{4} d}\right]"," ",0,"[1/6*(2*b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)*sin(d*x + c) - 3*(2*a^3 - 3*a*b^2)*d*x - 3*(a^2 - b^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(a^2*b - b^3)*cos(d*x + c))/(b^4*d), 1/6*(2*b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)*sin(d*x + c) - 3*(2*a^3 - 3*a*b^2)*d*x - 6*(a^2 - b^2)^(3/2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 6*(a^2*b - b^3)*cos(d*x + c))/(b^4*d)]","A",0
433,1,214,0,1.201605," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, a d x + 2 \, b \cos\left(d x + c\right) + \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, b^{2} d}, \frac{a d x + b \cos\left(d x + c\right) + \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{b^{2} d}\right]"," ",0,"[1/2*(2*a*d*x + 2*b*cos(d*x + c) + sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/(b^2*d), (a*d*x + b*cos(d*x + c) + sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/(b^2*d)]","A",0
434,1,305,0,1.014938," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} b^{2} \cos\left(d x + c\right) \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, a^{2} b + 2 \, b^{3} + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}, \frac{\sqrt{a^{2} - b^{2}} b^{2} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) - a^{2} b + b^{3} + {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*b^2*cos(d*x + c)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*a^2*b + 2*b^3 + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)), (sqrt(a^2 - b^2)*b^2*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c) - a^2*b + b^3 + (a^3 - a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c))]","A",0
435,1,466,0,1.141712," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} + b^{2}} b^{4} \cos\left(d x + c\right)^{3} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} - 6 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + {\left(2 \, a^{5} - 7 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}, -\frac{3 \, \sqrt{a^{2} - b^{2}} b^{4} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} + a^{4} b - 2 \, a^{2} b^{3} + b^{5} - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + {\left(2 \, a^{5} - 7 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/6*(3*sqrt(-a^2 + b^2)*b^4*cos(d*x + c)^3*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*a^4*b - 4*a^2*b^3 + 2*b^5 - 6*(a^2*b^3 - b^5)*cos(d*x + c)^2 - 2*(a^5 - 2*a^3*b^2 + a*b^4 + (2*a^5 - 7*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3), -1/3*(3*sqrt(a^2 - b^2)*b^4*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)^3 + a^4*b - 2*a^2*b^3 + b^5 - 3*(a^2*b^3 - b^5)*cos(d*x + c)^2 - (a^5 - 2*a^3*b^2 + a*b^4 + (2*a^5 - 7*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","A",0
436,1,666,0,1.268140," ","integrate(sec(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{-a^{2} + b^{2}} b^{6} \cos\left(d x + c\right)^{5} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, a^{6} b + 18 \, a^{4} b^{3} - 18 \, a^{2} b^{5} + 6 \, b^{7} - 30 \, {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{7} - 9 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 3 \, a b^{6} + {\left(8 \, a^{7} - 34 \, a^{5} b^{2} + 59 \, a^{3} b^{4} - 33 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{7} - 17 \, a^{5} b^{2} + 22 \, a^{3} b^{4} - 9 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{5}}, \frac{15 \, \sqrt{a^{2} - b^{2}} b^{6} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right)^{5} - 3 \, a^{6} b + 9 \, a^{4} b^{3} - 9 \, a^{2} b^{5} + 3 \, b^{7} - 15 \, {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{7} - 9 \, a^{5} b^{2} + 9 \, a^{3} b^{4} - 3 \, a b^{6} + {\left(8 \, a^{7} - 34 \, a^{5} b^{2} + 59 \, a^{3} b^{4} - 33 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{7} - 17 \, a^{5} b^{2} + 22 \, a^{3} b^{4} - 9 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{5}}\right]"," ",0,"[1/30*(15*sqrt(-a^2 + b^2)*b^6*cos(d*x + c)^5*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*a^6*b + 18*a^4*b^3 - 18*a^2*b^5 + 6*b^7 - 30*(a^2*b^5 - b^7)*cos(d*x + c)^4 + 10*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2 + 2*(3*a^7 - 9*a^5*b^2 + 9*a^3*b^4 - 3*a*b^6 + (8*a^7 - 34*a^5*b^2 + 59*a^3*b^4 - 33*a*b^6)*cos(d*x + c)^4 + (4*a^7 - 17*a^5*b^2 + 22*a^3*b^4 - 9*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^5), 1/15*(15*sqrt(a^2 - b^2)*b^6*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)^5 - 3*a^6*b + 9*a^4*b^3 - 9*a^2*b^5 + 3*b^7 - 15*(a^2*b^5 - b^7)*cos(d*x + c)^4 + 5*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2 + (3*a^7 - 9*a^5*b^2 + 9*a^3*b^4 - 3*a*b^6 + (8*a^7 - 34*a^5*b^2 + 59*a^3*b^4 - 33*a*b^6)*cos(d*x + c)^4 + (4*a^7 - 17*a^5*b^2 + 22*a^3*b^4 - 9*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^5)]","A",0
437,1,243,0,1.228964," ","integrate(cos(d*x+c)^7/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, b^{6} \cos\left(d x + c\right)^{6} + 80 \, a^{6} - 560 \, a^{4} b^{2} + 785 \, a^{2} b^{4} - 256 \, b^{6} - 8 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(15 \, a^{4} b^{2} - 25 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 480 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(24 \, a b^{5} \cos\left(d x + c\right)^{4} - 400 \, a^{5} b + 720 \, a^{3} b^{3} - 271 \, a b^{5} - 16 \, {\left(5 \, a^{3} b^{3} - 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{80 \, {\left(b^{8} d \sin\left(d x + c\right) + a b^{7} d\right)}}"," ",0,"1/80*(16*b^6*cos(d*x + c)^6 + 80*a^6 - 560*a^4*b^2 + 785*a^2*b^4 - 256*b^6 - 8*(5*a^2*b^4 - 4*b^6)*cos(d*x + c)^4 + 16*(15*a^4*b^2 - 25*a^2*b^4 + 8*b^6)*cos(d*x + c)^2 + 480*(a^6 - 2*a^4*b^2 + a^2*b^4 + (a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c))*log(b*sin(d*x + c) + a) + (24*a*b^5*cos(d*x + c)^4 - 400*a^5*b + 720*a^3*b^3 - 271*a*b^5 - 16*(5*a^3*b^3 - 7*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^8*d*sin(d*x + c) + a*b^7*d)","A",0
438,1,156,0,1.238734," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, b^{4} \cos\left(d x + c\right)^{4} - 6 \, a^{4} + 27 \, a^{2} b^{2} - 16 \, b^{4} - 4 \, {\left(3 \, a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 24 \, {\left(a^{4} - a^{2} b^{2} + {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(4 \, a b^{3} \cos\left(d x + c\right)^{2} + 18 \, a^{3} b - 13 \, a b^{3}\right)} \sin\left(d x + c\right)}{6 \, {\left(b^{6} d \sin\left(d x + c\right) + a b^{5} d\right)}}"," ",0,"1/6*(2*b^4*cos(d*x + c)^4 - 6*a^4 + 27*a^2*b^2 - 16*b^4 - 4*(3*a^2*b^2 - 2*b^4)*cos(d*x + c)^2 - 24*(a^4 - a^2*b^2 + (a^3*b - a*b^3)*sin(d*x + c))*log(b*sin(d*x + c) + a) + (4*a*b^3*cos(d*x + c)^2 + 18*a^3*b - 13*a*b^3)*sin(d*x + c))/(b^6*d*sin(d*x + c) + a*b^5*d)","A",0
439,1,78,0,1.112867," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{b^{2} \cos\left(d x + c\right)^{2} - a b \sin\left(d x + c\right) + a^{2} - 2 \, b^{2} + 2 \, {\left(a b \sin\left(d x + c\right) + a^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{4} d \sin\left(d x + c\right) + a b^{3} d}"," ",0,"(b^2*cos(d*x + c)^2 - a*b*sin(d*x + c) + a^2 - 2*b^2 + 2*(a*b*sin(d*x + c) + a^2)*log(b*sin(d*x + c) + a))/(b^4*d*sin(d*x + c) + a*b^3*d)","A",0
440,1,20,0,1.065167," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{1}{b^{2} d \sin\left(d x + c\right) + a b d}"," ",0,"-1/(b^2*d*sin(d*x + c) + a*b*d)","A",0
441,1,188,0,1.234538," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} b - 2 \, b^{3} - 4 \, {\left(a b^{2} \sin\left(d x + c\right) + a^{2} b\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(a^{3} + 2 \, a^{2} b + a b^{2} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{3} - 2 \, a^{2} b + a b^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \sin\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}"," ",0,"1/2*(2*a^2*b - 2*b^3 - 4*(a*b^2*sin(d*x + c) + a^2*b)*log(b*sin(d*x + c) + a) + (a^3 + 2*a^2*b + a*b^2 + (a^2*b + 2*a*b^2 + b^3)*sin(d*x + c))*log(sin(d*x + c) + 1) - (a^3 - 2*a^2*b + a*b^2 + (a^2*b - 2*a*b^2 + b^3)*sin(d*x + c))*log(-sin(d*x + c) + 1))/((a^4*b - 2*a^2*b^3 + b^5)*d*sin(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d)","A",0
442,1,381,0,1.417164," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - 16 \, {\left(a b^{4} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a^{2} b^{3} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - {\left({\left(a^{4} b - 6 \, a^{2} b^{3} - 8 \, a b^{4} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{5} - 6 \, a^{3} b^{2} - 8 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{4} b - 6 \, a^{2} b^{3} + 8 \, a b^{4} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{5} - 6 \, a^{3} b^{2} + 8 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/4*(2*a^4*b - 4*a^2*b^3 + 2*b^5 + 2*(a^4*b + 2*a^2*b^3 - 3*b^5)*cos(d*x + c)^2 - 16*(a*b^4*cos(d*x + c)^2*sin(d*x + c) + a^2*b^3*cos(d*x + c)^2)*log(b*sin(d*x + c) + a) - ((a^4*b - 6*a^2*b^3 - 8*a*b^4 - 3*b^5)*cos(d*x + c)^2*sin(d*x + c) + (a^5 - 6*a^3*b^2 - 8*a^2*b^3 - 3*a*b^4)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^4*b - 6*a^2*b^3 + 8*a*b^4 - 3*b^5)*cos(d*x + c)^2*sin(d*x + c) + (a^5 - 6*a^3*b^2 + 8*a^2*b^3 - 3*a*b^4)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)^2*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)^2)","B",0
443,1,527,0,2.059793," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a^{6} b - 12 \, a^{4} b^{3} + 12 \, a^{2} b^{5} - 4 \, b^{7} + 6 \, {\left(a^{6} b - 5 \, a^{4} b^{3} - a^{2} b^{5} + 5 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} - 9 \, a^{2} b^{5} + 5 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 96 \, {\left(a b^{6} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + a^{2} b^{5} \cos\left(d x + c\right)^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 3 \, {\left({\left(a^{6} b - 5 \, a^{4} b^{3} + 15 \, a^{2} b^{5} + 16 \, a b^{6} + 5 \, b^{7}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(a^{7} - 5 \, a^{5} b^{2} + 15 \, a^{3} b^{4} + 16 \, a^{2} b^{5} + 5 \, a b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(a^{6} b - 5 \, a^{4} b^{3} + 15 \, a^{2} b^{5} - 16 \, a b^{6} + 5 \, b^{7}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(a^{7} - 5 \, a^{5} b^{2} + 15 \, a^{3} b^{4} - 16 \, a^{2} b^{5} + 5 \, a b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} + 3 \, {\left(a^{7} - 5 \, a^{5} b^{2} + 7 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"-1/16*(4*a^6*b - 12*a^4*b^3 + 12*a^2*b^5 - 4*b^7 + 6*(a^6*b - 5*a^4*b^3 - a^2*b^5 + 5*b^7)*cos(d*x + c)^4 - 2*(a^6*b + 3*a^4*b^3 - 9*a^2*b^5 + 5*b^7)*cos(d*x + c)^2 + 96*(a*b^6*cos(d*x + c)^4*sin(d*x + c) + a^2*b^5*cos(d*x + c)^4)*log(b*sin(d*x + c) + a) - 3*((a^6*b - 5*a^4*b^3 + 15*a^2*b^5 + 16*a*b^6 + 5*b^7)*cos(d*x + c)^4*sin(d*x + c) + (a^7 - 5*a^5*b^2 + 15*a^3*b^4 + 16*a^2*b^5 + 5*a*b^6)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) + 3*((a^6*b - 5*a^4*b^3 + 15*a^2*b^5 - 16*a*b^6 + 5*b^7)*cos(d*x + c)^4*sin(d*x + c) + (a^7 - 5*a^5*b^2 + 15*a^3*b^4 - 16*a^2*b^5 + 5*a*b^6)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) - 2*(2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 + 3*(a^7 - 5*a^5*b^2 + 7*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^4*sin(d*x + c) + (a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c)^4)","B",0
444,1,599,0,1.314888," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{6 \, b^{5} \cos\left(d x + c\right)^{5} - 5 \, {\left(4 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(8 \, a^{5} - 12 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d x - 60 \, {\left(a^{4} - a^{2} b^{2} + {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 15 \, {\left(8 \, a^{4} b - 12 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right) + 5 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} b - 12 \, a^{2} b^{3} + 3 \, b^{5}\right)} d x - 3 \, {\left(4 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(b^{7} d \sin\left(d x + c\right) + a b^{6} d\right)}}, \frac{6 \, b^{5} \cos\left(d x + c\right)^{5} - 5 \, {\left(4 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(8 \, a^{5} - 12 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d x - 120 \, {\left(a^{4} - a^{2} b^{2} + {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 15 \, {\left(8 \, a^{4} b - 12 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right) + 5 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} b - 12 \, a^{2} b^{3} + 3 \, b^{5}\right)} d x - 3 \, {\left(4 \, a^{3} b^{2} - 5 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(b^{7} d \sin\left(d x + c\right) + a b^{6} d\right)}}\right]"," ",0,"[1/24*(6*b^5*cos(d*x + c)^5 - 5*(4*a^2*b^3 - 3*b^5)*cos(d*x + c)^3 - 15*(8*a^5 - 12*a^3*b^2 + 3*a*b^4)*d*x - 60*(a^4 - a^2*b^2 + (a^3*b - a*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 15*(8*a^4*b - 12*a^2*b^3 + 3*b^5)*cos(d*x + c) + 5*(2*a*b^4*cos(d*x + c)^3 - 3*(8*a^4*b - 12*a^2*b^3 + 3*b^5)*d*x - 3*(4*a^3*b^2 - 5*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^7*d*sin(d*x + c) + a*b^6*d), 1/24*(6*b^5*cos(d*x + c)^5 - 5*(4*a^2*b^3 - 3*b^5)*cos(d*x + c)^3 - 15*(8*a^5 - 12*a^3*b^2 + 3*a*b^4)*d*x - 120*(a^4 - a^2*b^2 + (a^3*b - a*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 15*(8*a^4*b - 12*a^2*b^3 + 3*b^5)*cos(d*x + c) + 5*(2*a*b^4*cos(d*x + c)^3 - 3*(8*a^4*b - 12*a^2*b^3 + 3*b^5)*d*x - 3*(4*a^3*b^2 - 5*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^7*d*sin(d*x + c) + a*b^6*d)]","A",0
445,1,411,0,0.767946," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} - a b^{2}\right)} d x + 3 \, {\left(a b \sin\left(d x + c\right) + a^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 3 \, {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right) + 3 \, {\left(a b^{2} \cos\left(d x + c\right) + {\left(2 \, a^{2} b - b^{3}\right)} d x\right)} \sin\left(d x + c\right)}{2 \, {\left(b^{5} d \sin\left(d x + c\right) + a b^{4} d\right)}}, \frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} - a b^{2}\right)} d x + 6 \, {\left(a b \sin\left(d x + c\right) + a^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 3 \, {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right) + 3 \, {\left(a b^{2} \cos\left(d x + c\right) + {\left(2 \, a^{2} b - b^{3}\right)} d x\right)} \sin\left(d x + c\right)}{2 \, {\left(b^{5} d \sin\left(d x + c\right) + a b^{4} d\right)}}\right]"," ",0,"[1/2*(b^3*cos(d*x + c)^3 + 3*(2*a^3 - a*b^2)*d*x + 3*(a*b*sin(d*x + c) + a^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 3*(2*a^2*b - b^3)*cos(d*x + c) + 3*(a*b^2*cos(d*x + c) + (2*a^2*b - b^3)*d*x)*sin(d*x + c))/(b^5*d*sin(d*x + c) + a*b^4*d), 1/2*(b^3*cos(d*x + c)^3 + 3*(2*a^3 - a*b^2)*d*x + 6*(a*b*sin(d*x + c) + a^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 3*(2*a^2*b - b^3)*cos(d*x + c) + 3*(a*b^2*cos(d*x + c) + (2*a^2*b - b^3)*d*x)*sin(d*x + c))/(b^5*d*sin(d*x + c) + a*b^4*d)]","A",0
446,1,388,0,1.432886," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{2} b - b^{3}\right)} d x \sin\left(d x + c\right) + 2 \, {\left(a^{3} - a b^{2}\right)} d x + {\left(a b \sin\left(d x + c\right) + a^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{3} - b^{5}\right)} d \sin\left(d x + c\right) + {\left(a^{3} b^{2} - a b^{4}\right)} d\right)}}, -\frac{{\left(a^{2} b - b^{3}\right)} d x \sin\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} d x + {\left(a b \sin\left(d x + c\right) + a^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)}{{\left(a^{2} b^{3} - b^{5}\right)} d \sin\left(d x + c\right) + {\left(a^{3} b^{2} - a b^{4}\right)} d}\right]"," ",0,"[-1/2*(2*(a^2*b - b^3)*d*x*sin(d*x + c) + 2*(a^3 - a*b^2)*d*x + (a*b*sin(d*x + c) + a^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(a^2*b - b^3)*cos(d*x + c))/((a^2*b^3 - b^5)*d*sin(d*x + c) + (a^3*b^2 - a*b^4)*d), -((a^2*b - b^3)*d*x*sin(d*x + c) + (a^3 - a*b^2)*d*x + (a*b*sin(d*x + c) + a^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + (a^2*b - b^3)*cos(d*x + c))/((a^2*b^3 - b^5)*d*sin(d*x + c) + (a^3*b^2 - a*b^4)*d)]","A",0
447,1,538,0,1.091826," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} + 2 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a b^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + a^{2} b^{2} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{a^{4} b - 2 \, a^{2} b^{3} + b^{5} + {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a b^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + a^{2} b^{2} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(2*a^4*b - 4*a^2*b^3 + 2*b^5 + 2*(a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + 3*(a*b^3*cos(d*x + c)*sin(d*x + c) + a^2*b^2*cos(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)), -(a^4*b - 2*a^2*b^3 + b^5 + (a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c)^2 - 3*(a*b^3*cos(d*x + c)*sin(d*x + c) + a^2*b^2*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c))]","A",0
448,1,782,0,1.333412," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} + 2 \, {\left(2 \, a^{6} b - 11 \, a^{4} b^{3} + a^{2} b^{5} + 8 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} - 7 \, a^{2} b^{5} + 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left(a b^{5} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a^{2} b^{4} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} + {\left(2 \, a^{7} - 11 \, a^{5} b^{2} + 16 \, a^{3} b^{4} - 7 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3}\right)}}, -\frac{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7} + {\left(2 \, a^{6} b - 11 \, a^{4} b^{3} + a^{2} b^{5} + 8 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{6} b + 2 \, a^{4} b^{3} - 7 \, a^{2} b^{5} + 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(a b^{5} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a^{2} b^{4} \cos\left(d x + c\right)^{3}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} + {\left(2 \, a^{7} - 11 \, a^{5} b^{2} + 16 \, a^{3} b^{4} - 7 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[-1/6*(2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 + 2*(2*a^6*b - 11*a^4*b^3 + a^2*b^5 + 8*b^7)*cos(d*x + c)^4 - 2*(a^6*b + 2*a^4*b^3 - 7*a^2*b^5 + 4*b^7)*cos(d*x + c)^2 - 15*(a*b^5*cos(d*x + c)^3*sin(d*x + c) + a^2*b^4*cos(d*x + c)^3)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 + (2*a^7 - 11*a^5*b^2 + 16*a^3*b^4 - 7*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^3*sin(d*x + c) + (a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3), -1/3*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7 + (2*a^6*b - 11*a^4*b^3 + a^2*b^5 + 8*b^7)*cos(d*x + c)^4 - (a^6*b + 2*a^4*b^3 - 7*a^2*b^5 + 4*b^7)*cos(d*x + c)^2 + 15*(a*b^5*cos(d*x + c)^3*sin(d*x + c) + a^2*b^4*cos(d*x + c)^3)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 + (2*a^7 - 11*a^5*b^2 + 16*a^3*b^4 - 7*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^3*sin(d*x + c) + (a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3)]","A",0
449,1,304,0,1.231663," ","integrate(cos(d*x+c)^7/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, b^{6} \cos\left(d x + c\right)^{6} - 176 \, a^{6} + 928 \, a^{4} b^{2} - 685 \, a^{2} b^{4} + 3 \, b^{6} - 8 \, {\left(5 \, a^{2} b^{4} - 3 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(544 \, a^{4} b^{2} - 560 \, a^{2} b^{4} + 51 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 96 \, {\left(5 \, a^{6} - a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6} - {\left(5 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{5} b - 6 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 2 \, {\left(8 \, a b^{5} \cos\left(d x + c\right)^{4} + 64 \, a^{5} b + 176 \, a^{3} b^{3} - 205 \, a b^{5} - 80 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{32 \, {\left(b^{9} d \cos\left(d x + c\right)^{2} - 2 \, a b^{8} d \sin\left(d x + c\right) - {\left(a^{2} b^{7} + b^{9}\right)} d\right)}}"," ",0,"-1/32*(8*b^6*cos(d*x + c)^6 - 176*a^6 + 928*a^4*b^2 - 685*a^2*b^4 + 3*b^6 - 8*(5*a^2*b^4 - 3*b^6)*cos(d*x + c)^4 - (544*a^4*b^2 - 560*a^2*b^4 + 51*b^6)*cos(d*x + c)^2 - 96*(5*a^6 - a^4*b^2 - 5*a^2*b^4 + b^6 - (5*a^4*b^2 - 6*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(5*a^5*b - 6*a^3*b^3 + a*b^5)*sin(d*x + c))*log(b*sin(d*x + c) + a) + 2*(8*a*b^5*cos(d*x + c)^4 + 64*a^5*b + 176*a^3*b^3 - 205*a*b^5 - 80*(a^3*b^3 - a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^9*d*cos(d*x + c)^2 - 2*a*b^8*d*sin(d*x + c) - (a^2*b^7 + b^9)*d)","A",0
450,1,212,0,1.138462," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, b^{4} \cos\left(d x + c\right)^{4} + 14 \, a^{4} - 35 \, a^{2} b^{2} - b^{4} + {\left(22 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4} - {\left(3 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 2 \, {\left(4 \, a b^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} b - 13 \, a b^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(b^{7} d \cos\left(d x + c\right)^{2} - 2 \, a b^{6} d \sin\left(d x + c\right) - {\left(a^{2} b^{5} + b^{7}\right)} d\right)}}"," ",0,"-1/4*(2*b^4*cos(d*x + c)^4 + 14*a^4 - 35*a^2*b^2 - b^4 + (22*a^2*b^2 - 3*b^4)*cos(d*x + c)^2 + 8*(3*a^4 + 2*a^2*b^2 - b^4 - (3*a^2*b^2 - b^4)*cos(d*x + c)^2 + 2*(3*a^3*b - a*b^3)*sin(d*x + c))*log(b*sin(d*x + c) + a) + 2*(4*a*b^3*cos(d*x + c)^2 + 2*a^3*b - 13*a*b^3)*sin(d*x + c))/(b^7*d*cos(d*x + c)^2 - 2*a*b^6*d*sin(d*x + c) - (a^2*b^5 + b^7)*d)","A",0
451,1,110,0,1.180710," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a b \sin\left(d x + c\right) + 3 \, a^{2} + b^{2} - 2 \, {\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{2 \, {\left(b^{5} d \cos\left(d x + c\right)^{2} - 2 \, a b^{4} d \sin\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} d\right)}}"," ",0,"1/2*(4*a*b*sin(d*x + c) + 3*a^2 + b^2 - 2*(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*log(b*sin(d*x + c) + a))/(b^5*d*cos(d*x + c)^2 - 2*a*b^4*d*sin(d*x + c) - (a^2*b^3 + b^5)*d)","A",0
452,1,43,0,0.877424," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{1}{2 \, {\left(b^{3} d \cos\left(d x + c\right)^{2} - 2 \, a b^{2} d \sin\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} d\right)}}"," ",0,"1/2/(b^3*d*cos(d*x + c)^2 - 2*a*b^2*d*sin(d*x + c) - (a^2*b + b^3)*d)","B",0
453,1,462,0,1.283971," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{5 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5} - 2 \, {\left(3 \, a^{4} b + 4 \, a^{2} b^{3} + b^{5} - {\left(3 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(a^{5} + 3 \, a^{4} b + 4 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} - {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{5} - 3 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\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)} d \sin\left(d x + c\right) - {\left(a^{8} - 2 \, a^{6} b^{2} + 2 \, a^{2} b^{6} - b^{8}\right)} d\right)}}"," ",0,"-1/2*(5*a^4*b - 6*a^2*b^3 + b^5 - 2*(3*a^4*b + 4*a^2*b^3 + b^5 - (3*a^2*b^3 + b^5)*cos(d*x + c)^2 + 2*(3*a^3*b^2 + a*b^4)*sin(d*x + c))*log(b*sin(d*x + c) + a) + (a^5 + 3*a^4*b + 4*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4 + b^5 - (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cos(d*x + c)^2 + 2*(a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*sin(d*x + c))*log(sin(d*x + c) + 1) - (a^5 - 3*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 + 3*a*b^4 - b^5 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(d*x + c)^2 + 2*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 4*(a^3*b^2 - a*b^4)*sin(d*x + c))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*sin(d*x + c) - (a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8)*d)","B",0
454,1,707,0,1.953971," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} + 4 \, {\left(a^{6} b + 5 \, a^{4} b^{3} - 7 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left({\left(5 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(5 \, a^{4} b^{3} + 6 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left({\left(a^{5} b^{2} - 10 \, a^{3} b^{4} - 20 \, a^{2} b^{5} - 15 \, a b^{6} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 10 \, a^{4} b^{3} - 20 \, a^{3} b^{4} - 15 \, a^{2} b^{5} - 4 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(a^{7} - 9 \, a^{5} b^{2} - 20 \, a^{4} b^{3} - 25 \, a^{3} b^{4} - 24 \, a^{2} b^{5} - 15 \, a b^{6} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(a^{5} b^{2} - 10 \, a^{3} b^{4} + 20 \, a^{2} b^{5} - 15 \, a b^{6} + 4 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 10 \, a^{4} b^{3} + 20 \, a^{3} b^{4} - 15 \, a^{2} b^{5} + 4 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(a^{7} - 9 \, a^{5} b^{2} + 20 \, a^{4} b^{3} - 25 \, a^{3} b^{4} + 24 \, a^{2} b^{5} - 15 \, a b^{6} + 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} - {\left(a^{5} b^{2} + 10 \, a^{3} b^{4} - 11 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/4*(2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 + 4*(a^6*b + 5*a^4*b^3 - 7*a^2*b^5 + b^7)*cos(d*x + c)^2 + 8*((5*a^2*b^5 + b^7)*cos(d*x + c)^4 - 2*(5*a^3*b^4 + a*b^6)*cos(d*x + c)^2*sin(d*x + c) - (5*a^4*b^3 + 6*a^2*b^5 + b^7)*cos(d*x + c)^2)*log(b*sin(d*x + c) + a) + ((a^5*b^2 - 10*a^3*b^4 - 20*a^2*b^5 - 15*a*b^6 - 4*b^7)*cos(d*x + c)^4 - 2*(a^6*b - 10*a^4*b^3 - 20*a^3*b^4 - 15*a^2*b^5 - 4*a*b^6)*cos(d*x + c)^2*sin(d*x + c) - (a^7 - 9*a^5*b^2 - 20*a^4*b^3 - 25*a^3*b^4 - 24*a^2*b^5 - 15*a*b^6 - 4*b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((a^5*b^2 - 10*a^3*b^4 + 20*a^2*b^5 - 15*a*b^6 + 4*b^7)*cos(d*x + c)^4 - 2*(a^6*b - 10*a^4*b^3 + 20*a^3*b^4 - 15*a^2*b^5 + 4*a*b^6)*cos(d*x + c)^2*sin(d*x + c) - (a^7 - 9*a^5*b^2 + 20*a^4*b^3 - 25*a^3*b^4 + 24*a^2*b^5 - 15*a*b^6 + 4*b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 - (a^5*b^2 + 10*a^3*b^4 - 11*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^4 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)^2*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c)^2)","B",0
455,1,895,0,2.374475," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{8} b - 16 \, a^{6} b^{3} + 24 \, a^{4} b^{5} - 16 \, a^{2} b^{7} + 4 \, b^{9} + 12 \, {\left(a^{8} b - 7 \, a^{6} b^{3} - 7 \, a^{4} b^{5} + 15 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{8} b - 6 \, a^{4} b^{5} + 8 \, a^{2} b^{7} - 3 \, b^{9}\right)} \cos\left(d x + c\right)^{2} - 48 \, {\left({\left(7 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(7 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(7 \, a^{4} b^{5} + 8 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 3 \, {\left({\left(a^{7} b^{2} - 7 \, a^{5} b^{4} + 35 \, a^{3} b^{6} + 56 \, a^{2} b^{7} + 35 \, a b^{8} + 8 \, b^{9}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(a^{8} b - 7 \, a^{6} b^{3} + 35 \, a^{4} b^{5} + 56 \, a^{3} b^{6} + 35 \, a^{2} b^{7} + 8 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(a^{9} - 6 \, a^{7} b^{2} + 28 \, a^{5} b^{4} + 56 \, a^{4} b^{5} + 70 \, a^{3} b^{6} + 64 \, a^{2} b^{7} + 35 \, a b^{8} + 8 \, b^{9}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(a^{7} b^{2} - 7 \, a^{5} b^{4} + 35 \, a^{3} b^{6} - 56 \, a^{2} b^{7} + 35 \, a b^{8} - 8 \, b^{9}\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(a^{8} b - 7 \, a^{6} b^{3} + 35 \, a^{4} b^{5} - 56 \, a^{3} b^{6} + 35 \, a^{2} b^{7} - 8 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(a^{9} - 6 \, a^{7} b^{2} + 28 \, a^{5} b^{4} - 56 \, a^{4} b^{5} + 70 \, a^{3} b^{6} - 64 \, a^{2} b^{7} + 35 \, a b^{8} - 8 \, b^{9}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a^{9} - 8 \, a^{7} b^{2} + 12 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 2 \, a b^{8} - 3 \, {\left(a^{7} b^{2} - 7 \, a^{5} b^{4} - 21 \, a^{3} b^{6} + 27 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{9} - 20 \, a^{7} b^{2} + 42 \, a^{5} b^{4} - 36 \, a^{3} b^{6} + 11 \, a b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{10} b^{2} - 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} - 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{6} - 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(a^{12} - 4 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 5 \, a^{4} b^{8} + 4 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/16*(4*a^8*b - 16*a^6*b^3 + 24*a^4*b^5 - 16*a^2*b^7 + 4*b^9 + 12*(a^8*b - 7*a^6*b^3 - 7*a^4*b^5 + 15*a^2*b^7 - 2*b^9)*cos(d*x + c)^4 - 4*(a^8*b - 6*a^4*b^5 + 8*a^2*b^7 - 3*b^9)*cos(d*x + c)^2 - 48*((7*a^2*b^7 + b^9)*cos(d*x + c)^6 - 2*(7*a^3*b^6 + a*b^8)*cos(d*x + c)^4*sin(d*x + c) - (7*a^4*b^5 + 8*a^2*b^7 + b^9)*cos(d*x + c)^4)*log(b*sin(d*x + c) + a) + 3*((a^7*b^2 - 7*a^5*b^4 + 35*a^3*b^6 + 56*a^2*b^7 + 35*a*b^8 + 8*b^9)*cos(d*x + c)^6 - 2*(a^8*b - 7*a^6*b^3 + 35*a^4*b^5 + 56*a^3*b^6 + 35*a^2*b^7 + 8*a*b^8)*cos(d*x + c)^4*sin(d*x + c) - (a^9 - 6*a^7*b^2 + 28*a^5*b^4 + 56*a^4*b^5 + 70*a^3*b^6 + 64*a^2*b^7 + 35*a*b^8 + 8*b^9)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - 3*((a^7*b^2 - 7*a^5*b^4 + 35*a^3*b^6 - 56*a^2*b^7 + 35*a*b^8 - 8*b^9)*cos(d*x + c)^6 - 2*(a^8*b - 7*a^6*b^3 + 35*a^4*b^5 - 56*a^3*b^6 + 35*a^2*b^7 - 8*a*b^8)*cos(d*x + c)^4*sin(d*x + c) - (a^9 - 6*a^7*b^2 + 28*a^5*b^4 - 56*a^4*b^5 + 70*a^3*b^6 - 64*a^2*b^7 + 35*a*b^8 - 8*b^9)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) - 2*(2*a^9 - 8*a^7*b^2 + 12*a^5*b^4 - 8*a^3*b^6 + 2*a*b^8 - 3*(a^7*b^2 - 7*a^5*b^4 - 21*a^3*b^6 + 27*a*b^8)*cos(d*x + c)^4 + (3*a^9 - 20*a^7*b^2 + 42*a^5*b^4 - 36*a^3*b^6 + 11*a*b^8)*cos(d*x + c)^2)*sin(d*x + c))/((a^10*b^2 - 5*a^8*b^4 + 10*a^6*b^6 - 10*a^4*b^8 + 5*a^2*b^10 - b^12)*d*cos(d*x + c)^6 - 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c)^4*sin(d*x + c) - (a^12 - 4*a^10*b^2 + 5*a^8*b^4 - 5*a^4*b^8 + 4*a^2*b^10 - b^12)*d*cos(d*x + c)^4)","B",0
456,1,752,0,1.364111," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, b^{5} \cos\left(d x + c\right)^{5} - 30 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d x \cos\left(d x + c\right)^{2} - 20 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} + 30 \, {\left(4 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4}\right)} d x - 15 \, {\left(4 \, a^{4} + 3 \, a^{2} b^{2} - b^{4} - {\left(4 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 30 \, {\left(4 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right) + 10 \, {\left(a b^{4} \cos\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{4} b - 3 \, a^{2} b^{3}\right)} d x + 6 \, {\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(b^{8} d \cos\left(d x + c\right)^{2} - 2 \, a b^{7} d \sin\left(d x + c\right) - {\left(a^{2} b^{6} + b^{8}\right)} d\right)}}, -\frac{2 \, b^{5} \cos\left(d x + c\right)^{5} - 15 \, {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d x \cos\left(d x + c\right)^{2} - 10 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(4 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4}\right)} d x + 15 \, {\left(4 \, a^{4} + 3 \, a^{2} b^{2} - b^{4} - {\left(4 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 15 \, {\left(4 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right) + 5 \, {\left(a b^{4} \cos\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{4} b - 3 \, a^{2} b^{3}\right)} d x + 6 \, {\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(b^{8} d \cos\left(d x + c\right)^{2} - 2 \, a b^{7} d \sin\left(d x + c\right) - {\left(a^{2} b^{6} + b^{8}\right)} d\right)}}\right]"," ",0,"[-1/12*(4*b^5*cos(d*x + c)^5 - 30*(4*a^3*b^2 - 3*a*b^4)*d*x*cos(d*x + c)^2 - 20*(2*a^2*b^3 - b^5)*cos(d*x + c)^3 + 30*(4*a^5 + a^3*b^2 - 3*a*b^4)*d*x - 15*(4*a^4 + 3*a^2*b^2 - b^4 - (4*a^2*b^2 - b^4)*cos(d*x + c)^2 + 2*(4*a^3*b - a*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 30*(4*a^4*b - a^2*b^3 - b^5)*cos(d*x + c) + 10*(a*b^4*cos(d*x + c)^3 + 6*(4*a^4*b - 3*a^2*b^3)*d*x + 6*(3*a^3*b^2 - 2*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^8*d*cos(d*x + c)^2 - 2*a*b^7*d*sin(d*x + c) - (a^2*b^6 + b^8)*d), -1/6*(2*b^5*cos(d*x + c)^5 - 15*(4*a^3*b^2 - 3*a*b^4)*d*x*cos(d*x + c)^2 - 10*(2*a^2*b^3 - b^5)*cos(d*x + c)^3 + 15*(4*a^5 + a^3*b^2 - 3*a*b^4)*d*x + 15*(4*a^4 + 3*a^2*b^2 - b^4 - (4*a^2*b^2 - b^4)*cos(d*x + c)^2 + 2*(4*a^3*b - a*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 15*(4*a^4*b - a^2*b^3 - b^5)*cos(d*x + c) + 5*(a*b^4*cos(d*x + c)^3 + 6*(4*a^4*b - 3*a^2*b^3)*d*x + 6*(3*a^3*b^2 - 2*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^8*d*cos(d*x + c)^2 - 2*a*b^7*d*sin(d*x + c) - (a^2*b^6 + b^8)*d)]","A",0
457,1,716,0,1.478236," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} - 12 \, {\left(a^{5} - a b^{4}\right)} d x + 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4} - {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right) - 6 \, {\left(4 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{5} - a b^{7}\right)} d \sin\left(d x + c\right) - {\left(a^{4} b^{4} - b^{8}\right)} d\right)}}, -\frac{6 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(a^{5} - a b^{4}\right)} d x - 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4} - {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right) - 3 \, {\left(4 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{5} - a b^{7}\right)} d \sin\left(d x + c\right) - {\left(a^{4} b^{4} - b^{8}\right)} d\right)}}\right]"," ",0,"[-1/4*(12*(a^3*b^2 - a*b^4)*d*x*cos(d*x + c)^2 + 4*(a^2*b^3 - b^5)*cos(d*x + c)^3 - 12*(a^5 - a*b^4)*d*x + 3*(2*a^4 + a^2*b^2 - b^4 - (2*a^2*b^2 - b^4)*cos(d*x + c)^2 + 2*(2*a^3*b - a*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(2*a^4*b - a^2*b^3 - b^5)*cos(d*x + c) - 6*(4*(a^4*b - a^2*b^3)*d*x + 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(a^3*b^5 - a*b^7)*d*sin(d*x + c) - (a^4*b^4 - b^8)*d), -1/2*(6*(a^3*b^2 - a*b^4)*d*x*cos(d*x + c)^2 + 2*(a^2*b^3 - b^5)*cos(d*x + c)^3 - 6*(a^5 - a*b^4)*d*x - 3*(2*a^4 + a^2*b^2 - b^4 - (2*a^2*b^2 - b^4)*cos(d*x + c)^2 + 2*(2*a^3*b - a*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*(2*a^4*b - a^2*b^3 - b^5)*cos(d*x + c) - 3*(4*(a^4*b - a^2*b^3)*d*x + 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(a^3*b^5 - a*b^7)*d*sin(d*x + c) - (a^4*b^4 - b^8)*d)]","B",0
458,1,501,0,1.391445," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)}{4 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d \sin\left(d x + c\right) - {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d\right)}}, -\frac{{\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d \sin\left(d x + c\right) - {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*(2*(a^3 - a*b^2)*cos(d*x + c)*sin(d*x + c) - (b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(a^2*b - b^3)*cos(d*x + c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d*cos(d*x + c)^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*sin(d*x + c) - (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d), -1/2*((a^3 - a*b^2)*cos(d*x + c)*sin(d*x + c) + (b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + (a^2*b - b^3)*cos(d*x + c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d*cos(d*x + c)^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*sin(d*x + c) - (a^6 - a^4*b^2 - a^2*b^4 + b^6)*d)]","A",0
459,1,894,0,1.432008," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, a^{6} b - 12 \, a^{4} b^{3} + 12 \, a^{2} b^{5} - 4 \, b^{7} + 2 \, {\left(4 \, a^{6} b + 10 \, a^{4} b^{3} - 17 \, a^{2} b^{5} + 3 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(4 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(4 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(4 \, a^{4} b^{2} + 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} - {\left(2 \, a^{5} b^{2} + 11 \, a^{3} b^{4} - 13 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}, \frac{2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} + {\left(4 \, a^{6} b + 10 \, a^{4} b^{3} - 17 \, a^{2} b^{5} + 3 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(4 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(4 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(4 \, a^{4} b^{2} + 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} - {\left(2 \, a^{5} b^{2} + 11 \, a^{3} b^{4} - 13 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a^6*b - 12*a^4*b^3 + 12*a^2*b^5 - 4*b^7 + 2*(4*a^6*b + 10*a^4*b^3 - 17*a^2*b^5 + 3*b^7)*cos(d*x + c)^2 + 3*((4*a^2*b^4 + b^6)*cos(d*x + c)^3 - 2*(4*a^3*b^3 + a*b^5)*cos(d*x + c)*sin(d*x + c) - (4*a^4*b^2 + 5*a^2*b^4 + b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 - (2*a^5*b^2 + 11*a^3*b^4 - 13*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c)), 1/2*(2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 + (4*a^6*b + 10*a^4*b^3 - 17*a^2*b^5 + 3*b^7)*cos(d*x + c)^2 + 3*((4*a^2*b^4 + b^6)*cos(d*x + c)^3 - 2*(4*a^3*b^3 + a*b^5)*cos(d*x + c)*sin(d*x + c) - (4*a^4*b^2 + 5*a^2*b^4 + b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 - (2*a^5*b^2 + 11*a^3*b^4 - 13*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c))]","B",0
460,1,1200,0,1.507936," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, a^{8} b - 16 \, a^{6} b^{3} + 24 \, a^{4} b^{5} - 16 \, a^{2} b^{7} + 4 \, b^{9} + 2 \, {\left(8 \, a^{8} b - 64 \, a^{6} b^{3} - 16 \, a^{4} b^{5} + 87 \, a^{2} b^{7} - 15 \, b^{9}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(2 \, a^{8} b - a^{6} b^{3} - 9 \, a^{4} b^{5} + 13 \, a^{2} b^{7} - 5 \, b^{9}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left({\left(6 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - {\left(6 \, a^{4} b^{4} + 7 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{9} - 8 \, a^{7} b^{2} + 12 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 2 \, a b^{8} - {\left(4 \, a^{7} b^{2} - 32 \, a^{5} b^{4} - 53 \, a^{3} b^{6} + 81 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{9} - 15 \, a^{7} b^{2} + 33 \, a^{5} b^{4} - 29 \, a^{3} b^{6} + 9 \, a b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{10} b^{2} - 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} - 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{5} - 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - {\left(a^{12} - 4 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 5 \, a^{4} b^{8} + 4 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{3}\right)}}, \frac{2 \, a^{8} b - 8 \, a^{6} b^{3} + 12 \, a^{4} b^{5} - 8 \, a^{2} b^{7} + 2 \, b^{9} + {\left(8 \, a^{8} b - 64 \, a^{6} b^{3} - 16 \, a^{4} b^{5} + 87 \, a^{2} b^{7} - 15 \, b^{9}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{8} b - a^{6} b^{3} - 9 \, a^{4} b^{5} + 13 \, a^{2} b^{7} - 5 \, b^{9}\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left({\left(6 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - {\left(6 \, a^{4} b^{4} + 7 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{9} - 8 \, a^{7} b^{2} + 12 \, a^{5} b^{4} - 8 \, a^{3} b^{6} + 2 \, a b^{8} - {\left(4 \, a^{7} b^{2} - 32 \, a^{5} b^{4} - 53 \, a^{3} b^{6} + 81 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{9} - 15 \, a^{7} b^{2} + 33 \, a^{5} b^{4} - 29 \, a^{3} b^{6} + 9 \, a b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{10} b^{2} - 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} - 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{5} - 2 \, {\left(a^{11} b - 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} - 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - {\left(a^{12} - 4 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 5 \, a^{4} b^{8} + 4 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/12*(4*a^8*b - 16*a^6*b^3 + 24*a^4*b^5 - 16*a^2*b^7 + 4*b^9 + 2*(8*a^8*b - 64*a^6*b^3 - 16*a^4*b^5 + 87*a^2*b^7 - 15*b^9)*cos(d*x + c)^4 - 4*(2*a^8*b - a^6*b^3 - 9*a^4*b^5 + 13*a^2*b^7 - 5*b^9)*cos(d*x + c)^2 - 15*((6*a^2*b^6 + b^8)*cos(d*x + c)^5 - 2*(6*a^3*b^5 + a*b^7)*cos(d*x + c)^3*sin(d*x + c) - (6*a^4*b^4 + 7*a^2*b^6 + b^8)*cos(d*x + c)^3)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^9 - 8*a^7*b^2 + 12*a^5*b^4 - 8*a^3*b^6 + 2*a*b^8 - (4*a^7*b^2 - 32*a^5*b^4 - 53*a^3*b^6 + 81*a*b^8)*cos(d*x + c)^4 + 2*(2*a^9 - 15*a^7*b^2 + 33*a^5*b^4 - 29*a^3*b^6 + 9*a*b^8)*cos(d*x + c)^2)*sin(d*x + c))/((a^10*b^2 - 5*a^8*b^4 + 10*a^6*b^6 - 10*a^4*b^8 + 5*a^2*b^10 - b^12)*d*cos(d*x + c)^5 - 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c)^3*sin(d*x + c) - (a^12 - 4*a^10*b^2 + 5*a^8*b^4 - 5*a^4*b^8 + 4*a^2*b^10 - b^12)*d*cos(d*x + c)^3), 1/6*(2*a^8*b - 8*a^6*b^3 + 12*a^4*b^5 - 8*a^2*b^7 + 2*b^9 + (8*a^8*b - 64*a^6*b^3 - 16*a^4*b^5 + 87*a^2*b^7 - 15*b^9)*cos(d*x + c)^4 - 2*(2*a^8*b - a^6*b^3 - 9*a^4*b^5 + 13*a^2*b^7 - 5*b^9)*cos(d*x + c)^2 - 15*((6*a^2*b^6 + b^8)*cos(d*x + c)^5 - 2*(6*a^3*b^5 + a*b^7)*cos(d*x + c)^3*sin(d*x + c) - (6*a^4*b^4 + 7*a^2*b^6 + b^8)*cos(d*x + c)^3)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^9 - 8*a^7*b^2 + 12*a^5*b^4 - 8*a^3*b^6 + 2*a*b^8 - (4*a^7*b^2 - 32*a^5*b^4 - 53*a^3*b^6 + 81*a*b^8)*cos(d*x + c)^4 + 2*(2*a^9 - 15*a^7*b^2 + 33*a^5*b^4 - 29*a^3*b^6 + 9*a*b^8)*cos(d*x + c)^2)*sin(d*x + c))/((a^10*b^2 - 5*a^8*b^4 + 10*a^6*b^6 - 10*a^4*b^8 + 5*a^2*b^10 - b^12)*d*cos(d*x + c)^5 - 2*(a^11*b - 5*a^9*b^3 + 10*a^7*b^5 - 10*a^5*b^7 + 5*a^3*b^9 - a*b^11)*d*cos(d*x + c)^3*sin(d*x + c) - (a^12 - 4*a^10*b^2 + 5*a^8*b^4 - 5*a^4*b^8 + 4*a^2*b^10 - b^12)*d*cos(d*x + c)^3)]","B",0
461,1,382,0,1.246153," ","integrate(cos(d*x+c)^7/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{35 \, b^{6} \cos\left(d x + c\right)^{6} - 5 \, a^{6} - 104 \, a^{4} b^{2} - 155 \, a^{2} b^{4} - 16 \, b^{6} - 35 \, {\left(5 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 7 \, {\left(15 \, a^{4} b^{2} + 47 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 7 \, {\left(15 \, a b^{5} \cos\left(d x + c\right)^{4} + 5 \, a^{5} b + 24 \, a^{3} b^{3} + 11 \, a b^{5} - 25 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{35 \, {\left(7 \, a b^{13} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{3} b^{11} + 3 \, a b^{13}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{5} b^{9} + 10 \, a^{3} b^{11} + 3 \, a b^{13}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} b^{7} + 21 \, a^{5} b^{9} + 35 \, a^{3} b^{11} + 7 \, a b^{13}\right)} d + {\left(b^{14} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{2} b^{12} + b^{14}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{4} b^{10} + 42 \, a^{2} b^{12} + 3 \, b^{14}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{6} b^{8} + 35 \, a^{4} b^{10} + 21 \, a^{2} b^{12} + b^{14}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/35*(35*b^6*cos(d*x + c)^6 - 5*a^6 - 104*a^4*b^2 - 155*a^2*b^4 - 16*b^6 - 35*(5*a^2*b^4 + 2*b^6)*cos(d*x + c)^4 + 7*(15*a^4*b^2 + 47*a^2*b^4 + 8*b^6)*cos(d*x + c)^2 - 7*(15*a*b^5*cos(d*x + c)^4 + 5*a^5*b + 24*a^3*b^3 + 11*a*b^5 - 25*(a^3*b^3 + a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(7*a*b^13*d*cos(d*x + c)^6 - 7*(5*a^3*b^11 + 3*a*b^13)*d*cos(d*x + c)^4 + 7*(3*a^5*b^9 + 10*a^3*b^11 + 3*a*b^13)*d*cos(d*x + c)^2 - (a^7*b^7 + 21*a^5*b^9 + 35*a^3*b^11 + 7*a*b^13)*d + (b^14*d*cos(d*x + c)^6 - 3*(7*a^2*b^12 + b^14)*d*cos(d*x + c)^4 + (35*a^4*b^10 + 42*a^2*b^12 + 3*b^14)*d*cos(d*x + c)^2 - (7*a^6*b^8 + 35*a^4*b^10 + 21*a^2*b^12 + b^14)*d)*sin(d*x + c))","A",0
462,1,309,0,1.377587," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{35 \, b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 19 \, a^{2} b^{2} + 8 \, b^{4} - 7 \, {\left(3 \, a^{2} b^{2} + 4 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 7 \, {\left(5 \, a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - 3 \, a b^{3}\right)} \sin\left(d x + c\right)}{105 \, {\left(7 \, a b^{11} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{3} b^{9} + 3 \, a b^{11}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{5} b^{7} + 10 \, a^{3} b^{9} + 3 \, a b^{11}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} b^{5} + 21 \, a^{5} b^{7} + 35 \, a^{3} b^{9} + 7 \, a b^{11}\right)} d + {\left(b^{12} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{2} b^{10} + b^{12}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{4} b^{8} + 42 \, a^{2} b^{10} + 3 \, b^{12}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{6} b^{6} + 35 \, a^{4} b^{8} + 21 \, a^{2} b^{10} + b^{12}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/105*(35*b^4*cos(d*x + c)^4 + a^4 + 19*a^2*b^2 + 8*b^4 - 7*(3*a^2*b^2 + 4*b^4)*cos(d*x + c)^2 - 7*(5*a*b^3*cos(d*x + c)^2 - a^3*b - 3*a*b^3)*sin(d*x + c))/(7*a*b^11*d*cos(d*x + c)^6 - 7*(5*a^3*b^9 + 3*a*b^11)*d*cos(d*x + c)^4 + 7*(3*a^5*b^7 + 10*a^3*b^9 + 3*a*b^11)*d*cos(d*x + c)^2 - (a^7*b^5 + 21*a^5*b^7 + 35*a^3*b^9 + 7*a*b^11)*d + (b^12*d*cos(d*x + c)^6 - 3*(7*a^2*b^10 + b^12)*d*cos(d*x + c)^4 + (35*a^4*b^8 + 42*a^2*b^10 + 3*b^12)*d*cos(d*x + c)^2 - (7*a^6*b^6 + 35*a^4*b^8 + 21*a^2*b^10 + b^12)*d)*sin(d*x + c))","B",0
463,1,254,0,1.058182," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{21 \, b^{2} \cos\left(d x + c\right)^{2} - 7 \, a b \sin\left(d x + c\right) - a^{2} - 6 \, b^{2}}{105 \, {\left(7 \, a b^{9} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{3} b^{7} + 3 \, a b^{9}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{5} b^{5} + 10 \, a^{3} b^{7} + 3 \, a b^{9}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} b^{3} + 21 \, a^{5} b^{5} + 35 \, a^{3} b^{7} + 7 \, a b^{9}\right)} d + {\left(b^{10} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{4} b^{6} + 42 \, a^{2} b^{8} + 3 \, b^{10}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{6} b^{4} + 35 \, a^{4} b^{6} + 21 \, a^{2} b^{8} + b^{10}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/105*(21*b^2*cos(d*x + c)^2 - 7*a*b*sin(d*x + c) - a^2 - 6*b^2)/(7*a*b^9*d*cos(d*x + c)^6 - 7*(5*a^3*b^7 + 3*a*b^9)*d*cos(d*x + c)^4 + 7*(3*a^5*b^5 + 10*a^3*b^7 + 3*a*b^9)*d*cos(d*x + c)^2 - (a^7*b^3 + 21*a^5*b^5 + 35*a^3*b^7 + 7*a*b^9)*d + (b^10*d*cos(d*x + c)^6 - 3*(7*a^2*b^8 + b^10)*d*cos(d*x + c)^4 + (35*a^4*b^6 + 42*a^2*b^8 + 3*b^10)*d*cos(d*x + c)^2 - (7*a^6*b^4 + 35*a^4*b^6 + 21*a^2*b^8 + b^10)*d)*sin(d*x + c))","B",0
464,1,218,0,0.781454," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{1}{7 \, {\left(7 \, a b^{7} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{5} b^{3} + 10 \, a^{3} b^{5} + 3 \, a b^{7}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} b + 21 \, a^{5} b^{3} + 35 \, a^{3} b^{5} + 7 \, a b^{7}\right)} d + {\left(b^{8} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{4} b^{4} + 42 \, a^{2} b^{6} + 3 \, b^{8}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{6} b^{2} + 35 \, a^{4} b^{4} + 21 \, a^{2} b^{6} + b^{8}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/7/(7*a*b^7*d*cos(d*x + c)^6 - 7*(5*a^3*b^5 + 3*a*b^7)*d*cos(d*x + c)^4 + 7*(3*a^5*b^3 + 10*a^3*b^5 + 3*a*b^7)*d*cos(d*x + c)^2 - (a^7*b + 21*a^5*b^3 + 35*a^3*b^5 + 7*a*b^7)*d + (b^8*d*cos(d*x + c)^6 - 3*(7*a^2*b^6 + b^8)*d*cos(d*x + c)^4 + (35*a^4*b^4 + 42*a^2*b^6 + 3*b^8)*d*cos(d*x + c)^2 - (7*a^6*b^2 + 35*a^4*b^4 + 21*a^2*b^6 + b^8)*d)*sin(d*x + c))","B",0
465,1,3165,0,6.624289," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","-\frac{2886 \, a^{14} b + 35728 \, a^{12} b^{3} + 113862 \, a^{10} b^{5} + 11760 \, a^{8} b^{7} - 97230 \, a^{6} b^{9} - 62496 \, a^{4} b^{11} - 4158 \, a^{2} b^{13} - 352 \, b^{15} - 210 \, {\left(7 \, a^{8} b^{7} + 28 \, a^{6} b^{9} - 14 \, a^{4} b^{11} - 20 \, a^{2} b^{13} - b^{15}\right)} \cos\left(d x + c\right)^{6} + 70 \, {\left(365 \, a^{10} b^{5} + 1378 \, a^{8} b^{7} - 602 \, a^{6} b^{9} - 944 \, a^{4} b^{11} - 187 \, a^{2} b^{13} - 10 \, b^{15}\right)} \cos\left(d x + c\right)^{4} - 14 \, {\left(2229 \, a^{12} b^{3} + 10223 \, a^{10} b^{5} + 7960 \, a^{8} b^{7} - 10490 \, a^{6} b^{9} - 8915 \, a^{4} b^{11} - 949 \, a^{2} b^{13} - 58 \, b^{15}\right)} \cos\left(d x + c\right)^{2} - 1680 \, {\left(a^{14} b + 28 \, a^{12} b^{3} + 189 \, a^{10} b^{5} + 400 \, a^{8} b^{7} + 315 \, a^{6} b^{9} + 84 \, a^{4} b^{11} + 7 \, a^{2} b^{13} - 7 \, {\left(a^{8} b^{7} + 7 \, a^{6} b^{9} + 7 \, a^{4} b^{11} + a^{2} b^{13}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(5 \, a^{10} b^{5} + 38 \, a^{8} b^{7} + 56 \, a^{6} b^{9} + 26 \, a^{4} b^{11} + 3 \, a^{2} b^{13}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(3 \, a^{12} b^{3} + 31 \, a^{10} b^{5} + 94 \, a^{8} b^{7} + 94 \, a^{6} b^{9} + 31 \, a^{4} b^{11} + 3 \, a^{2} b^{13}\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, a^{13} b^{2} + 84 \, a^{11} b^{4} + 315 \, a^{9} b^{6} + 400 \, a^{7} b^{8} + 189 \, a^{5} b^{10} + 28 \, a^{3} b^{12} + a b^{14} - {\left(a^{7} b^{8} + 7 \, a^{5} b^{10} + 7 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(7 \, a^{9} b^{6} + 50 \, a^{7} b^{8} + 56 \, a^{5} b^{10} + 14 \, a^{3} b^{12} + a b^{14}\right)} \cos\left(d x + c\right)^{4} - {\left(35 \, a^{11} b^{4} + 287 \, a^{9} b^{6} + 542 \, a^{7} b^{8} + 350 \, a^{5} b^{10} + 63 \, a^{3} b^{12} + 3 \, a b^{14}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 105 \, {\left(a^{15} + 8 \, a^{14} b + 49 \, a^{13} b^{2} + 224 \, a^{12} b^{3} + 693 \, a^{11} b^{4} + 1512 \, a^{10} b^{5} + 2485 \, a^{9} b^{6} + 3200 \, a^{8} b^{7} + 3235 \, a^{7} b^{8} + 2520 \, a^{6} b^{9} + 1491 \, a^{5} b^{10} + 672 \, a^{4} b^{11} + 231 \, a^{3} b^{12} + 56 \, a^{2} b^{13} + 7 \, a b^{14} - 7 \, {\left(a^{9} b^{6} + 8 \, a^{8} b^{7} + 28 \, a^{7} b^{8} + 56 \, a^{6} b^{9} + 70 \, a^{5} b^{10} + 56 \, a^{4} b^{11} + 28 \, a^{3} b^{12} + 8 \, a^{2} b^{13} + a b^{14}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(5 \, a^{11} b^{4} + 40 \, a^{10} b^{5} + 143 \, a^{9} b^{6} + 304 \, a^{8} b^{7} + 434 \, a^{7} b^{8} + 448 \, a^{6} b^{9} + 350 \, a^{5} b^{10} + 208 \, a^{4} b^{11} + 89 \, a^{3} b^{12} + 24 \, a^{2} b^{13} + 3 \, a b^{14}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(3 \, a^{13} b^{2} + 24 \, a^{12} b^{3} + 94 \, a^{11} b^{4} + 248 \, a^{10} b^{5} + 493 \, a^{9} b^{6} + 752 \, a^{8} b^{7} + 868 \, a^{7} b^{8} + 752 \, a^{6} b^{9} + 493 \, a^{5} b^{10} + 248 \, a^{4} b^{11} + 94 \, a^{3} b^{12} + 24 \, a^{2} b^{13} + 3 \, a b^{14}\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, a^{14} b + 56 \, a^{13} b^{2} + 231 \, a^{12} b^{3} + 672 \, a^{11} b^{4} + 1491 \, a^{10} b^{5} + 2520 \, a^{9} b^{6} + 3235 \, a^{8} b^{7} + 3200 \, a^{7} b^{8} + 2485 \, a^{6} b^{9} + 1512 \, a^{5} b^{10} + 693 \, a^{4} b^{11} + 224 \, a^{3} b^{12} + 49 \, a^{2} b^{13} + 8 \, a b^{14} + b^{15} - {\left(a^{8} b^{7} + 8 \, a^{7} b^{8} + 28 \, a^{6} b^{9} + 56 \, a^{5} b^{10} + 70 \, a^{4} b^{11} + 56 \, a^{3} b^{12} + 28 \, a^{2} b^{13} + 8 \, a b^{14} + b^{15}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(7 \, a^{10} b^{5} + 56 \, a^{9} b^{6} + 197 \, a^{8} b^{7} + 400 \, a^{7} b^{8} + 518 \, a^{6} b^{9} + 448 \, a^{5} b^{10} + 266 \, a^{4} b^{11} + 112 \, a^{3} b^{12} + 35 \, a^{2} b^{13} + 8 \, a b^{14} + b^{15}\right)} \cos\left(d x + c\right)^{4} - {\left(35 \, a^{12} b^{3} + 280 \, a^{11} b^{4} + 1022 \, a^{10} b^{5} + 2296 \, a^{9} b^{6} + 3629 \, a^{8} b^{7} + 4336 \, a^{7} b^{8} + 4004 \, a^{6} b^{9} + 2800 \, a^{5} b^{10} + 1421 \, a^{4} b^{11} + 504 \, a^{3} b^{12} + 126 \, a^{2} b^{13} + 24 \, a b^{14} + 3 \, b^{15}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(a^{15} - 8 \, a^{14} b + 49 \, a^{13} b^{2} - 224 \, a^{12} b^{3} + 693 \, a^{11} b^{4} - 1512 \, a^{10} b^{5} + 2485 \, a^{9} b^{6} - 3200 \, a^{8} b^{7} + 3235 \, a^{7} b^{8} - 2520 \, a^{6} b^{9} + 1491 \, a^{5} b^{10} - 672 \, a^{4} b^{11} + 231 \, a^{3} b^{12} - 56 \, a^{2} b^{13} + 7 \, a b^{14} - 7 \, {\left(a^{9} b^{6} - 8 \, a^{8} b^{7} + 28 \, a^{7} b^{8} - 56 \, a^{6} b^{9} + 70 \, a^{5} b^{10} - 56 \, a^{4} b^{11} + 28 \, a^{3} b^{12} - 8 \, a^{2} b^{13} + a b^{14}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(5 \, a^{11} b^{4} - 40 \, a^{10} b^{5} + 143 \, a^{9} b^{6} - 304 \, a^{8} b^{7} + 434 \, a^{7} b^{8} - 448 \, a^{6} b^{9} + 350 \, a^{5} b^{10} - 208 \, a^{4} b^{11} + 89 \, a^{3} b^{12} - 24 \, a^{2} b^{13} + 3 \, a b^{14}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(3 \, a^{13} b^{2} - 24 \, a^{12} b^{3} + 94 \, a^{11} b^{4} - 248 \, a^{10} b^{5} + 493 \, a^{9} b^{6} - 752 \, a^{8} b^{7} + 868 \, a^{7} b^{8} - 752 \, a^{6} b^{9} + 493 \, a^{5} b^{10} - 248 \, a^{4} b^{11} + 94 \, a^{3} b^{12} - 24 \, a^{2} b^{13} + 3 \, a b^{14}\right)} \cos\left(d x + c\right)^{2} + {\left(7 \, a^{14} b - 56 \, a^{13} b^{2} + 231 \, a^{12} b^{3} - 672 \, a^{11} b^{4} + 1491 \, a^{10} b^{5} - 2520 \, a^{9} b^{6} + 3235 \, a^{8} b^{7} - 3200 \, a^{7} b^{8} + 2485 \, a^{6} b^{9} - 1512 \, a^{5} b^{10} + 693 \, a^{4} b^{11} - 224 \, a^{3} b^{12} + 49 \, a^{2} b^{13} - 8 \, a b^{14} + b^{15} - {\left(a^{8} b^{7} - 8 \, a^{7} b^{8} + 28 \, a^{6} b^{9} - 56 \, a^{5} b^{10} + 70 \, a^{4} b^{11} - 56 \, a^{3} b^{12} + 28 \, a^{2} b^{13} - 8 \, a b^{14} + b^{15}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(7 \, a^{10} b^{5} - 56 \, a^{9} b^{6} + 197 \, a^{8} b^{7} - 400 \, a^{7} b^{8} + 518 \, a^{6} b^{9} - 448 \, a^{5} b^{10} + 266 \, a^{4} b^{11} - 112 \, a^{3} b^{12} + 35 \, a^{2} b^{13} - 8 \, a b^{14} + b^{15}\right)} \cos\left(d x + c\right)^{4} - {\left(35 \, a^{12} b^{3} - 280 \, a^{11} b^{4} + 1022 \, a^{10} b^{5} - 2296 \, a^{9} b^{6} + 3629 \, a^{8} b^{7} - 4336 \, a^{7} b^{8} + 4004 \, a^{6} b^{9} - 2800 \, a^{5} b^{10} + 1421 \, a^{4} b^{11} - 504 \, a^{3} b^{12} + 126 \, a^{2} b^{13} - 24 \, a b^{14} + 3 \, b^{15}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 14 \, {\left(1023 \, a^{13} b^{2} + 5136 \, a^{11} b^{4} + 7255 \, a^{9} b^{6} - 5160 \, a^{7} b^{8} - 6435 \, a^{5} b^{10} - 1768 \, a^{3} b^{12} - 51 \, a b^{14} + 15 \, {\left(45 \, a^{9} b^{6} + 172 \, a^{7} b^{8} - 98 \, a^{5} b^{10} - 116 \, a^{3} b^{12} - 3 \, a b^{14}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(533 \, a^{11} b^{4} + 2041 \, a^{9} b^{6} - 278 \, a^{7} b^{8} - 1574 \, a^{5} b^{10} - 703 \, a^{3} b^{12} - 19 \, a b^{14}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{210 \, {\left(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)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{19} b^{4} - 37 \, a^{17} b^{6} + 116 \, a^{15} b^{8} - 196 \, a^{13} b^{10} + 182 \, a^{11} b^{12} - 70 \, a^{9} b^{14} - 28 \, a^{7} b^{16} + 44 \, a^{5} b^{18} - 19 \, a^{3} b^{20} + 3 \, a b^{22}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{21} b^{2} - 14 \, a^{19} b^{4} + 7 \, a^{17} b^{6} + 88 \, a^{15} b^{8} - 266 \, a^{13} b^{10} + 364 \, a^{11} b^{12} - 266 \, a^{9} b^{14} + 88 \, a^{7} b^{16} + 7 \, a^{5} b^{18} - 14 \, a^{3} b^{20} + 3 \, a b^{22}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{23} + 13 \, a^{21} b^{2} - 105 \, a^{19} b^{4} + 259 \, a^{17} b^{6} - 182 \, a^{15} b^{8} - 350 \, a^{13} b^{10} + 910 \, a^{11} b^{12} - 890 \, a^{9} b^{14} + 421 \, a^{7} b^{16} - 63 \, a^{5} b^{18} - 21 \, a^{3} b^{20} + 7 \, a b^{22}\right)} d + {\left({\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)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{18} b^{5} - 55 \, a^{16} b^{7} + 188 \, a^{14} b^{9} - 364 \, a^{12} b^{11} + 434 \, a^{10} b^{13} - 322 \, a^{8} b^{15} + 140 \, a^{6} b^{17} - 28 \, a^{4} b^{19} - a^{2} b^{21} + b^{23}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{20} b^{3} - 238 \, a^{18} b^{5} + 647 \, a^{16} b^{7} - 808 \, a^{14} b^{9} + 182 \, a^{12} b^{11} + 812 \, a^{10} b^{13} - 1162 \, a^{8} b^{15} + 728 \, a^{6} b^{17} - 217 \, a^{4} b^{19} + 18 \, a^{2} b^{21} + 3 \, b^{23}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{22} b - 21 \, a^{20} b^{3} - 63 \, a^{18} b^{5} + 421 \, a^{16} b^{7} - 890 \, a^{14} b^{9} + 910 \, a^{12} b^{11} - 350 \, a^{10} b^{13} - 182 \, a^{8} b^{15} + 259 \, a^{6} b^{17} - 105 \, a^{4} b^{19} + 13 \, a^{2} b^{21} + b^{23}\right)} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/210*(2886*a^14*b + 35728*a^12*b^3 + 113862*a^10*b^5 + 11760*a^8*b^7 - 97230*a^6*b^9 - 62496*a^4*b^11 - 4158*a^2*b^13 - 352*b^15 - 210*(7*a^8*b^7 + 28*a^6*b^9 - 14*a^4*b^11 - 20*a^2*b^13 - b^15)*cos(d*x + c)^6 + 70*(365*a^10*b^5 + 1378*a^8*b^7 - 602*a^6*b^9 - 944*a^4*b^11 - 187*a^2*b^13 - 10*b^15)*cos(d*x + c)^4 - 14*(2229*a^12*b^3 + 10223*a^10*b^5 + 7960*a^8*b^7 - 10490*a^6*b^9 - 8915*a^4*b^11 - 949*a^2*b^13 - 58*b^15)*cos(d*x + c)^2 - 1680*(a^14*b + 28*a^12*b^3 + 189*a^10*b^5 + 400*a^8*b^7 + 315*a^6*b^9 + 84*a^4*b^11 + 7*a^2*b^13 - 7*(a^8*b^7 + 7*a^6*b^9 + 7*a^4*b^11 + a^2*b^13)*cos(d*x + c)^6 + 7*(5*a^10*b^5 + 38*a^8*b^7 + 56*a^6*b^9 + 26*a^4*b^11 + 3*a^2*b^13)*cos(d*x + c)^4 - 7*(3*a^12*b^3 + 31*a^10*b^5 + 94*a^8*b^7 + 94*a^6*b^9 + 31*a^4*b^11 + 3*a^2*b^13)*cos(d*x + c)^2 + (7*a^13*b^2 + 84*a^11*b^4 + 315*a^9*b^6 + 400*a^7*b^8 + 189*a^5*b^10 + 28*a^3*b^12 + a*b^14 - (a^7*b^8 + 7*a^5*b^10 + 7*a^3*b^12 + a*b^14)*cos(d*x + c)^6 + 3*(7*a^9*b^6 + 50*a^7*b^8 + 56*a^5*b^10 + 14*a^3*b^12 + a*b^14)*cos(d*x + c)^4 - (35*a^11*b^4 + 287*a^9*b^6 + 542*a^7*b^8 + 350*a^5*b^10 + 63*a^3*b^12 + 3*a*b^14)*cos(d*x + c)^2)*sin(d*x + c))*log(b*sin(d*x + c) + a) + 105*(a^15 + 8*a^14*b + 49*a^13*b^2 + 224*a^12*b^3 + 693*a^11*b^4 + 1512*a^10*b^5 + 2485*a^9*b^6 + 3200*a^8*b^7 + 3235*a^7*b^8 + 2520*a^6*b^9 + 1491*a^5*b^10 + 672*a^4*b^11 + 231*a^3*b^12 + 56*a^2*b^13 + 7*a*b^14 - 7*(a^9*b^6 + 8*a^8*b^7 + 28*a^7*b^8 + 56*a^6*b^9 + 70*a^5*b^10 + 56*a^4*b^11 + 28*a^3*b^12 + 8*a^2*b^13 + a*b^14)*cos(d*x + c)^6 + 7*(5*a^11*b^4 + 40*a^10*b^5 + 143*a^9*b^6 + 304*a^8*b^7 + 434*a^7*b^8 + 448*a^6*b^9 + 350*a^5*b^10 + 208*a^4*b^11 + 89*a^3*b^12 + 24*a^2*b^13 + 3*a*b^14)*cos(d*x + c)^4 - 7*(3*a^13*b^2 + 24*a^12*b^3 + 94*a^11*b^4 + 248*a^10*b^5 + 493*a^9*b^6 + 752*a^8*b^7 + 868*a^7*b^8 + 752*a^6*b^9 + 493*a^5*b^10 + 248*a^4*b^11 + 94*a^3*b^12 + 24*a^2*b^13 + 3*a*b^14)*cos(d*x + c)^2 + (7*a^14*b + 56*a^13*b^2 + 231*a^12*b^3 + 672*a^11*b^4 + 1491*a^10*b^5 + 2520*a^9*b^6 + 3235*a^8*b^7 + 3200*a^7*b^8 + 2485*a^6*b^9 + 1512*a^5*b^10 + 693*a^4*b^11 + 224*a^3*b^12 + 49*a^2*b^13 + 8*a*b^14 + b^15 - (a^8*b^7 + 8*a^7*b^8 + 28*a^6*b^9 + 56*a^5*b^10 + 70*a^4*b^11 + 56*a^3*b^12 + 28*a^2*b^13 + 8*a*b^14 + b^15)*cos(d*x + c)^6 + 3*(7*a^10*b^5 + 56*a^9*b^6 + 197*a^8*b^7 + 400*a^7*b^8 + 518*a^6*b^9 + 448*a^5*b^10 + 266*a^4*b^11 + 112*a^3*b^12 + 35*a^2*b^13 + 8*a*b^14 + b^15)*cos(d*x + c)^4 - (35*a^12*b^3 + 280*a^11*b^4 + 1022*a^10*b^5 + 2296*a^9*b^6 + 3629*a^8*b^7 + 4336*a^7*b^8 + 4004*a^6*b^9 + 2800*a^5*b^10 + 1421*a^4*b^11 + 504*a^3*b^12 + 126*a^2*b^13 + 24*a*b^14 + 3*b^15)*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) - 105*(a^15 - 8*a^14*b + 49*a^13*b^2 - 224*a^12*b^3 + 693*a^11*b^4 - 1512*a^10*b^5 + 2485*a^9*b^6 - 3200*a^8*b^7 + 3235*a^7*b^8 - 2520*a^6*b^9 + 1491*a^5*b^10 - 672*a^4*b^11 + 231*a^3*b^12 - 56*a^2*b^13 + 7*a*b^14 - 7*(a^9*b^6 - 8*a^8*b^7 + 28*a^7*b^8 - 56*a^6*b^9 + 70*a^5*b^10 - 56*a^4*b^11 + 28*a^3*b^12 - 8*a^2*b^13 + a*b^14)*cos(d*x + c)^6 + 7*(5*a^11*b^4 - 40*a^10*b^5 + 143*a^9*b^6 - 304*a^8*b^7 + 434*a^7*b^8 - 448*a^6*b^9 + 350*a^5*b^10 - 208*a^4*b^11 + 89*a^3*b^12 - 24*a^2*b^13 + 3*a*b^14)*cos(d*x + c)^4 - 7*(3*a^13*b^2 - 24*a^12*b^3 + 94*a^11*b^4 - 248*a^10*b^5 + 493*a^9*b^6 - 752*a^8*b^7 + 868*a^7*b^8 - 752*a^6*b^9 + 493*a^5*b^10 - 248*a^4*b^11 + 94*a^3*b^12 - 24*a^2*b^13 + 3*a*b^14)*cos(d*x + c)^2 + (7*a^14*b - 56*a^13*b^2 + 231*a^12*b^3 - 672*a^11*b^4 + 1491*a^10*b^5 - 2520*a^9*b^6 + 3235*a^8*b^7 - 3200*a^7*b^8 + 2485*a^6*b^9 - 1512*a^5*b^10 + 693*a^4*b^11 - 224*a^3*b^12 + 49*a^2*b^13 - 8*a*b^14 + b^15 - (a^8*b^7 - 8*a^7*b^8 + 28*a^6*b^9 - 56*a^5*b^10 + 70*a^4*b^11 - 56*a^3*b^12 + 28*a^2*b^13 - 8*a*b^14 + b^15)*cos(d*x + c)^6 + 3*(7*a^10*b^5 - 56*a^9*b^6 + 197*a^8*b^7 - 400*a^7*b^8 + 518*a^6*b^9 - 448*a^5*b^10 + 266*a^4*b^11 - 112*a^3*b^12 + 35*a^2*b^13 - 8*a*b^14 + b^15)*cos(d*x + c)^4 - (35*a^12*b^3 - 280*a^11*b^4 + 1022*a^10*b^5 - 2296*a^9*b^6 + 3629*a^8*b^7 - 4336*a^7*b^8 + 4004*a^6*b^9 - 2800*a^5*b^10 + 1421*a^4*b^11 - 504*a^3*b^12 + 126*a^2*b^13 - 24*a*b^14 + 3*b^15)*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 14*(1023*a^13*b^2 + 5136*a^11*b^4 + 7255*a^9*b^6 - 5160*a^7*b^8 - 6435*a^5*b^10 - 1768*a^3*b^12 - 51*a*b^14 + 15*(45*a^9*b^6 + 172*a^7*b^8 - 98*a^5*b^10 - 116*a^3*b^12 - 3*a*b^14)*cos(d*x + c)^4 - 5*(533*a^11*b^4 + 2041*a^9*b^6 - 278*a^7*b^8 - 1574*a^5*b^10 - 703*a^3*b^12 - 19*a*b^14)*cos(d*x + c)^2)*sin(d*x + c))/(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)*d*cos(d*x + c)^6 - 7*(5*a^19*b^4 - 37*a^17*b^6 + 116*a^15*b^8 - 196*a^13*b^10 + 182*a^11*b^12 - 70*a^9*b^14 - 28*a^7*b^16 + 44*a^5*b^18 - 19*a^3*b^20 + 3*a*b^22)*d*cos(d*x + c)^4 + 7*(3*a^21*b^2 - 14*a^19*b^4 + 7*a^17*b^6 + 88*a^15*b^8 - 266*a^13*b^10 + 364*a^11*b^12 - 266*a^9*b^14 + 88*a^7*b^16 + 7*a^5*b^18 - 14*a^3*b^20 + 3*a*b^22)*d*cos(d*x + c)^2 - (a^23 + 13*a^21*b^2 - 105*a^19*b^4 + 259*a^17*b^6 - 182*a^15*b^8 - 350*a^13*b^10 + 910*a^11*b^12 - 890*a^9*b^14 + 421*a^7*b^16 - 63*a^5*b^18 - 21*a^3*b^20 + 7*a*b^22)*d + ((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)*d*cos(d*x + c)^6 - 3*(7*a^18*b^5 - 55*a^16*b^7 + 188*a^14*b^9 - 364*a^12*b^11 + 434*a^10*b^13 - 322*a^8*b^15 + 140*a^6*b^17 - 28*a^4*b^19 - a^2*b^21 + b^23)*d*cos(d*x + c)^4 + (35*a^20*b^3 - 238*a^18*b^5 + 647*a^16*b^7 - 808*a^14*b^9 + 182*a^12*b^11 + 812*a^10*b^13 - 1162*a^8*b^15 + 728*a^6*b^17 - 217*a^4*b^19 + 18*a^2*b^21 + 3*b^23)*d*cos(d*x + c)^2 - (7*a^22*b - 21*a^20*b^3 - 63*a^18*b^5 + 421*a^16*b^7 - 890*a^14*b^9 + 910*a^12*b^11 - 350*a^10*b^13 - 182*a^8*b^15 + 259*a^6*b^17 - 105*a^4*b^19 + 13*a^2*b^21 + b^23)*d)*sin(d*x + c))","B",0
466,1,3678,0,12.143875," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\frac{210 \, a^{16} b - 1680 \, a^{14} b^{3} + 5880 \, a^{12} b^{5} - 11760 \, a^{10} b^{7} + 14700 \, a^{8} b^{9} - 11760 \, a^{6} b^{11} + 5880 \, a^{4} b^{13} - 1680 \, a^{2} b^{15} + 210 \, b^{17} - 210 \, {\left(a^{10} b^{7} + 195 \, a^{8} b^{9} + 378 \, a^{6} b^{11} - 330 \, a^{4} b^{13} - 235 \, a^{2} b^{15} - 9 \, b^{17}\right)} \cos\left(d x + c\right)^{8} + 70 \, {\left(63 \, a^{12} b^{5} + 10015 \, a^{10} b^{7} + 18468 \, a^{8} b^{9} - 14274 \, a^{6} b^{11} - 12025 \, a^{4} b^{13} - 2157 \, a^{2} b^{15} - 90 \, b^{17}\right)} \cos\left(d x + c\right)^{6} - 14 \, {\left(525 \, a^{14} b^{3} + 59730 \, a^{12} b^{5} + 174637 \, a^{10} b^{7} + 77130 \, a^{8} b^{9} - 194265 \, a^{6} b^{11} - 106450 \, a^{4} b^{13} - 10785 \, a^{2} b^{15} - 522 \, b^{17}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(735 \, a^{16} b + 37165 \, a^{14} b^{3} + 437199 \, a^{12} b^{5} + 836549 \, a^{10} b^{7} - 111195 \, a^{8} b^{9} - 812385 \, a^{6} b^{11} - 362915 \, a^{4} b^{13} - 23569 \, a^{2} b^{15} - 1584 \, b^{17}\right)} \cos\left(d x + c\right)^{2} + 3360 \, {\left(7 \, {\left(15 \, a^{8} b^{9} + 63 \, a^{6} b^{11} + 45 \, a^{4} b^{13} + 5 \, a^{2} b^{15}\right)} \cos\left(d x + c\right)^{8} - 7 \, {\left(75 \, a^{10} b^{7} + 360 \, a^{8} b^{9} + 414 \, a^{6} b^{11} + 160 \, a^{4} b^{13} + 15 \, a^{2} b^{15}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(45 \, a^{12} b^{5} + 339 \, a^{10} b^{7} + 810 \, a^{8} b^{9} + 654 \, a^{6} b^{11} + 185 \, a^{4} b^{13} + 15 \, a^{2} b^{15}\right)} \cos\left(d x + c\right)^{4} - {\left(15 \, a^{14} b^{3} + 378 \, a^{12} b^{5} + 1893 \, a^{10} b^{7} + 3260 \, a^{8} b^{9} + 2121 \, a^{6} b^{11} + 490 \, a^{4} b^{13} + 35 \, a^{2} b^{15}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(15 \, a^{7} b^{10} + 63 \, a^{5} b^{12} + 45 \, a^{3} b^{14} + 5 \, a b^{16}\right)} \cos\left(d x + c\right)^{8} - 3 \, {\left(105 \, a^{9} b^{8} + 456 \, a^{7} b^{10} + 378 \, a^{5} b^{12} + 80 \, a^{3} b^{14} + 5 \, a b^{16}\right)} \cos\left(d x + c\right)^{6} + {\left(525 \, a^{11} b^{6} + 2835 \, a^{9} b^{8} + 4266 \, a^{7} b^{10} + 2254 \, a^{5} b^{12} + 345 \, a^{3} b^{14} + 15 \, a b^{16}\right)} \cos\left(d x + c\right)^{4} - {\left(105 \, a^{13} b^{4} + 966 \, a^{11} b^{6} + 2835 \, a^{9} b^{8} + 2948 \, a^{7} b^{10} + 1183 \, a^{5} b^{12} + 150 \, a^{3} b^{14} + 5 \, a b^{16}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 105 \, {\left(7 \, {\left(a^{11} b^{6} - 45 \, a^{9} b^{8} - 240 \, a^{8} b^{9} - 630 \, a^{7} b^{10} - 1008 \, a^{6} b^{11} - 1050 \, a^{5} b^{12} - 720 \, a^{4} b^{13} - 315 \, a^{3} b^{14} - 80 \, a^{2} b^{15} - 9 \, a b^{16}\right)} \cos\left(d x + c\right)^{8} - 7 \, {\left(5 \, a^{13} b^{4} - 222 \, a^{11} b^{6} - 1200 \, a^{10} b^{7} - 3285 \, a^{9} b^{8} - 5760 \, a^{8} b^{9} - 7140 \, a^{7} b^{10} - 6624 \, a^{6} b^{11} - 4725 \, a^{5} b^{12} - 2560 \, a^{4} b^{13} - 990 \, a^{3} b^{14} - 240 \, a^{2} b^{15} - 27 \, a b^{16}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(3 \, a^{15} b^{2} - 125 \, a^{13} b^{4} - 720 \, a^{12} b^{5} - 2337 \, a^{11} b^{6} - 5424 \, a^{10} b^{7} - 9585 \, a^{9} b^{8} - 12960 \, a^{8} b^{9} - 13335 \, a^{7} b^{10} - 10464 \, a^{6} b^{11} - 6327 \, a^{5} b^{12} - 2960 \, a^{4} b^{13} - 1035 \, a^{3} b^{14} - 240 \, a^{2} b^{15} - 27 \, a b^{16}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{17} - 24 \, a^{15} b^{2} - 240 \, a^{14} b^{3} - 1540 \, a^{13} b^{4} - 6048 \, a^{12} b^{5} - 15848 \, a^{11} b^{6} - 30288 \, a^{10} b^{7} - 44730 \, a^{9} b^{8} - 52160 \, a^{8} b^{9} - 47784 \, a^{7} b^{10} - 33936 \, a^{6} b^{11} - 18564 \, a^{5} b^{12} - 7840 \, a^{4} b^{13} - 2520 \, a^{3} b^{14} - 560 \, a^{2} b^{15} - 63 \, a b^{16}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{10} b^{7} - 45 \, a^{8} b^{9} - 240 \, a^{7} b^{10} - 630 \, a^{6} b^{11} - 1008 \, a^{5} b^{12} - 1050 \, a^{4} b^{13} - 720 \, a^{3} b^{14} - 315 \, a^{2} b^{15} - 80 \, a b^{16} - 9 \, b^{17}\right)} \cos\left(d x + c\right)^{8} - 3 \, {\left(7 \, a^{12} b^{5} - 314 \, a^{10} b^{7} - 1680 \, a^{9} b^{8} - 4455 \, a^{8} b^{9} - 7296 \, a^{7} b^{10} - 7980 \, a^{6} b^{11} - 6048 \, a^{5} b^{12} - 3255 \, a^{4} b^{13} - 1280 \, a^{3} b^{14} - 378 \, a^{2} b^{15} - 80 \, a b^{16} - 9 \, b^{17}\right)} \cos\left(d x + c\right)^{6} + {\left(35 \, a^{14} b^{3} - 1533 \, a^{12} b^{5} - 8400 \, a^{11} b^{6} - 23937 \, a^{10} b^{7} - 45360 \, a^{9} b^{8} - 63345 \, a^{8} b^{9} - 68256 \, a^{7} b^{10} - 57015 \, a^{6} b^{11} - 36064 \, a^{5} b^{12} - 16695 \, a^{4} b^{13} - 5520 \, a^{3} b^{14} - 1323 \, a^{2} b^{15} - 240 \, a b^{16} - 27 \, b^{17}\right)} \cos\left(d x + c\right)^{4} - {\left(7 \, a^{16} b - 280 \, a^{14} b^{3} - 1680 \, a^{13} b^{4} - 5964 \, a^{12} b^{5} - 15456 \, a^{11} b^{6} - 30344 \, a^{10} b^{7} - 45360 \, a^{9} b^{8} - 52230 \, a^{8} b^{9} - 47168 \, a^{7} b^{10} - 33768 \, a^{6} b^{11} - 18928 \, a^{5} b^{12} - 7980 \, a^{4} b^{13} - 2400 \, a^{3} b^{14} - 504 \, a^{2} b^{15} - 80 \, a b^{16} - 9 \, b^{17}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(7 \, {\left(a^{11} b^{6} - 45 \, a^{9} b^{8} + 240 \, a^{8} b^{9} - 630 \, a^{7} b^{10} + 1008 \, a^{6} b^{11} - 1050 \, a^{5} b^{12} + 720 \, a^{4} b^{13} - 315 \, a^{3} b^{14} + 80 \, a^{2} b^{15} - 9 \, a b^{16}\right)} \cos\left(d x + c\right)^{8} - 7 \, {\left(5 \, a^{13} b^{4} - 222 \, a^{11} b^{6} + 1200 \, a^{10} b^{7} - 3285 \, a^{9} b^{8} + 5760 \, a^{8} b^{9} - 7140 \, a^{7} b^{10} + 6624 \, a^{6} b^{11} - 4725 \, a^{5} b^{12} + 2560 \, a^{4} b^{13} - 990 \, a^{3} b^{14} + 240 \, a^{2} b^{15} - 27 \, a b^{16}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(3 \, a^{15} b^{2} - 125 \, a^{13} b^{4} + 720 \, a^{12} b^{5} - 2337 \, a^{11} b^{6} + 5424 \, a^{10} b^{7} - 9585 \, a^{9} b^{8} + 12960 \, a^{8} b^{9} - 13335 \, a^{7} b^{10} + 10464 \, a^{6} b^{11} - 6327 \, a^{5} b^{12} + 2960 \, a^{4} b^{13} - 1035 \, a^{3} b^{14} + 240 \, a^{2} b^{15} - 27 \, a b^{16}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{17} - 24 \, a^{15} b^{2} + 240 \, a^{14} b^{3} - 1540 \, a^{13} b^{4} + 6048 \, a^{12} b^{5} - 15848 \, a^{11} b^{6} + 30288 \, a^{10} b^{7} - 44730 \, a^{9} b^{8} + 52160 \, a^{8} b^{9} - 47784 \, a^{7} b^{10} + 33936 \, a^{6} b^{11} - 18564 \, a^{5} b^{12} + 7840 \, a^{4} b^{13} - 2520 \, a^{3} b^{14} + 560 \, a^{2} b^{15} - 63 \, a b^{16}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{10} b^{7} - 45 \, a^{8} b^{9} + 240 \, a^{7} b^{10} - 630 \, a^{6} b^{11} + 1008 \, a^{5} b^{12} - 1050 \, a^{4} b^{13} + 720 \, a^{3} b^{14} - 315 \, a^{2} b^{15} + 80 \, a b^{16} - 9 \, b^{17}\right)} \cos\left(d x + c\right)^{8} - 3 \, {\left(7 \, a^{12} b^{5} - 314 \, a^{10} b^{7} + 1680 \, a^{9} b^{8} - 4455 \, a^{8} b^{9} + 7296 \, a^{7} b^{10} - 7980 \, a^{6} b^{11} + 6048 \, a^{5} b^{12} - 3255 \, a^{4} b^{13} + 1280 \, a^{3} b^{14} - 378 \, a^{2} b^{15} + 80 \, a b^{16} - 9 \, b^{17}\right)} \cos\left(d x + c\right)^{6} + {\left(35 \, a^{14} b^{3} - 1533 \, a^{12} b^{5} + 8400 \, a^{11} b^{6} - 23937 \, a^{10} b^{7} + 45360 \, a^{9} b^{8} - 63345 \, a^{8} b^{9} + 68256 \, a^{7} b^{10} - 57015 \, a^{6} b^{11} + 36064 \, a^{5} b^{12} - 16695 \, a^{4} b^{13} + 5520 \, a^{3} b^{14} - 1323 \, a^{2} b^{15} + 240 \, a b^{16} - 27 \, b^{17}\right)} \cos\left(d x + c\right)^{4} - {\left(7 \, a^{16} b - 280 \, a^{14} b^{3} + 1680 \, a^{13} b^{4} - 5964 \, a^{12} b^{5} + 15456 \, a^{11} b^{6} - 30344 \, a^{10} b^{7} + 45360 \, a^{9} b^{8} - 52230 \, a^{8} b^{9} + 47168 \, a^{7} b^{10} - 33768 \, a^{6} b^{11} + 18928 \, a^{5} b^{12} - 7980 \, a^{4} b^{13} + 2400 \, a^{3} b^{14} - 504 \, a^{2} b^{15} + 80 \, a b^{16} - 9 \, b^{17}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 14 \, {\left(15 \, a^{17} - 120 \, a^{15} b^{2} + 420 \, a^{13} b^{4} - 840 \, a^{11} b^{6} + 1050 \, a^{9} b^{8} - 840 \, a^{7} b^{10} + 420 \, a^{5} b^{12} - 120 \, a^{3} b^{14} + 15 \, a b^{16} - 15 \, {\left(7 \, a^{11} b^{6} + 1245 \, a^{9} b^{8} + 2262 \, a^{7} b^{10} - 2166 \, a^{5} b^{12} - 1325 \, a^{3} b^{14} - 23 \, a b^{16}\right)} \cos\left(d x + c\right)^{6} + 5 \, {\left(105 \, a^{13} b^{4} + 14464 \, a^{11} b^{6} + 28953 \, a^{9} b^{8} - 11736 \, a^{7} b^{10} - 23605 \, a^{5} b^{12} - 8040 \, a^{3} b^{14} - 141 \, a b^{16}\right)} \cos\left(d x + c\right)^{4} - {\left(315 \, a^{15} b^{2} + 26665 \, a^{13} b^{4} + 97499 \, a^{11} b^{6} + 88065 \, a^{9} b^{8} - 106455 \, a^{7} b^{10} - 85325 \, a^{5} b^{12} - 20415 \, a^{3} b^{14} - 349 \, a b^{16}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{420 \, {\left(7 \, {\left(a^{19} b^{6} - 9 \, a^{17} b^{8} + 36 \, a^{15} b^{10} - 84 \, a^{13} b^{12} + 126 \, a^{11} b^{14} - 126 \, a^{9} b^{16} + 84 \, a^{7} b^{18} - 36 \, a^{5} b^{20} + 9 \, a^{3} b^{22} - a b^{24}\right)} d \cos\left(d x + c\right)^{8} - 7 \, {\left(5 \, a^{21} b^{4} - 42 \, a^{19} b^{6} + 153 \, a^{17} b^{8} - 312 \, a^{15} b^{10} + 378 \, a^{13} b^{12} - 252 \, a^{11} b^{14} + 42 \, a^{9} b^{16} + 72 \, a^{7} b^{18} - 63 \, a^{5} b^{20} + 22 \, a^{3} b^{22} - 3 \, a b^{24}\right)} d \cos\left(d x + c\right)^{6} + 7 \, {\left(3 \, a^{23} b^{2} - 17 \, a^{21} b^{4} + 21 \, a^{19} b^{6} + 81 \, a^{17} b^{8} - 354 \, a^{15} b^{10} + 630 \, a^{13} b^{12} - 630 \, a^{11} b^{14} + 354 \, a^{9} b^{16} - 81 \, a^{7} b^{18} - 21 \, a^{5} b^{20} + 17 \, a^{3} b^{22} - 3 \, a b^{24}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{25} + 12 \, a^{23} b^{2} - 118 \, a^{21} b^{4} + 364 \, a^{19} b^{6} - 441 \, a^{17} b^{8} - 168 \, a^{15} b^{10} + 1260 \, a^{13} b^{12} - 1800 \, a^{11} b^{14} + 1311 \, a^{9} b^{16} - 484 \, a^{7} b^{18} + 42 \, a^{5} b^{20} + 28 \, a^{3} b^{22} - 7 \, a b^{24}\right)} d \cos\left(d x + c\right)^{2} + {\left({\left(a^{18} b^{7} - 9 \, a^{16} b^{9} + 36 \, a^{14} b^{11} - 84 \, a^{12} b^{13} + 126 \, a^{10} b^{15} - 126 \, a^{8} b^{17} + 84 \, a^{6} b^{19} - 36 \, a^{4} b^{21} + 9 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)^{8} - 3 \, {\left(7 \, a^{20} b^{5} - 62 \, a^{18} b^{7} + 243 \, a^{16} b^{9} - 552 \, a^{14} b^{11} + 798 \, a^{12} b^{13} - 756 \, a^{10} b^{15} + 462 \, a^{8} b^{17} - 168 \, a^{6} b^{19} + 27 \, a^{4} b^{21} + 2 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)^{6} + {\left(35 \, a^{22} b^{3} - 273 \, a^{20} b^{5} + 885 \, a^{18} b^{7} - 1455 \, a^{16} b^{9} + 990 \, a^{14} b^{11} + 630 \, a^{12} b^{13} - 1974 \, a^{10} b^{15} + 1890 \, a^{8} b^{17} - 945 \, a^{6} b^{19} + 235 \, a^{4} b^{21} - 15 \, a^{2} b^{23} - 3 \, b^{25}\right)} d \cos\left(d x + c\right)^{4} - {\left(7 \, a^{24} b - 28 \, a^{22} b^{3} - 42 \, a^{20} b^{5} + 484 \, a^{18} b^{7} - 1311 \, a^{16} b^{9} + 1800 \, a^{14} b^{11} - 1260 \, a^{12} b^{13} + 168 \, a^{10} b^{15} + 441 \, a^{8} b^{17} - 364 \, a^{6} b^{19} + 118 \, a^{4} b^{21} - 12 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/420*(210*a^16*b - 1680*a^14*b^3 + 5880*a^12*b^5 - 11760*a^10*b^7 + 14700*a^8*b^9 - 11760*a^6*b^11 + 5880*a^4*b^13 - 1680*a^2*b^15 + 210*b^17 - 210*(a^10*b^7 + 195*a^8*b^9 + 378*a^6*b^11 - 330*a^4*b^13 - 235*a^2*b^15 - 9*b^17)*cos(d*x + c)^8 + 70*(63*a^12*b^5 + 10015*a^10*b^7 + 18468*a^8*b^9 - 14274*a^6*b^11 - 12025*a^4*b^13 - 2157*a^2*b^15 - 90*b^17)*cos(d*x + c)^6 - 14*(525*a^14*b^3 + 59730*a^12*b^5 + 174637*a^10*b^7 + 77130*a^8*b^9 - 194265*a^6*b^11 - 106450*a^4*b^13 - 10785*a^2*b^15 - 522*b^17)*cos(d*x + c)^4 + 2*(735*a^16*b + 37165*a^14*b^3 + 437199*a^12*b^5 + 836549*a^10*b^7 - 111195*a^8*b^9 - 812385*a^6*b^11 - 362915*a^4*b^13 - 23569*a^2*b^15 - 1584*b^17)*cos(d*x + c)^2 + 3360*(7*(15*a^8*b^9 + 63*a^6*b^11 + 45*a^4*b^13 + 5*a^2*b^15)*cos(d*x + c)^8 - 7*(75*a^10*b^7 + 360*a^8*b^9 + 414*a^6*b^11 + 160*a^4*b^13 + 15*a^2*b^15)*cos(d*x + c)^6 + 7*(45*a^12*b^5 + 339*a^10*b^7 + 810*a^8*b^9 + 654*a^6*b^11 + 185*a^4*b^13 + 15*a^2*b^15)*cos(d*x + c)^4 - (15*a^14*b^3 + 378*a^12*b^5 + 1893*a^10*b^7 + 3260*a^8*b^9 + 2121*a^6*b^11 + 490*a^4*b^13 + 35*a^2*b^15)*cos(d*x + c)^2 + ((15*a^7*b^10 + 63*a^5*b^12 + 45*a^3*b^14 + 5*a*b^16)*cos(d*x + c)^8 - 3*(105*a^9*b^8 + 456*a^7*b^10 + 378*a^5*b^12 + 80*a^3*b^14 + 5*a*b^16)*cos(d*x + c)^6 + (525*a^11*b^6 + 2835*a^9*b^8 + 4266*a^7*b^10 + 2254*a^5*b^12 + 345*a^3*b^14 + 15*a*b^16)*cos(d*x + c)^4 - (105*a^13*b^4 + 966*a^11*b^6 + 2835*a^9*b^8 + 2948*a^7*b^10 + 1183*a^5*b^12 + 150*a^3*b^14 + 5*a*b^16)*cos(d*x + c)^2)*sin(d*x + c))*log(b*sin(d*x + c) + a) + 105*(7*(a^11*b^6 - 45*a^9*b^8 - 240*a^8*b^9 - 630*a^7*b^10 - 1008*a^6*b^11 - 1050*a^5*b^12 - 720*a^4*b^13 - 315*a^3*b^14 - 80*a^2*b^15 - 9*a*b^16)*cos(d*x + c)^8 - 7*(5*a^13*b^4 - 222*a^11*b^6 - 1200*a^10*b^7 - 3285*a^9*b^8 - 5760*a^8*b^9 - 7140*a^7*b^10 - 6624*a^6*b^11 - 4725*a^5*b^12 - 2560*a^4*b^13 - 990*a^3*b^14 - 240*a^2*b^15 - 27*a*b^16)*cos(d*x + c)^6 + 7*(3*a^15*b^2 - 125*a^13*b^4 - 720*a^12*b^5 - 2337*a^11*b^6 - 5424*a^10*b^7 - 9585*a^9*b^8 - 12960*a^8*b^9 - 13335*a^7*b^10 - 10464*a^6*b^11 - 6327*a^5*b^12 - 2960*a^4*b^13 - 1035*a^3*b^14 - 240*a^2*b^15 - 27*a*b^16)*cos(d*x + c)^4 - (a^17 - 24*a^15*b^2 - 240*a^14*b^3 - 1540*a^13*b^4 - 6048*a^12*b^5 - 15848*a^11*b^6 - 30288*a^10*b^7 - 44730*a^9*b^8 - 52160*a^8*b^9 - 47784*a^7*b^10 - 33936*a^6*b^11 - 18564*a^5*b^12 - 7840*a^4*b^13 - 2520*a^3*b^14 - 560*a^2*b^15 - 63*a*b^16)*cos(d*x + c)^2 + ((a^10*b^7 - 45*a^8*b^9 - 240*a^7*b^10 - 630*a^6*b^11 - 1008*a^5*b^12 - 1050*a^4*b^13 - 720*a^3*b^14 - 315*a^2*b^15 - 80*a*b^16 - 9*b^17)*cos(d*x + c)^8 - 3*(7*a^12*b^5 - 314*a^10*b^7 - 1680*a^9*b^8 - 4455*a^8*b^9 - 7296*a^7*b^10 - 7980*a^6*b^11 - 6048*a^5*b^12 - 3255*a^4*b^13 - 1280*a^3*b^14 - 378*a^2*b^15 - 80*a*b^16 - 9*b^17)*cos(d*x + c)^6 + (35*a^14*b^3 - 1533*a^12*b^5 - 8400*a^11*b^6 - 23937*a^10*b^7 - 45360*a^9*b^8 - 63345*a^8*b^9 - 68256*a^7*b^10 - 57015*a^6*b^11 - 36064*a^5*b^12 - 16695*a^4*b^13 - 5520*a^3*b^14 - 1323*a^2*b^15 - 240*a*b^16 - 27*b^17)*cos(d*x + c)^4 - (7*a^16*b - 280*a^14*b^3 - 1680*a^13*b^4 - 5964*a^12*b^5 - 15456*a^11*b^6 - 30344*a^10*b^7 - 45360*a^9*b^8 - 52230*a^8*b^9 - 47168*a^7*b^10 - 33768*a^6*b^11 - 18928*a^5*b^12 - 7980*a^4*b^13 - 2400*a^3*b^14 - 504*a^2*b^15 - 80*a*b^16 - 9*b^17)*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) - 105*(7*(a^11*b^6 - 45*a^9*b^8 + 240*a^8*b^9 - 630*a^7*b^10 + 1008*a^6*b^11 - 1050*a^5*b^12 + 720*a^4*b^13 - 315*a^3*b^14 + 80*a^2*b^15 - 9*a*b^16)*cos(d*x + c)^8 - 7*(5*a^13*b^4 - 222*a^11*b^6 + 1200*a^10*b^7 - 3285*a^9*b^8 + 5760*a^8*b^9 - 7140*a^7*b^10 + 6624*a^6*b^11 - 4725*a^5*b^12 + 2560*a^4*b^13 - 990*a^3*b^14 + 240*a^2*b^15 - 27*a*b^16)*cos(d*x + c)^6 + 7*(3*a^15*b^2 - 125*a^13*b^4 + 720*a^12*b^5 - 2337*a^11*b^6 + 5424*a^10*b^7 - 9585*a^9*b^8 + 12960*a^8*b^9 - 13335*a^7*b^10 + 10464*a^6*b^11 - 6327*a^5*b^12 + 2960*a^4*b^13 - 1035*a^3*b^14 + 240*a^2*b^15 - 27*a*b^16)*cos(d*x + c)^4 - (a^17 - 24*a^15*b^2 + 240*a^14*b^3 - 1540*a^13*b^4 + 6048*a^12*b^5 - 15848*a^11*b^6 + 30288*a^10*b^7 - 44730*a^9*b^8 + 52160*a^8*b^9 - 47784*a^7*b^10 + 33936*a^6*b^11 - 18564*a^5*b^12 + 7840*a^4*b^13 - 2520*a^3*b^14 + 560*a^2*b^15 - 63*a*b^16)*cos(d*x + c)^2 + ((a^10*b^7 - 45*a^8*b^9 + 240*a^7*b^10 - 630*a^6*b^11 + 1008*a^5*b^12 - 1050*a^4*b^13 + 720*a^3*b^14 - 315*a^2*b^15 + 80*a*b^16 - 9*b^17)*cos(d*x + c)^8 - 3*(7*a^12*b^5 - 314*a^10*b^7 + 1680*a^9*b^8 - 4455*a^8*b^9 + 7296*a^7*b^10 - 7980*a^6*b^11 + 6048*a^5*b^12 - 3255*a^4*b^13 + 1280*a^3*b^14 - 378*a^2*b^15 + 80*a*b^16 - 9*b^17)*cos(d*x + c)^6 + (35*a^14*b^3 - 1533*a^12*b^5 + 8400*a^11*b^6 - 23937*a^10*b^7 + 45360*a^9*b^8 - 63345*a^8*b^9 + 68256*a^7*b^10 - 57015*a^6*b^11 + 36064*a^5*b^12 - 16695*a^4*b^13 + 5520*a^3*b^14 - 1323*a^2*b^15 + 240*a*b^16 - 27*b^17)*cos(d*x + c)^4 - (7*a^16*b - 280*a^14*b^3 + 1680*a^13*b^4 - 5964*a^12*b^5 + 15456*a^11*b^6 - 30344*a^10*b^7 + 45360*a^9*b^8 - 52230*a^8*b^9 + 47168*a^7*b^10 - 33768*a^6*b^11 + 18928*a^5*b^12 - 7980*a^4*b^13 + 2400*a^3*b^14 - 504*a^2*b^15 + 80*a*b^16 - 9*b^17)*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) - 14*(15*a^17 - 120*a^15*b^2 + 420*a^13*b^4 - 840*a^11*b^6 + 1050*a^9*b^8 - 840*a^7*b^10 + 420*a^5*b^12 - 120*a^3*b^14 + 15*a*b^16 - 15*(7*a^11*b^6 + 1245*a^9*b^8 + 2262*a^7*b^10 - 2166*a^5*b^12 - 1325*a^3*b^14 - 23*a*b^16)*cos(d*x + c)^6 + 5*(105*a^13*b^4 + 14464*a^11*b^6 + 28953*a^9*b^8 - 11736*a^7*b^10 - 23605*a^5*b^12 - 8040*a^3*b^14 - 141*a*b^16)*cos(d*x + c)^4 - (315*a^15*b^2 + 26665*a^13*b^4 + 97499*a^11*b^6 + 88065*a^9*b^8 - 106455*a^7*b^10 - 85325*a^5*b^12 - 20415*a^3*b^14 - 349*a*b^16)*cos(d*x + c)^2)*sin(d*x + c))/(7*(a^19*b^6 - 9*a^17*b^8 + 36*a^15*b^10 - 84*a^13*b^12 + 126*a^11*b^14 - 126*a^9*b^16 + 84*a^7*b^18 - 36*a^5*b^20 + 9*a^3*b^22 - a*b^24)*d*cos(d*x + c)^8 - 7*(5*a^21*b^4 - 42*a^19*b^6 + 153*a^17*b^8 - 312*a^15*b^10 + 378*a^13*b^12 - 252*a^11*b^14 + 42*a^9*b^16 + 72*a^7*b^18 - 63*a^5*b^20 + 22*a^3*b^22 - 3*a*b^24)*d*cos(d*x + c)^6 + 7*(3*a^23*b^2 - 17*a^21*b^4 + 21*a^19*b^6 + 81*a^17*b^8 - 354*a^15*b^10 + 630*a^13*b^12 - 630*a^11*b^14 + 354*a^9*b^16 - 81*a^7*b^18 - 21*a^5*b^20 + 17*a^3*b^22 - 3*a*b^24)*d*cos(d*x + c)^4 - (a^25 + 12*a^23*b^2 - 118*a^21*b^4 + 364*a^19*b^6 - 441*a^17*b^8 - 168*a^15*b^10 + 1260*a^13*b^12 - 1800*a^11*b^14 + 1311*a^9*b^16 - 484*a^7*b^18 + 42*a^5*b^20 + 28*a^3*b^22 - 7*a*b^24)*d*cos(d*x + c)^2 + ((a^18*b^7 - 9*a^16*b^9 + 36*a^14*b^11 - 84*a^12*b^13 + 126*a^10*b^15 - 126*a^8*b^17 + 84*a^6*b^19 - 36*a^4*b^21 + 9*a^2*b^23 - b^25)*d*cos(d*x + c)^8 - 3*(7*a^20*b^5 - 62*a^18*b^7 + 243*a^16*b^9 - 552*a^14*b^11 + 798*a^12*b^13 - 756*a^10*b^15 + 462*a^8*b^17 - 168*a^6*b^19 + 27*a^4*b^21 + 2*a^2*b^23 - b^25)*d*cos(d*x + c)^6 + (35*a^22*b^3 - 273*a^20*b^5 + 885*a^18*b^7 - 1455*a^16*b^9 + 990*a^14*b^11 + 630*a^12*b^13 - 1974*a^10*b^15 + 1890*a^8*b^17 - 945*a^6*b^19 + 235*a^4*b^21 - 15*a^2*b^23 - 3*b^25)*d*cos(d*x + c)^4 - (7*a^24*b - 28*a^22*b^3 - 42*a^20*b^5 + 484*a^18*b^7 - 1311*a^16*b^9 + 1800*a^14*b^11 - 1260*a^12*b^13 + 168*a^10*b^15 + 441*a^8*b^17 - 364*a^6*b^19 + 118*a^4*b^21 - 12*a^2*b^23 - b^25)*d*cos(d*x + c)^2)*sin(d*x + c))","B",0
467,1,3721,0,2.846603," ","integrate(cos(d*x+c)^8/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\left[\frac{23520 \, {\left(a^{9} b^{6} - 4 \, a^{7} b^{8} + 6 \, a^{5} b^{10} - 4 \, a^{3} b^{12} + a b^{14}\right)} d x \cos\left(d x + c\right)^{6} + 2 \, {\left(4356 \, a^{8} b^{7} - 16864 \, a^{6} b^{9} + 24001 \, a^{4} b^{11} - 14309 \, a^{2} b^{13} + 2816 \, b^{15}\right)} \cos\left(d x + c\right)^{7} - 23520 \, {\left(5 \, a^{11} b^{4} - 17 \, a^{9} b^{6} + 18 \, a^{7} b^{8} - 2 \, a^{5} b^{10} - 7 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d x \cos\left(d x + c\right)^{4} - 28 \, {\left(2754 \, a^{10} b^{5} - 9717 \, a^{8} b^{7} + 11528 \, a^{6} b^{9} - 3782 \, a^{4} b^{11} - 1247 \, a^{2} b^{13} + 464 \, b^{15}\right)} \cos\left(d x + c\right)^{5} + 23520 \, {\left(3 \, a^{13} b^{2} - 2 \, a^{11} b^{4} - 19 \, a^{9} b^{6} + 36 \, a^{7} b^{8} - 19 \, a^{5} b^{10} - 2 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d x \cos\left(d x + c\right)^{2} + 70 \, {\left(856 \, a^{12} b^{3} - 1090 \, a^{10} b^{5} - 3477 \, a^{8} b^{7} + 7907 \, a^{6} b^{9} - 4423 \, a^{4} b^{11} + 67 \, a^{2} b^{13} + 160 \, b^{15}\right)} \cos\left(d x + c\right)^{3} - 3360 \, {\left(a^{15} + 17 \, a^{13} b^{2} - 43 \, a^{11} b^{4} - 11 \, a^{9} b^{6} + 99 \, a^{7} b^{8} - 77 \, a^{5} b^{10} + 7 \, a^{3} b^{12} + 7 \, a b^{14}\right)} d x + 105 \, {\left(16 \, a^{14} + 280 \, a^{12} b^{2} - 546 \, a^{10} b^{4} - 413 \, a^{8} b^{6} + 1323 \, a^{6} b^{8} - 735 \, a^{4} b^{10} - 245 \, a^{2} b^{12} - 7 \, {\left(16 \, a^{8} b^{6} - 56 \, a^{6} b^{8} + 70 \, a^{4} b^{10} - 35 \, a^{2} b^{12}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(80 \, a^{10} b^{4} - 232 \, a^{8} b^{6} + 182 \, a^{6} b^{8} + 35 \, a^{4} b^{10} - 105 \, a^{2} b^{12}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(48 \, a^{12} b^{2} - 8 \, a^{10} b^{4} - 302 \, a^{8} b^{6} + 427 \, a^{6} b^{8} - 140 \, a^{4} b^{10} - 105 \, a^{2} b^{12}\right)} \cos\left(d x + c\right)^{2} + {\left(112 \, a^{13} b + 168 \, a^{11} b^{3} - 1134 \, a^{9} b^{5} + 1045 \, a^{7} b^{7} + 189 \, a^{5} b^{9} - 665 \, a^{3} b^{11} - 35 \, a b^{13} - {\left(16 \, a^{7} b^{7} - 56 \, a^{5} b^{9} + 70 \, a^{3} b^{11} - 35 \, a b^{13}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(112 \, a^{9} b^{5} - 376 \, a^{7} b^{7} + 434 \, a^{5} b^{9} - 175 \, a^{3} b^{11} - 35 \, a b^{13}\right)} \cos\left(d x + c\right)^{4} - {\left(560 \, a^{11} b^{3} - 1288 \, a^{9} b^{5} + 146 \, a^{7} b^{7} + 1547 \, a^{5} b^{9} - 1260 \, a^{3} b^{11} - 105 \, a b^{13}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 420 \, {\left(8 \, a^{14} b + 112 \, a^{12} b^{3} - 322 \, a^{10} b^{5} + 63 \, a^{8} b^{7} + 479 \, a^{6} b^{9} - 379 \, a^{4} b^{11} + 31 \, a^{2} b^{13} + 8 \, b^{15}\right)} \cos\left(d x + c\right) + 14 \, {\left(240 \, {\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d x \cos\left(d x + c\right)^{6} - 720 \, {\left(7 \, a^{10} b^{5} - 27 \, a^{8} b^{7} + 38 \, a^{6} b^{9} - 22 \, a^{4} b^{11} + 3 \, a^{2} b^{13} + b^{15}\right)} d x \cos\left(d x + c\right)^{4} - {\left(2676 \, a^{9} b^{6} - 10264 \, a^{7} b^{8} + 14371 \, a^{5} b^{10} - 8204 \, a^{3} b^{12} + 1421 \, a b^{14}\right)} \cos\left(d x + c\right)^{5} + 240 \, {\left(35 \, a^{12} b^{3} - 98 \, a^{10} b^{5} + 45 \, a^{8} b^{7} + 100 \, a^{6} b^{9} - 115 \, a^{4} b^{11} + 30 \, a^{2} b^{13} + 3 \, b^{15}\right)} d x \cos\left(d x + c\right)^{2} + 10 \, {\left(638 \, a^{11} b^{4} - 1925 \, a^{9} b^{6} + 1427 \, a^{7} b^{8} + 861 \, a^{5} b^{10} - 1253 \, a^{3} b^{12} + 252 \, a b^{14}\right)} \cos\left(d x + c\right)^{3} - 240 \, {\left(7 \, a^{14} b + 7 \, a^{12} b^{3} - 77 \, a^{10} b^{5} + 99 \, a^{8} b^{7} - 11 \, a^{6} b^{9} - 43 \, a^{4} b^{11} + 17 \, a^{2} b^{13} + b^{15}\right)} d x - 15 \, {\left(104 \, a^{13} b^{2} + 26 \, a^{11} b^{4} - 897 \, a^{9} b^{6} + 1306 \, a^{7} b^{8} - 308 \, a^{5} b^{10} - 308 \, a^{3} b^{12} + 77 \, a b^{14}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3360 \, {\left(7 \, {\left(a^{9} b^{14} - 4 \, a^{7} b^{16} + 6 \, a^{5} b^{18} - 4 \, a^{3} b^{20} + a b^{22}\right)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{11} b^{12} - 17 \, a^{9} b^{14} + 18 \, a^{7} b^{16} - 2 \, a^{5} b^{18} - 7 \, a^{3} b^{20} + 3 \, a b^{22}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{13} b^{10} - 2 \, a^{11} b^{12} - 19 \, a^{9} b^{14} + 36 \, a^{7} b^{16} - 19 \, a^{5} b^{18} - 2 \, a^{3} b^{20} + 3 \, a b^{22}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{15} b^{8} + 17 \, a^{13} b^{10} - 43 \, a^{11} b^{12} - 11 \, a^{9} b^{14} + 99 \, a^{7} b^{16} - 77 \, a^{5} b^{18} + 7 \, a^{3} b^{20} + 7 \, a b^{22}\right)} d + {\left({\left(a^{8} b^{15} - 4 \, a^{6} b^{17} + 6 \, a^{4} b^{19} - 4 \, a^{2} b^{21} + b^{23}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{10} b^{13} - 27 \, a^{8} b^{15} + 38 \, a^{6} b^{17} - 22 \, a^{4} b^{19} + 3 \, a^{2} b^{21} + b^{23}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{12} b^{11} - 98 \, a^{10} b^{13} + 45 \, a^{8} b^{15} + 100 \, a^{6} b^{17} - 115 \, a^{4} b^{19} + 30 \, a^{2} b^{21} + 3 \, b^{23}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{14} b^{9} + 7 \, a^{12} b^{11} - 77 \, a^{10} b^{13} + 99 \, a^{8} b^{15} - 11 \, a^{6} b^{17} - 43 \, a^{4} b^{19} + 17 \, a^{2} b^{21} + b^{23}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{11760 \, {\left(a^{9} b^{6} - 4 \, a^{7} b^{8} + 6 \, a^{5} b^{10} - 4 \, a^{3} b^{12} + a b^{14}\right)} d x \cos\left(d x + c\right)^{6} + {\left(4356 \, a^{8} b^{7} - 16864 \, a^{6} b^{9} + 24001 \, a^{4} b^{11} - 14309 \, a^{2} b^{13} + 2816 \, b^{15}\right)} \cos\left(d x + c\right)^{7} - 11760 \, {\left(5 \, a^{11} b^{4} - 17 \, a^{9} b^{6} + 18 \, a^{7} b^{8} - 2 \, a^{5} b^{10} - 7 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d x \cos\left(d x + c\right)^{4} - 14 \, {\left(2754 \, a^{10} b^{5} - 9717 \, a^{8} b^{7} + 11528 \, a^{6} b^{9} - 3782 \, a^{4} b^{11} - 1247 \, a^{2} b^{13} + 464 \, b^{15}\right)} \cos\left(d x + c\right)^{5} + 11760 \, {\left(3 \, a^{13} b^{2} - 2 \, a^{11} b^{4} - 19 \, a^{9} b^{6} + 36 \, a^{7} b^{8} - 19 \, a^{5} b^{10} - 2 \, a^{3} b^{12} + 3 \, a b^{14}\right)} d x \cos\left(d x + c\right)^{2} + 35 \, {\left(856 \, a^{12} b^{3} - 1090 \, a^{10} b^{5} - 3477 \, a^{8} b^{7} + 7907 \, a^{6} b^{9} - 4423 \, a^{4} b^{11} + 67 \, a^{2} b^{13} + 160 \, b^{15}\right)} \cos\left(d x + c\right)^{3} - 1680 \, {\left(a^{15} + 17 \, a^{13} b^{2} - 43 \, a^{11} b^{4} - 11 \, a^{9} b^{6} + 99 \, a^{7} b^{8} - 77 \, a^{5} b^{10} + 7 \, a^{3} b^{12} + 7 \, a b^{14}\right)} d x - 105 \, {\left(16 \, a^{14} + 280 \, a^{12} b^{2} - 546 \, a^{10} b^{4} - 413 \, a^{8} b^{6} + 1323 \, a^{6} b^{8} - 735 \, a^{4} b^{10} - 245 \, a^{2} b^{12} - 7 \, {\left(16 \, a^{8} b^{6} - 56 \, a^{6} b^{8} + 70 \, a^{4} b^{10} - 35 \, a^{2} b^{12}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(80 \, a^{10} b^{4} - 232 \, a^{8} b^{6} + 182 \, a^{6} b^{8} + 35 \, a^{4} b^{10} - 105 \, a^{2} b^{12}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(48 \, a^{12} b^{2} - 8 \, a^{10} b^{4} - 302 \, a^{8} b^{6} + 427 \, a^{6} b^{8} - 140 \, a^{4} b^{10} - 105 \, a^{2} b^{12}\right)} \cos\left(d x + c\right)^{2} + {\left(112 \, a^{13} b + 168 \, a^{11} b^{3} - 1134 \, a^{9} b^{5} + 1045 \, a^{7} b^{7} + 189 \, a^{5} b^{9} - 665 \, a^{3} b^{11} - 35 \, a b^{13} - {\left(16 \, a^{7} b^{7} - 56 \, a^{5} b^{9} + 70 \, a^{3} b^{11} - 35 \, a b^{13}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(112 \, a^{9} b^{5} - 376 \, a^{7} b^{7} + 434 \, a^{5} b^{9} - 175 \, a^{3} b^{11} - 35 \, a b^{13}\right)} \cos\left(d x + c\right)^{4} - {\left(560 \, a^{11} b^{3} - 1288 \, a^{9} b^{5} + 146 \, a^{7} b^{7} + 1547 \, a^{5} b^{9} - 1260 \, a^{3} b^{11} - 105 \, a b^{13}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 210 \, {\left(8 \, a^{14} b + 112 \, a^{12} b^{3} - 322 \, a^{10} b^{5} + 63 \, a^{8} b^{7} + 479 \, a^{6} b^{9} - 379 \, a^{4} b^{11} + 31 \, a^{2} b^{13} + 8 \, b^{15}\right)} \cos\left(d x + c\right) + 7 \, {\left(240 \, {\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d x \cos\left(d x + c\right)^{6} - 720 \, {\left(7 \, a^{10} b^{5} - 27 \, a^{8} b^{7} + 38 \, a^{6} b^{9} - 22 \, a^{4} b^{11} + 3 \, a^{2} b^{13} + b^{15}\right)} d x \cos\left(d x + c\right)^{4} - {\left(2676 \, a^{9} b^{6} - 10264 \, a^{7} b^{8} + 14371 \, a^{5} b^{10} - 8204 \, a^{3} b^{12} + 1421 \, a b^{14}\right)} \cos\left(d x + c\right)^{5} + 240 \, {\left(35 \, a^{12} b^{3} - 98 \, a^{10} b^{5} + 45 \, a^{8} b^{7} + 100 \, a^{6} b^{9} - 115 \, a^{4} b^{11} + 30 \, a^{2} b^{13} + 3 \, b^{15}\right)} d x \cos\left(d x + c\right)^{2} + 10 \, {\left(638 \, a^{11} b^{4} - 1925 \, a^{9} b^{6} + 1427 \, a^{7} b^{8} + 861 \, a^{5} b^{10} - 1253 \, a^{3} b^{12} + 252 \, a b^{14}\right)} \cos\left(d x + c\right)^{3} - 240 \, {\left(7 \, a^{14} b + 7 \, a^{12} b^{3} - 77 \, a^{10} b^{5} + 99 \, a^{8} b^{7} - 11 \, a^{6} b^{9} - 43 \, a^{4} b^{11} + 17 \, a^{2} b^{13} + b^{15}\right)} d x - 15 \, {\left(104 \, a^{13} b^{2} + 26 \, a^{11} b^{4} - 897 \, a^{9} b^{6} + 1306 \, a^{7} b^{8} - 308 \, a^{5} b^{10} - 308 \, a^{3} b^{12} + 77 \, a b^{14}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, {\left(7 \, {\left(a^{9} b^{14} - 4 \, a^{7} b^{16} + 6 \, a^{5} b^{18} - 4 \, a^{3} b^{20} + a b^{22}\right)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{11} b^{12} - 17 \, a^{9} b^{14} + 18 \, a^{7} b^{16} - 2 \, a^{5} b^{18} - 7 \, a^{3} b^{20} + 3 \, a b^{22}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{13} b^{10} - 2 \, a^{11} b^{12} - 19 \, a^{9} b^{14} + 36 \, a^{7} b^{16} - 19 \, a^{5} b^{18} - 2 \, a^{3} b^{20} + 3 \, a b^{22}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{15} b^{8} + 17 \, a^{13} b^{10} - 43 \, a^{11} b^{12} - 11 \, a^{9} b^{14} + 99 \, a^{7} b^{16} - 77 \, a^{5} b^{18} + 7 \, a^{3} b^{20} + 7 \, a b^{22}\right)} d + {\left({\left(a^{8} b^{15} - 4 \, a^{6} b^{17} + 6 \, a^{4} b^{19} - 4 \, a^{2} b^{21} + b^{23}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{10} b^{13} - 27 \, a^{8} b^{15} + 38 \, a^{6} b^{17} - 22 \, a^{4} b^{19} + 3 \, a^{2} b^{21} + b^{23}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{12} b^{11} - 98 \, a^{10} b^{13} + 45 \, a^{8} b^{15} + 100 \, a^{6} b^{17} - 115 \, a^{4} b^{19} + 30 \, a^{2} b^{21} + 3 \, b^{23}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{14} b^{9} + 7 \, a^{12} b^{11} - 77 \, a^{10} b^{13} + 99 \, a^{8} b^{15} - 11 \, a^{6} b^{17} - 43 \, a^{4} b^{19} + 17 \, a^{2} b^{21} + b^{23}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/3360*(23520*(a^9*b^6 - 4*a^7*b^8 + 6*a^5*b^10 - 4*a^3*b^12 + a*b^14)*d*x*cos(d*x + c)^6 + 2*(4356*a^8*b^7 - 16864*a^6*b^9 + 24001*a^4*b^11 - 14309*a^2*b^13 + 2816*b^15)*cos(d*x + c)^7 - 23520*(5*a^11*b^4 - 17*a^9*b^6 + 18*a^7*b^8 - 2*a^5*b^10 - 7*a^3*b^12 + 3*a*b^14)*d*x*cos(d*x + c)^4 - 28*(2754*a^10*b^5 - 9717*a^8*b^7 + 11528*a^6*b^9 - 3782*a^4*b^11 - 1247*a^2*b^13 + 464*b^15)*cos(d*x + c)^5 + 23520*(3*a^13*b^2 - 2*a^11*b^4 - 19*a^9*b^6 + 36*a^7*b^8 - 19*a^5*b^10 - 2*a^3*b^12 + 3*a*b^14)*d*x*cos(d*x + c)^2 + 70*(856*a^12*b^3 - 1090*a^10*b^5 - 3477*a^8*b^7 + 7907*a^6*b^9 - 4423*a^4*b^11 + 67*a^2*b^13 + 160*b^15)*cos(d*x + c)^3 - 3360*(a^15 + 17*a^13*b^2 - 43*a^11*b^4 - 11*a^9*b^6 + 99*a^7*b^8 - 77*a^5*b^10 + 7*a^3*b^12 + 7*a*b^14)*d*x + 105*(16*a^14 + 280*a^12*b^2 - 546*a^10*b^4 - 413*a^8*b^6 + 1323*a^6*b^8 - 735*a^4*b^10 - 245*a^2*b^12 - 7*(16*a^8*b^6 - 56*a^6*b^8 + 70*a^4*b^10 - 35*a^2*b^12)*cos(d*x + c)^6 + 7*(80*a^10*b^4 - 232*a^8*b^6 + 182*a^6*b^8 + 35*a^4*b^10 - 105*a^2*b^12)*cos(d*x + c)^4 - 7*(48*a^12*b^2 - 8*a^10*b^4 - 302*a^8*b^6 + 427*a^6*b^8 - 140*a^4*b^10 - 105*a^2*b^12)*cos(d*x + c)^2 + (112*a^13*b + 168*a^11*b^3 - 1134*a^9*b^5 + 1045*a^7*b^7 + 189*a^5*b^9 - 665*a^3*b^11 - 35*a*b^13 - (16*a^7*b^7 - 56*a^5*b^9 + 70*a^3*b^11 - 35*a*b^13)*cos(d*x + c)^6 + 3*(112*a^9*b^5 - 376*a^7*b^7 + 434*a^5*b^9 - 175*a^3*b^11 - 35*a*b^13)*cos(d*x + c)^4 - (560*a^11*b^3 - 1288*a^9*b^5 + 146*a^7*b^7 + 1547*a^5*b^9 - 1260*a^3*b^11 - 105*a*b^13)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 420*(8*a^14*b + 112*a^12*b^3 - 322*a^10*b^5 + 63*a^8*b^7 + 479*a^6*b^9 - 379*a^4*b^11 + 31*a^2*b^13 + 8*b^15)*cos(d*x + c) + 14*(240*(a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d*x*cos(d*x + c)^6 - 720*(7*a^10*b^5 - 27*a^8*b^7 + 38*a^6*b^9 - 22*a^4*b^11 + 3*a^2*b^13 + b^15)*d*x*cos(d*x + c)^4 - (2676*a^9*b^6 - 10264*a^7*b^8 + 14371*a^5*b^10 - 8204*a^3*b^12 + 1421*a*b^14)*cos(d*x + c)^5 + 240*(35*a^12*b^3 - 98*a^10*b^5 + 45*a^8*b^7 + 100*a^6*b^9 - 115*a^4*b^11 + 30*a^2*b^13 + 3*b^15)*d*x*cos(d*x + c)^2 + 10*(638*a^11*b^4 - 1925*a^9*b^6 + 1427*a^7*b^8 + 861*a^5*b^10 - 1253*a^3*b^12 + 252*a*b^14)*cos(d*x + c)^3 - 240*(7*a^14*b + 7*a^12*b^3 - 77*a^10*b^5 + 99*a^8*b^7 - 11*a^6*b^9 - 43*a^4*b^11 + 17*a^2*b^13 + b^15)*d*x - 15*(104*a^13*b^2 + 26*a^11*b^4 - 897*a^9*b^6 + 1306*a^7*b^8 - 308*a^5*b^10 - 308*a^3*b^12 + 77*a*b^14)*cos(d*x + c))*sin(d*x + c))/(7*(a^9*b^14 - 4*a^7*b^16 + 6*a^5*b^18 - 4*a^3*b^20 + a*b^22)*d*cos(d*x + c)^6 - 7*(5*a^11*b^12 - 17*a^9*b^14 + 18*a^7*b^16 - 2*a^5*b^18 - 7*a^3*b^20 + 3*a*b^22)*d*cos(d*x + c)^4 + 7*(3*a^13*b^10 - 2*a^11*b^12 - 19*a^9*b^14 + 36*a^7*b^16 - 19*a^5*b^18 - 2*a^3*b^20 + 3*a*b^22)*d*cos(d*x + c)^2 - (a^15*b^8 + 17*a^13*b^10 - 43*a^11*b^12 - 11*a^9*b^14 + 99*a^7*b^16 - 77*a^5*b^18 + 7*a^3*b^20 + 7*a*b^22)*d + ((a^8*b^15 - 4*a^6*b^17 + 6*a^4*b^19 - 4*a^2*b^21 + b^23)*d*cos(d*x + c)^6 - 3*(7*a^10*b^13 - 27*a^8*b^15 + 38*a^6*b^17 - 22*a^4*b^19 + 3*a^2*b^21 + b^23)*d*cos(d*x + c)^4 + (35*a^12*b^11 - 98*a^10*b^13 + 45*a^8*b^15 + 100*a^6*b^17 - 115*a^4*b^19 + 30*a^2*b^21 + 3*b^23)*d*cos(d*x + c)^2 - (7*a^14*b^9 + 7*a^12*b^11 - 77*a^10*b^13 + 99*a^8*b^15 - 11*a^6*b^17 - 43*a^4*b^19 + 17*a^2*b^21 + b^23)*d)*sin(d*x + c)), 1/1680*(11760*(a^9*b^6 - 4*a^7*b^8 + 6*a^5*b^10 - 4*a^3*b^12 + a*b^14)*d*x*cos(d*x + c)^6 + (4356*a^8*b^7 - 16864*a^6*b^9 + 24001*a^4*b^11 - 14309*a^2*b^13 + 2816*b^15)*cos(d*x + c)^7 - 11760*(5*a^11*b^4 - 17*a^9*b^6 + 18*a^7*b^8 - 2*a^5*b^10 - 7*a^3*b^12 + 3*a*b^14)*d*x*cos(d*x + c)^4 - 14*(2754*a^10*b^5 - 9717*a^8*b^7 + 11528*a^6*b^9 - 3782*a^4*b^11 - 1247*a^2*b^13 + 464*b^15)*cos(d*x + c)^5 + 11760*(3*a^13*b^2 - 2*a^11*b^4 - 19*a^9*b^6 + 36*a^7*b^8 - 19*a^5*b^10 - 2*a^3*b^12 + 3*a*b^14)*d*x*cos(d*x + c)^2 + 35*(856*a^12*b^3 - 1090*a^10*b^5 - 3477*a^8*b^7 + 7907*a^6*b^9 - 4423*a^4*b^11 + 67*a^2*b^13 + 160*b^15)*cos(d*x + c)^3 - 1680*(a^15 + 17*a^13*b^2 - 43*a^11*b^4 - 11*a^9*b^6 + 99*a^7*b^8 - 77*a^5*b^10 + 7*a^3*b^12 + 7*a*b^14)*d*x - 105*(16*a^14 + 280*a^12*b^2 - 546*a^10*b^4 - 413*a^8*b^6 + 1323*a^6*b^8 - 735*a^4*b^10 - 245*a^2*b^12 - 7*(16*a^8*b^6 - 56*a^6*b^8 + 70*a^4*b^10 - 35*a^2*b^12)*cos(d*x + c)^6 + 7*(80*a^10*b^4 - 232*a^8*b^6 + 182*a^6*b^8 + 35*a^4*b^10 - 105*a^2*b^12)*cos(d*x + c)^4 - 7*(48*a^12*b^2 - 8*a^10*b^4 - 302*a^8*b^6 + 427*a^6*b^8 - 140*a^4*b^10 - 105*a^2*b^12)*cos(d*x + c)^2 + (112*a^13*b + 168*a^11*b^3 - 1134*a^9*b^5 + 1045*a^7*b^7 + 189*a^5*b^9 - 665*a^3*b^11 - 35*a*b^13 - (16*a^7*b^7 - 56*a^5*b^9 + 70*a^3*b^11 - 35*a*b^13)*cos(d*x + c)^6 + 3*(112*a^9*b^5 - 376*a^7*b^7 + 434*a^5*b^9 - 175*a^3*b^11 - 35*a*b^13)*cos(d*x + c)^4 - (560*a^11*b^3 - 1288*a^9*b^5 + 146*a^7*b^7 + 1547*a^5*b^9 - 1260*a^3*b^11 - 105*a*b^13)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 210*(8*a^14*b + 112*a^12*b^3 - 322*a^10*b^5 + 63*a^8*b^7 + 479*a^6*b^9 - 379*a^4*b^11 + 31*a^2*b^13 + 8*b^15)*cos(d*x + c) + 7*(240*(a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d*x*cos(d*x + c)^6 - 720*(7*a^10*b^5 - 27*a^8*b^7 + 38*a^6*b^9 - 22*a^4*b^11 + 3*a^2*b^13 + b^15)*d*x*cos(d*x + c)^4 - (2676*a^9*b^6 - 10264*a^7*b^8 + 14371*a^5*b^10 - 8204*a^3*b^12 + 1421*a*b^14)*cos(d*x + c)^5 + 240*(35*a^12*b^3 - 98*a^10*b^5 + 45*a^8*b^7 + 100*a^6*b^9 - 115*a^4*b^11 + 30*a^2*b^13 + 3*b^15)*d*x*cos(d*x + c)^2 + 10*(638*a^11*b^4 - 1925*a^9*b^6 + 1427*a^7*b^8 + 861*a^5*b^10 - 1253*a^3*b^12 + 252*a*b^14)*cos(d*x + c)^3 - 240*(7*a^14*b + 7*a^12*b^3 - 77*a^10*b^5 + 99*a^8*b^7 - 11*a^6*b^9 - 43*a^4*b^11 + 17*a^2*b^13 + b^15)*d*x - 15*(104*a^13*b^2 + 26*a^11*b^4 - 897*a^9*b^6 + 1306*a^7*b^8 - 308*a^5*b^10 - 308*a^3*b^12 + 77*a*b^14)*cos(d*x + c))*sin(d*x + c))/(7*(a^9*b^14 - 4*a^7*b^16 + 6*a^5*b^18 - 4*a^3*b^20 + a*b^22)*d*cos(d*x + c)^6 - 7*(5*a^11*b^12 - 17*a^9*b^14 + 18*a^7*b^16 - 2*a^5*b^18 - 7*a^3*b^20 + 3*a*b^22)*d*cos(d*x + c)^4 + 7*(3*a^13*b^10 - 2*a^11*b^12 - 19*a^9*b^14 + 36*a^7*b^16 - 19*a^5*b^18 - 2*a^3*b^20 + 3*a*b^22)*d*cos(d*x + c)^2 - (a^15*b^8 + 17*a^13*b^10 - 43*a^11*b^12 - 11*a^9*b^14 + 99*a^7*b^16 - 77*a^5*b^18 + 7*a^3*b^20 + 7*a*b^22)*d + ((a^8*b^15 - 4*a^6*b^17 + 6*a^4*b^19 - 4*a^2*b^21 + b^23)*d*cos(d*x + c)^6 - 3*(7*a^10*b^13 - 27*a^8*b^15 + 38*a^6*b^17 - 22*a^4*b^19 + 3*a^2*b^21 + b^23)*d*cos(d*x + c)^4 + (35*a^12*b^11 - 98*a^10*b^13 + 45*a^8*b^15 + 100*a^6*b^17 - 115*a^4*b^19 + 30*a^2*b^21 + 3*b^23)*d*cos(d*x + c)^2 - (7*a^14*b^9 + 7*a^12*b^11 - 77*a^10*b^13 + 99*a^8*b^15 - 11*a^6*b^17 - 43*a^4*b^19 + 17*a^2*b^21 + b^23)*d)*sin(d*x + c))]","B",0
468,1,2250,0,1.705914," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(8 \, a^{8} b - 46 \, a^{6} b^{3} + 125 \, a^{4} b^{5} - 39 \, a^{2} b^{7} - 48 \, b^{9}\right)} \cos\left(d x + c\right)^{7} + 28 \, {\left(7 \, a^{8} b - 56 \, a^{6} b^{3} - 44 \, a^{4} b^{5} + 93 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{5} + 70 \, {\left(7 \, a^{8} b + 83 \, a^{6} b^{3} - 43 \, a^{4} b^{5} - 47 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(7 \, a^{2} b^{6} \cos\left(d x + c\right)^{6} - a^{8} - 21 \, a^{6} b^{2} - 35 \, a^{4} b^{4} - 7 \, a^{2} b^{6} - 7 \, {\left(5 \, a^{4} b^{4} + 3 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{6} b^{2} + 10 \, a^{4} b^{4} + 3 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a b^{7} \cos\left(d x + c\right)^{6} - 7 \, a^{7} b - 35 \, a^{5} b^{3} - 21 \, a^{3} b^{5} - a b^{7} - 3 \, {\left(7 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(35 \, a^{5} b^{3} + 42 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 420 \, {\left(3 \, a^{8} b + 7 \, a^{6} b^{3} - 7 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right) - 14 \, {\left({\left(8 \, a^{9} - 46 \, a^{7} b^{2} + 125 \, a^{5} b^{4} - 54 \, a^{3} b^{6} - 33 \, a b^{8}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(a^{9} - 11 \, a^{7} b^{2} - 25 \, a^{5} b^{4} + 31 \, a^{3} b^{6} + 4 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(a^{9} + 14 \, a^{7} b^{2} - 14 \, a^{3} b^{6} - a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{672 \, {\left(7 \, {\left(a^{11} b^{6} - 5 \, a^{9} b^{8} + 10 \, a^{7} b^{10} - 10 \, a^{5} b^{12} + 5 \, a^{3} b^{14} - a b^{16}\right)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{13} b^{4} - 22 \, a^{11} b^{6} + 35 \, a^{9} b^{8} - 20 \, a^{7} b^{10} - 5 \, a^{5} b^{12} + 10 \, a^{3} b^{14} - 3 \, a b^{16}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{15} b^{2} - 5 \, a^{13} b^{4} - 17 \, a^{11} b^{6} + 55 \, a^{9} b^{8} - 55 \, a^{7} b^{10} + 17 \, a^{5} b^{12} + 5 \, a^{3} b^{14} - 3 \, a b^{16}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{17} + 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} + 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} - 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d + {\left({\left(a^{10} b^{7} - 5 \, a^{8} b^{9} + 10 \, a^{6} b^{11} - 10 \, a^{4} b^{13} + 5 \, a^{2} b^{15} - b^{17}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{12} b^{5} - 34 \, a^{10} b^{7} + 65 \, a^{8} b^{9} - 60 \, a^{6} b^{11} + 25 \, a^{4} b^{13} - 2 \, a^{2} b^{15} - b^{17}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{14} b^{3} - 133 \, a^{12} b^{5} + 143 \, a^{10} b^{7} + 55 \, a^{8} b^{9} - 215 \, a^{6} b^{11} + 145 \, a^{4} b^{13} - 27 \, a^{2} b^{15} - 3 \, b^{17}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{16} b - 84 \, a^{12} b^{5} + 176 \, a^{10} b^{7} - 110 \, a^{8} b^{9} - 32 \, a^{6} b^{11} + 60 \, a^{4} b^{13} - 16 \, a^{2} b^{15} - b^{17}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{{\left(8 \, a^{8} b - 46 \, a^{6} b^{3} + 125 \, a^{4} b^{5} - 39 \, a^{2} b^{7} - 48 \, b^{9}\right)} \cos\left(d x + c\right)^{7} + 14 \, {\left(7 \, a^{8} b - 56 \, a^{6} b^{3} - 44 \, a^{4} b^{5} + 93 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{5} + 35 \, {\left(7 \, a^{8} b + 83 \, a^{6} b^{3} - 43 \, a^{4} b^{5} - 47 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(7 \, a^{2} b^{6} \cos\left(d x + c\right)^{6} - a^{8} - 21 \, a^{6} b^{2} - 35 \, a^{4} b^{4} - 7 \, a^{2} b^{6} - 7 \, {\left(5 \, a^{4} b^{4} + 3 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{6} b^{2} + 10 \, a^{4} b^{4} + 3 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a b^{7} \cos\left(d x + c\right)^{6} - 7 \, a^{7} b - 35 \, a^{5} b^{3} - 21 \, a^{3} b^{5} - a b^{7} - 3 \, {\left(7 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(35 \, a^{5} b^{3} + 42 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 210 \, {\left(3 \, a^{8} b + 7 \, a^{6} b^{3} - 7 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right) - 7 \, {\left({\left(8 \, a^{9} - 46 \, a^{7} b^{2} + 125 \, a^{5} b^{4} - 54 \, a^{3} b^{6} - 33 \, a b^{8}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(a^{9} - 11 \, a^{7} b^{2} - 25 \, a^{5} b^{4} + 31 \, a^{3} b^{6} + 4 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(a^{9} + 14 \, a^{7} b^{2} - 14 \, a^{3} b^{6} - a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{336 \, {\left(7 \, {\left(a^{11} b^{6} - 5 \, a^{9} b^{8} + 10 \, a^{7} b^{10} - 10 \, a^{5} b^{12} + 5 \, a^{3} b^{14} - a b^{16}\right)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{13} b^{4} - 22 \, a^{11} b^{6} + 35 \, a^{9} b^{8} - 20 \, a^{7} b^{10} - 5 \, a^{5} b^{12} + 10 \, a^{3} b^{14} - 3 \, a b^{16}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{15} b^{2} - 5 \, a^{13} b^{4} - 17 \, a^{11} b^{6} + 55 \, a^{9} b^{8} - 55 \, a^{7} b^{10} + 17 \, a^{5} b^{12} + 5 \, a^{3} b^{14} - 3 \, a b^{16}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{17} + 16 \, a^{15} b^{2} - 60 \, a^{13} b^{4} + 32 \, a^{11} b^{6} + 110 \, a^{9} b^{8} - 176 \, a^{7} b^{10} + 84 \, a^{5} b^{12} - 7 \, a b^{16}\right)} d + {\left({\left(a^{10} b^{7} - 5 \, a^{8} b^{9} + 10 \, a^{6} b^{11} - 10 \, a^{4} b^{13} + 5 \, a^{2} b^{15} - b^{17}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{12} b^{5} - 34 \, a^{10} b^{7} + 65 \, a^{8} b^{9} - 60 \, a^{6} b^{11} + 25 \, a^{4} b^{13} - 2 \, a^{2} b^{15} - b^{17}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{14} b^{3} - 133 \, a^{12} b^{5} + 143 \, a^{10} b^{7} + 55 \, a^{8} b^{9} - 215 \, a^{6} b^{11} + 145 \, a^{4} b^{13} - 27 \, a^{2} b^{15} - 3 \, b^{17}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{16} b - 84 \, a^{12} b^{5} + 176 \, a^{10} b^{7} - 110 \, a^{8} b^{9} - 32 \, a^{6} b^{11} + 60 \, a^{4} b^{13} - 16 \, a^{2} b^{15} - b^{17}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/672*(2*(8*a^8*b - 46*a^6*b^3 + 125*a^4*b^5 - 39*a^2*b^7 - 48*b^9)*cos(d*x + c)^7 + 28*(7*a^8*b - 56*a^6*b^3 - 44*a^4*b^5 + 93*a^2*b^7)*cos(d*x + c)^5 + 70*(7*a^8*b + 83*a^6*b^3 - 43*a^4*b^5 - 47*a^2*b^7)*cos(d*x + c)^3 - 105*(7*a^2*b^6*cos(d*x + c)^6 - a^8 - 21*a^6*b^2 - 35*a^4*b^4 - 7*a^2*b^6 - 7*(5*a^4*b^4 + 3*a^2*b^6)*cos(d*x + c)^4 + 7*(3*a^6*b^2 + 10*a^4*b^4 + 3*a^2*b^6)*cos(d*x + c)^2 + (a*b^7*cos(d*x + c)^6 - 7*a^7*b - 35*a^5*b^3 - 21*a^3*b^5 - a*b^7 - 3*(7*a^3*b^5 + a*b^7)*cos(d*x + c)^4 + (35*a^5*b^3 + 42*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 420*(3*a^8*b + 7*a^6*b^3 - 7*a^4*b^5 - 3*a^2*b^7)*cos(d*x + c) - 14*((8*a^9 - 46*a^7*b^2 + 125*a^5*b^4 - 54*a^3*b^6 - 33*a*b^8)*cos(d*x + c)^5 + 10*(a^9 - 11*a^7*b^2 - 25*a^5*b^4 + 31*a^3*b^6 + 4*a*b^8)*cos(d*x + c)^3 + 15*(a^9 + 14*a^7*b^2 - 14*a^3*b^6 - a*b^8)*cos(d*x + c))*sin(d*x + c))/(7*(a^11*b^6 - 5*a^9*b^8 + 10*a^7*b^10 - 10*a^5*b^12 + 5*a^3*b^14 - a*b^16)*d*cos(d*x + c)^6 - 7*(5*a^13*b^4 - 22*a^11*b^6 + 35*a^9*b^8 - 20*a^7*b^10 - 5*a^5*b^12 + 10*a^3*b^14 - 3*a*b^16)*d*cos(d*x + c)^4 + 7*(3*a^15*b^2 - 5*a^13*b^4 - 17*a^11*b^6 + 55*a^9*b^8 - 55*a^7*b^10 + 17*a^5*b^12 + 5*a^3*b^14 - 3*a*b^16)*d*cos(d*x + c)^2 - (a^17 + 16*a^15*b^2 - 60*a^13*b^4 + 32*a^11*b^6 + 110*a^9*b^8 - 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d + ((a^10*b^7 - 5*a^8*b^9 + 10*a^6*b^11 - 10*a^4*b^13 + 5*a^2*b^15 - b^17)*d*cos(d*x + c)^6 - 3*(7*a^12*b^5 - 34*a^10*b^7 + 65*a^8*b^9 - 60*a^6*b^11 + 25*a^4*b^13 - 2*a^2*b^15 - b^17)*d*cos(d*x + c)^4 + (35*a^14*b^3 - 133*a^12*b^5 + 143*a^10*b^7 + 55*a^8*b^9 - 215*a^6*b^11 + 145*a^4*b^13 - 27*a^2*b^15 - 3*b^17)*d*cos(d*x + c)^2 - (7*a^16*b - 84*a^12*b^5 + 176*a^10*b^7 - 110*a^8*b^9 - 32*a^6*b^11 + 60*a^4*b^13 - 16*a^2*b^15 - b^17)*d)*sin(d*x + c)), 1/336*((8*a^8*b - 46*a^6*b^3 + 125*a^4*b^5 - 39*a^2*b^7 - 48*b^9)*cos(d*x + c)^7 + 14*(7*a^8*b - 56*a^6*b^3 - 44*a^4*b^5 + 93*a^2*b^7)*cos(d*x + c)^5 + 35*(7*a^8*b + 83*a^6*b^3 - 43*a^4*b^5 - 47*a^2*b^7)*cos(d*x + c)^3 - 105*(7*a^2*b^6*cos(d*x + c)^6 - a^8 - 21*a^6*b^2 - 35*a^4*b^4 - 7*a^2*b^6 - 7*(5*a^4*b^4 + 3*a^2*b^6)*cos(d*x + c)^4 + 7*(3*a^6*b^2 + 10*a^4*b^4 + 3*a^2*b^6)*cos(d*x + c)^2 + (a*b^7*cos(d*x + c)^6 - 7*a^7*b - 35*a^5*b^3 - 21*a^3*b^5 - a*b^7 - 3*(7*a^3*b^5 + a*b^7)*cos(d*x + c)^4 + (35*a^5*b^3 + 42*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 210*(3*a^8*b + 7*a^6*b^3 - 7*a^4*b^5 - 3*a^2*b^7)*cos(d*x + c) - 7*((8*a^9 - 46*a^7*b^2 + 125*a^5*b^4 - 54*a^3*b^6 - 33*a*b^8)*cos(d*x + c)^5 + 10*(a^9 - 11*a^7*b^2 - 25*a^5*b^4 + 31*a^3*b^6 + 4*a*b^8)*cos(d*x + c)^3 + 15*(a^9 + 14*a^7*b^2 - 14*a^3*b^6 - a*b^8)*cos(d*x + c))*sin(d*x + c))/(7*(a^11*b^6 - 5*a^9*b^8 + 10*a^7*b^10 - 10*a^5*b^12 + 5*a^3*b^14 - a*b^16)*d*cos(d*x + c)^6 - 7*(5*a^13*b^4 - 22*a^11*b^6 + 35*a^9*b^8 - 20*a^7*b^10 - 5*a^5*b^12 + 10*a^3*b^14 - 3*a*b^16)*d*cos(d*x + c)^4 + 7*(3*a^15*b^2 - 5*a^13*b^4 - 17*a^11*b^6 + 55*a^9*b^8 - 55*a^7*b^10 + 17*a^5*b^12 + 5*a^3*b^14 - 3*a*b^16)*d*cos(d*x + c)^2 - (a^17 + 16*a^15*b^2 - 60*a^13*b^4 + 32*a^11*b^6 + 110*a^9*b^8 - 176*a^7*b^10 + 84*a^5*b^12 - 7*a*b^16)*d + ((a^10*b^7 - 5*a^8*b^9 + 10*a^6*b^11 - 10*a^4*b^13 + 5*a^2*b^15 - b^17)*d*cos(d*x + c)^6 - 3*(7*a^12*b^5 - 34*a^10*b^7 + 65*a^8*b^9 - 60*a^6*b^11 + 25*a^4*b^13 - 2*a^2*b^15 - b^17)*d*cos(d*x + c)^4 + (35*a^14*b^3 - 133*a^12*b^5 + 143*a^10*b^7 + 55*a^8*b^9 - 215*a^6*b^11 + 145*a^4*b^13 - 27*a^2*b^15 - 3*b^17)*d*cos(d*x + c)^2 - (7*a^16*b - 84*a^12*b^5 + 176*a^10*b^7 - 110*a^8*b^9 - 32*a^6*b^11 + 60*a^4*b^13 - 16*a^2*b^15 - b^17)*d)*sin(d*x + c))]","B",0
469,1,2657,0,1.983581," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(4 \, a^{8} b^{3} - 44 \, a^{6} b^{5} - 207 \, a^{4} b^{7} + 215 \, a^{2} b^{9} + 32 \, b^{11}\right)} \cos\left(d x + c\right)^{7} - 28 \, {\left(6 \, a^{10} b - 65 \, a^{8} b^{3} - 224 \, a^{6} b^{5} + 222 \, a^{4} b^{7} + 53 \, a^{2} b^{9} + 8 \, b^{11}\right)} \cos\left(d x + c\right)^{5} - 70 \, {\left(14 \, a^{10} b + 173 \, a^{8} b^{3} - 3 \, a^{6} b^{5} - 137 \, a^{4} b^{7} - 47 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{3} + 105 \, {\left(2 \, a^{10} + 43 \, a^{8} b^{2} + 91 \, a^{6} b^{4} + 49 \, a^{4} b^{6} + 7 \, a^{2} b^{8} - 7 \, {\left(2 \, a^{4} b^{6} + a^{2} b^{8}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(10 \, a^{6} b^{4} + 11 \, a^{4} b^{6} + 3 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(6 \, a^{8} b^{2} + 23 \, a^{6} b^{4} + 16 \, a^{4} b^{6} + 3 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(14 \, a^{9} b + 77 \, a^{7} b^{3} + 77 \, a^{5} b^{5} + 23 \, a^{3} b^{7} + a b^{9} - {\left(2 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(14 \, a^{5} b^{5} + 9 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)^{4} - {\left(70 \, a^{7} b^{3} + 119 \, a^{5} b^{5} + 48 \, a^{3} b^{7} + 3 \, a b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 420 \, {\left(6 \, a^{10} b + 17 \, a^{8} b^{3} - 7 \, a^{6} b^{5} - 13 \, a^{4} b^{7} - 3 \, a^{2} b^{9}\right)} \cos\left(d x + c\right) - 14 \, {\left({\left(4 \, a^{9} b^{2} - 44 \, a^{7} b^{4} - 177 \, a^{5} b^{6} + 200 \, a^{3} b^{8} + 17 \, a b^{10}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(2 \, a^{11} - 21 \, a^{9} b^{2} - 61 \, a^{7} b^{4} + 37 \, a^{5} b^{6} + 39 \, a^{3} b^{8} + 4 \, a b^{10}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(2 \, a^{11} + 29 \, a^{9} b^{2} + 14 \, a^{7} b^{4} - 28 \, a^{5} b^{6} - 16 \, a^{3} b^{8} - a b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1120 \, {\left(7 \, {\left(a^{13} b^{6} - 6 \, a^{11} b^{8} + 15 \, a^{9} b^{10} - 20 \, a^{7} b^{12} + 15 \, a^{5} b^{14} - 6 \, a^{3} b^{16} + a b^{18}\right)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{15} b^{4} - 27 \, a^{13} b^{6} + 57 \, a^{11} b^{8} - 55 \, a^{9} b^{10} + 15 \, a^{7} b^{12} + 15 \, a^{5} b^{14} - 13 \, a^{3} b^{16} + 3 \, a b^{18}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{17} b^{2} - 8 \, a^{15} b^{4} - 12 \, a^{13} b^{6} + 72 \, a^{11} b^{8} - 110 \, a^{9} b^{10} + 72 \, a^{7} b^{12} - 12 \, a^{5} b^{14} - 8 \, a^{3} b^{16} + 3 \, a b^{18}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{19} + 15 \, a^{17} b^{2} - 76 \, a^{15} b^{4} + 92 \, a^{13} b^{6} + 78 \, a^{11} b^{8} - 286 \, a^{9} b^{10} + 260 \, a^{7} b^{12} - 84 \, a^{5} b^{14} - 7 \, a^{3} b^{16} + 7 \, a b^{18}\right)} d + {\left({\left(a^{12} b^{7} - 6 \, a^{10} b^{9} + 15 \, a^{8} b^{11} - 20 \, a^{6} b^{13} + 15 \, a^{4} b^{15} - 6 \, a^{2} b^{17} + b^{19}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{14} b^{5} - 41 \, a^{12} b^{7} + 99 \, a^{10} b^{9} - 125 \, a^{8} b^{11} + 85 \, a^{6} b^{13} - 27 \, a^{4} b^{15} + a^{2} b^{17} + b^{19}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{16} b^{3} - 168 \, a^{14} b^{5} + 276 \, a^{12} b^{7} - 88 \, a^{10} b^{9} - 270 \, a^{8} b^{11} + 360 \, a^{6} b^{13} - 172 \, a^{4} b^{15} + 24 \, a^{2} b^{17} + 3 \, b^{19}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{18} b - 7 \, a^{16} b^{3} - 84 \, a^{14} b^{5} + 260 \, a^{12} b^{7} - 286 \, a^{10} b^{9} + 78 \, a^{8} b^{11} + 92 \, a^{6} b^{13} - 76 \, a^{4} b^{15} + 15 \, a^{2} b^{17} + b^{19}\right)} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{{\left(4 \, a^{8} b^{3} - 44 \, a^{6} b^{5} - 207 \, a^{4} b^{7} + 215 \, a^{2} b^{9} + 32 \, b^{11}\right)} \cos\left(d x + c\right)^{7} - 14 \, {\left(6 \, a^{10} b - 65 \, a^{8} b^{3} - 224 \, a^{6} b^{5} + 222 \, a^{4} b^{7} + 53 \, a^{2} b^{9} + 8 \, b^{11}\right)} \cos\left(d x + c\right)^{5} - 35 \, {\left(14 \, a^{10} b + 173 \, a^{8} b^{3} - 3 \, a^{6} b^{5} - 137 \, a^{4} b^{7} - 47 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(2 \, a^{10} + 43 \, a^{8} b^{2} + 91 \, a^{6} b^{4} + 49 \, a^{4} b^{6} + 7 \, a^{2} b^{8} - 7 \, {\left(2 \, a^{4} b^{6} + a^{2} b^{8}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(10 \, a^{6} b^{4} + 11 \, a^{4} b^{6} + 3 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(6 \, a^{8} b^{2} + 23 \, a^{6} b^{4} + 16 \, a^{4} b^{6} + 3 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(14 \, a^{9} b + 77 \, a^{7} b^{3} + 77 \, a^{5} b^{5} + 23 \, a^{3} b^{7} + a b^{9} - {\left(2 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(14 \, a^{5} b^{5} + 9 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right)^{4} - {\left(70 \, a^{7} b^{3} + 119 \, a^{5} b^{5} + 48 \, a^{3} b^{7} + 3 \, a b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 210 \, {\left(6 \, a^{10} b + 17 \, a^{8} b^{3} - 7 \, a^{6} b^{5} - 13 \, a^{4} b^{7} - 3 \, a^{2} b^{9}\right)} \cos\left(d x + c\right) - 7 \, {\left({\left(4 \, a^{9} b^{2} - 44 \, a^{7} b^{4} - 177 \, a^{5} b^{6} + 200 \, a^{3} b^{8} + 17 \, a b^{10}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(2 \, a^{11} - 21 \, a^{9} b^{2} - 61 \, a^{7} b^{4} + 37 \, a^{5} b^{6} + 39 \, a^{3} b^{8} + 4 \, a b^{10}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(2 \, a^{11} + 29 \, a^{9} b^{2} + 14 \, a^{7} b^{4} - 28 \, a^{5} b^{6} - 16 \, a^{3} b^{8} - a b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{560 \, {\left(7 \, {\left(a^{13} b^{6} - 6 \, a^{11} b^{8} + 15 \, a^{9} b^{10} - 20 \, a^{7} b^{12} + 15 \, a^{5} b^{14} - 6 \, a^{3} b^{16} + a b^{18}\right)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{15} b^{4} - 27 \, a^{13} b^{6} + 57 \, a^{11} b^{8} - 55 \, a^{9} b^{10} + 15 \, a^{7} b^{12} + 15 \, a^{5} b^{14} - 13 \, a^{3} b^{16} + 3 \, a b^{18}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{17} b^{2} - 8 \, a^{15} b^{4} - 12 \, a^{13} b^{6} + 72 \, a^{11} b^{8} - 110 \, a^{9} b^{10} + 72 \, a^{7} b^{12} - 12 \, a^{5} b^{14} - 8 \, a^{3} b^{16} + 3 \, a b^{18}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{19} + 15 \, a^{17} b^{2} - 76 \, a^{15} b^{4} + 92 \, a^{13} b^{6} + 78 \, a^{11} b^{8} - 286 \, a^{9} b^{10} + 260 \, a^{7} b^{12} - 84 \, a^{5} b^{14} - 7 \, a^{3} b^{16} + 7 \, a b^{18}\right)} d + {\left({\left(a^{12} b^{7} - 6 \, a^{10} b^{9} + 15 \, a^{8} b^{11} - 20 \, a^{6} b^{13} + 15 \, a^{4} b^{15} - 6 \, a^{2} b^{17} + b^{19}\right)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{14} b^{5} - 41 \, a^{12} b^{7} + 99 \, a^{10} b^{9} - 125 \, a^{8} b^{11} + 85 \, a^{6} b^{13} - 27 \, a^{4} b^{15} + a^{2} b^{17} + b^{19}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{16} b^{3} - 168 \, a^{14} b^{5} + 276 \, a^{12} b^{7} - 88 \, a^{10} b^{9} - 270 \, a^{8} b^{11} + 360 \, a^{6} b^{13} - 172 \, a^{4} b^{15} + 24 \, a^{2} b^{17} + 3 \, b^{19}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{18} b - 7 \, a^{16} b^{3} - 84 \, a^{14} b^{5} + 260 \, a^{12} b^{7} - 286 \, a^{10} b^{9} + 78 \, a^{8} b^{11} + 92 \, a^{6} b^{13} - 76 \, a^{4} b^{15} + 15 \, a^{2} b^{17} + b^{19}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/1120*(2*(4*a^8*b^3 - 44*a^6*b^5 - 207*a^4*b^7 + 215*a^2*b^9 + 32*b^11)*cos(d*x + c)^7 - 28*(6*a^10*b - 65*a^8*b^3 - 224*a^6*b^5 + 222*a^4*b^7 + 53*a^2*b^9 + 8*b^11)*cos(d*x + c)^5 - 70*(14*a^10*b + 173*a^8*b^3 - 3*a^6*b^5 - 137*a^4*b^7 - 47*a^2*b^9)*cos(d*x + c)^3 + 105*(2*a^10 + 43*a^8*b^2 + 91*a^6*b^4 + 49*a^4*b^6 + 7*a^2*b^8 - 7*(2*a^4*b^6 + a^2*b^8)*cos(d*x + c)^6 + 7*(10*a^6*b^4 + 11*a^4*b^6 + 3*a^2*b^8)*cos(d*x + c)^4 - 7*(6*a^8*b^2 + 23*a^6*b^4 + 16*a^4*b^6 + 3*a^2*b^8)*cos(d*x + c)^2 + (14*a^9*b + 77*a^7*b^3 + 77*a^5*b^5 + 23*a^3*b^7 + a*b^9 - (2*a^3*b^7 + a*b^9)*cos(d*x + c)^6 + 3*(14*a^5*b^5 + 9*a^3*b^7 + a*b^9)*cos(d*x + c)^4 - (70*a^7*b^3 + 119*a^5*b^5 + 48*a^3*b^7 + 3*a*b^9)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 420*(6*a^10*b + 17*a^8*b^3 - 7*a^6*b^5 - 13*a^4*b^7 - 3*a^2*b^9)*cos(d*x + c) - 14*((4*a^9*b^2 - 44*a^7*b^4 - 177*a^5*b^6 + 200*a^3*b^8 + 17*a*b^10)*cos(d*x + c)^5 - 10*(2*a^11 - 21*a^9*b^2 - 61*a^7*b^4 + 37*a^5*b^6 + 39*a^3*b^8 + 4*a*b^10)*cos(d*x + c)^3 - 15*(2*a^11 + 29*a^9*b^2 + 14*a^7*b^4 - 28*a^5*b^6 - 16*a^3*b^8 - a*b^10)*cos(d*x + c))*sin(d*x + c))/(7*(a^13*b^6 - 6*a^11*b^8 + 15*a^9*b^10 - 20*a^7*b^12 + 15*a^5*b^14 - 6*a^3*b^16 + a*b^18)*d*cos(d*x + c)^6 - 7*(5*a^15*b^4 - 27*a^13*b^6 + 57*a^11*b^8 - 55*a^9*b^10 + 15*a^7*b^12 + 15*a^5*b^14 - 13*a^3*b^16 + 3*a*b^18)*d*cos(d*x + c)^4 + 7*(3*a^17*b^2 - 8*a^15*b^4 - 12*a^13*b^6 + 72*a^11*b^8 - 110*a^9*b^10 + 72*a^7*b^12 - 12*a^5*b^14 - 8*a^3*b^16 + 3*a*b^18)*d*cos(d*x + c)^2 - (a^19 + 15*a^17*b^2 - 76*a^15*b^4 + 92*a^13*b^6 + 78*a^11*b^8 - 286*a^9*b^10 + 260*a^7*b^12 - 84*a^5*b^14 - 7*a^3*b^16 + 7*a*b^18)*d + ((a^12*b^7 - 6*a^10*b^9 + 15*a^8*b^11 - 20*a^6*b^13 + 15*a^4*b^15 - 6*a^2*b^17 + b^19)*d*cos(d*x + c)^6 - 3*(7*a^14*b^5 - 41*a^12*b^7 + 99*a^10*b^9 - 125*a^8*b^11 + 85*a^6*b^13 - 27*a^4*b^15 + a^2*b^17 + b^19)*d*cos(d*x + c)^4 + (35*a^16*b^3 - 168*a^14*b^5 + 276*a^12*b^7 - 88*a^10*b^9 - 270*a^8*b^11 + 360*a^6*b^13 - 172*a^4*b^15 + 24*a^2*b^17 + 3*b^19)*d*cos(d*x + c)^2 - (7*a^18*b - 7*a^16*b^3 - 84*a^14*b^5 + 260*a^12*b^7 - 286*a^10*b^9 + 78*a^8*b^11 + 92*a^6*b^13 - 76*a^4*b^15 + 15*a^2*b^17 + b^19)*d)*sin(d*x + c)), -1/560*((4*a^8*b^3 - 44*a^6*b^5 - 207*a^4*b^7 + 215*a^2*b^9 + 32*b^11)*cos(d*x + c)^7 - 14*(6*a^10*b - 65*a^8*b^3 - 224*a^6*b^5 + 222*a^4*b^7 + 53*a^2*b^9 + 8*b^11)*cos(d*x + c)^5 - 35*(14*a^10*b + 173*a^8*b^3 - 3*a^6*b^5 - 137*a^4*b^7 - 47*a^2*b^9)*cos(d*x + c)^3 - 105*(2*a^10 + 43*a^8*b^2 + 91*a^6*b^4 + 49*a^4*b^6 + 7*a^2*b^8 - 7*(2*a^4*b^6 + a^2*b^8)*cos(d*x + c)^6 + 7*(10*a^6*b^4 + 11*a^4*b^6 + 3*a^2*b^8)*cos(d*x + c)^4 - 7*(6*a^8*b^2 + 23*a^6*b^4 + 16*a^4*b^6 + 3*a^2*b^8)*cos(d*x + c)^2 + (14*a^9*b + 77*a^7*b^3 + 77*a^5*b^5 + 23*a^3*b^7 + a*b^9 - (2*a^3*b^7 + a*b^9)*cos(d*x + c)^6 + 3*(14*a^5*b^5 + 9*a^3*b^7 + a*b^9)*cos(d*x + c)^4 - (70*a^7*b^3 + 119*a^5*b^5 + 48*a^3*b^7 + 3*a*b^9)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 210*(6*a^10*b + 17*a^8*b^3 - 7*a^6*b^5 - 13*a^4*b^7 - 3*a^2*b^9)*cos(d*x + c) - 7*((4*a^9*b^2 - 44*a^7*b^4 - 177*a^5*b^6 + 200*a^3*b^8 + 17*a*b^10)*cos(d*x + c)^5 - 10*(2*a^11 - 21*a^9*b^2 - 61*a^7*b^4 + 37*a^5*b^6 + 39*a^3*b^8 + 4*a*b^10)*cos(d*x + c)^3 - 15*(2*a^11 + 29*a^9*b^2 + 14*a^7*b^4 - 28*a^5*b^6 - 16*a^3*b^8 - a*b^10)*cos(d*x + c))*sin(d*x + c))/(7*(a^13*b^6 - 6*a^11*b^8 + 15*a^9*b^10 - 20*a^7*b^12 + 15*a^5*b^14 - 6*a^3*b^16 + a*b^18)*d*cos(d*x + c)^6 - 7*(5*a^15*b^4 - 27*a^13*b^6 + 57*a^11*b^8 - 55*a^9*b^10 + 15*a^7*b^12 + 15*a^5*b^14 - 13*a^3*b^16 + 3*a*b^18)*d*cos(d*x + c)^4 + 7*(3*a^17*b^2 - 8*a^15*b^4 - 12*a^13*b^6 + 72*a^11*b^8 - 110*a^9*b^10 + 72*a^7*b^12 - 12*a^5*b^14 - 8*a^3*b^16 + 3*a*b^18)*d*cos(d*x + c)^2 - (a^19 + 15*a^17*b^2 - 76*a^15*b^4 + 92*a^13*b^6 + 78*a^11*b^8 - 286*a^9*b^10 + 260*a^7*b^12 - 84*a^5*b^14 - 7*a^3*b^16 + 7*a*b^18)*d + ((a^12*b^7 - 6*a^10*b^9 + 15*a^8*b^11 - 20*a^6*b^13 + 15*a^4*b^15 - 6*a^2*b^17 + b^19)*d*cos(d*x + c)^6 - 3*(7*a^14*b^5 - 41*a^12*b^7 + 99*a^10*b^9 - 125*a^8*b^11 + 85*a^6*b^13 - 27*a^4*b^15 + a^2*b^17 + b^19)*d*cos(d*x + c)^4 + (35*a^16*b^3 - 168*a^14*b^5 + 276*a^12*b^7 - 88*a^10*b^9 - 270*a^8*b^11 + 360*a^6*b^13 - 172*a^4*b^15 + 24*a^2*b^17 + 3*b^19)*d*cos(d*x + c)^2 - (7*a^18*b - 7*a^16*b^3 - 84*a^14*b^5 + 260*a^12*b^7 - 286*a^10*b^9 + 78*a^8*b^11 + 92*a^6*b^13 - 76*a^4*b^15 + 15*a^2*b^17 + b^19)*d)*sin(d*x + c))]","B",0
470,1,2972,0,1.889703," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(40 \, a^{8} b^{5} + 1478 \, a^{6} b^{7} + 261 \, a^{4} b^{9} - 1651 \, a^{2} b^{11} - 128 \, b^{13}\right)} \cos\left(d x + c\right)^{7} - 28 \, {\left(60 \, a^{10} b^{3} + 1837 \, a^{8} b^{5} + 176 \, a^{6} b^{7} - 1680 \, a^{4} b^{9} - 361 \, a^{2} b^{11} - 32 \, b^{13}\right)} \cos\left(d x + c\right)^{5} + 70 \, {\left(40 \, a^{12} b + 900 \, a^{10} b^{3} + 1111 \, a^{8} b^{5} - 501 \, a^{6} b^{7} - 1395 \, a^{4} b^{9} - 139 \, a^{2} b^{11} - 16 \, b^{13}\right)} \cos\left(d x + c\right)^{3} + 105 \, {\left(8 \, a^{12} + 188 \, a^{10} b^{2} + 705 \, a^{8} b^{4} + 861 \, a^{6} b^{6} + 315 \, a^{4} b^{8} + 35 \, a^{2} b^{10} - 7 \, {\left(8 \, a^{6} b^{6} + 20 \, a^{4} b^{8} + 5 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(40 \, a^{8} b^{4} + 124 \, a^{6} b^{6} + 85 \, a^{4} b^{8} + 15 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(24 \, a^{10} b^{2} + 140 \, a^{8} b^{4} + 239 \, a^{6} b^{6} + 110 \, a^{4} b^{8} + 15 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(56 \, a^{11} b + 420 \, a^{9} b^{3} + 903 \, a^{7} b^{5} + 603 \, a^{5} b^{7} + 125 \, a^{3} b^{9} + 5 \, a b^{11} - {\left(8 \, a^{5} b^{7} + 20 \, a^{3} b^{9} + 5 \, a b^{11}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(56 \, a^{7} b^{5} + 148 \, a^{5} b^{7} + 55 \, a^{3} b^{9} + 5 \, a b^{11}\right)} \cos\left(d x + c\right)^{4} - {\left(280 \, a^{9} b^{3} + 1036 \, a^{7} b^{5} + 1039 \, a^{5} b^{7} + 270 \, a^{3} b^{9} + 15 \, a b^{11}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 420 \, {\left(24 \, a^{12} b + 116 \, a^{10} b^{3} + 99 \, a^{8} b^{5} - 129 \, a^{6} b^{7} - 95 \, a^{4} b^{9} - 15 \, a^{2} b^{11}\right)} \cos\left(d x + c\right) - 14 \, {\left({\left(40 \, a^{9} b^{4} + 1358 \, a^{7} b^{6} + 81 \, a^{5} b^{8} - 1426 \, a^{3} b^{10} - 53 \, a b^{12}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(20 \, a^{11} b^{2} + 535 \, a^{9} b^{4} + 147 \, a^{7} b^{6} - 407 \, a^{5} b^{8} - 283 \, a^{3} b^{10} - 12 \, a b^{12}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{13} + 132 \, a^{11} b^{2} + 285 \, a^{9} b^{4} - 42 \, a^{7} b^{6} - 288 \, a^{5} b^{8} - 90 \, a^{3} b^{10} - 5 \, a b^{12}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3360 \, {\left(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)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{17} b^{4} - 32 \, a^{15} b^{6} + 84 \, a^{13} b^{8} - 112 \, a^{11} b^{10} + 70 \, a^{9} b^{12} - 28 \, a^{5} b^{16} + 16 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{19} b^{2} - 11 \, a^{17} b^{4} - 4 \, a^{15} b^{6} + 84 \, a^{13} b^{8} - 182 \, a^{11} b^{10} + 182 \, a^{9} b^{12} - 84 \, a^{7} b^{14} + 4 \, a^{5} b^{16} + 11 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{21} + 14 \, a^{19} b^{2} - 91 \, a^{17} b^{4} + 168 \, a^{15} b^{6} - 14 \, a^{13} b^{8} - 364 \, a^{11} b^{10} + 546 \, a^{9} b^{12} - 344 \, a^{7} b^{14} + 77 \, a^{5} b^{16} + 14 \, a^{3} b^{18} - 7 \, a b^{20}\right)} d + {\left({\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)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{16} b^{5} - 48 \, a^{14} b^{7} + 140 \, a^{12} b^{9} - 224 \, a^{10} b^{11} + 210 \, a^{8} b^{13} - 112 \, a^{6} b^{15} + 28 \, a^{4} b^{17} - b^{21}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{18} b^{3} - 203 \, a^{16} b^{5} + 444 \, a^{14} b^{7} - 364 \, a^{12} b^{9} - 182 \, a^{10} b^{11} + 630 \, a^{8} b^{13} - 532 \, a^{6} b^{15} + 196 \, a^{4} b^{17} - 21 \, a^{2} b^{19} - 3 \, b^{21}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{20} b - 14 \, a^{18} b^{3} - 77 \, a^{16} b^{5} + 344 \, a^{14} b^{7} - 546 \, a^{12} b^{9} + 364 \, a^{10} b^{11} + 14 \, a^{8} b^{13} - 168 \, a^{6} b^{15} + 91 \, a^{4} b^{17} - 14 \, a^{2} b^{19} - b^{21}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{{\left(40 \, a^{8} b^{5} + 1478 \, a^{6} b^{7} + 261 \, a^{4} b^{9} - 1651 \, a^{2} b^{11} - 128 \, b^{13}\right)} \cos\left(d x + c\right)^{7} - 14 \, {\left(60 \, a^{10} b^{3} + 1837 \, a^{8} b^{5} + 176 \, a^{6} b^{7} - 1680 \, a^{4} b^{9} - 361 \, a^{2} b^{11} - 32 \, b^{13}\right)} \cos\left(d x + c\right)^{5} + 35 \, {\left(40 \, a^{12} b + 900 \, a^{10} b^{3} + 1111 \, a^{8} b^{5} - 501 \, a^{6} b^{7} - 1395 \, a^{4} b^{9} - 139 \, a^{2} b^{11} - 16 \, b^{13}\right)} \cos\left(d x + c\right)^{3} + 105 \, {\left(8 \, a^{12} + 188 \, a^{10} b^{2} + 705 \, a^{8} b^{4} + 861 \, a^{6} b^{6} + 315 \, a^{4} b^{8} + 35 \, a^{2} b^{10} - 7 \, {\left(8 \, a^{6} b^{6} + 20 \, a^{4} b^{8} + 5 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{6} + 7 \, {\left(40 \, a^{8} b^{4} + 124 \, a^{6} b^{6} + 85 \, a^{4} b^{8} + 15 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{4} - 7 \, {\left(24 \, a^{10} b^{2} + 140 \, a^{8} b^{4} + 239 \, a^{6} b^{6} + 110 \, a^{4} b^{8} + 15 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(56 \, a^{11} b + 420 \, a^{9} b^{3} + 903 \, a^{7} b^{5} + 603 \, a^{5} b^{7} + 125 \, a^{3} b^{9} + 5 \, a b^{11} - {\left(8 \, a^{5} b^{7} + 20 \, a^{3} b^{9} + 5 \, a b^{11}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(56 \, a^{7} b^{5} + 148 \, a^{5} b^{7} + 55 \, a^{3} b^{9} + 5 \, a b^{11}\right)} \cos\left(d x + c\right)^{4} - {\left(280 \, a^{9} b^{3} + 1036 \, a^{7} b^{5} + 1039 \, a^{5} b^{7} + 270 \, a^{3} b^{9} + 15 \, a b^{11}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 210 \, {\left(24 \, a^{12} b + 116 \, a^{10} b^{3} + 99 \, a^{8} b^{5} - 129 \, a^{6} b^{7} - 95 \, a^{4} b^{9} - 15 \, a^{2} b^{11}\right)} \cos\left(d x + c\right) - 7 \, {\left({\left(40 \, a^{9} b^{4} + 1358 \, a^{7} b^{6} + 81 \, a^{5} b^{8} - 1426 \, a^{3} b^{10} - 53 \, a b^{12}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(20 \, a^{11} b^{2} + 535 \, a^{9} b^{4} + 147 \, a^{7} b^{6} - 407 \, a^{5} b^{8} - 283 \, a^{3} b^{10} - 12 \, a b^{12}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{13} + 132 \, a^{11} b^{2} + 285 \, a^{9} b^{4} - 42 \, a^{7} b^{6} - 288 \, a^{5} b^{8} - 90 \, a^{3} b^{10} - 5 \, a b^{12}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, {\left(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)} d \cos\left(d x + c\right)^{6} - 7 \, {\left(5 \, a^{17} b^{4} - 32 \, a^{15} b^{6} + 84 \, a^{13} b^{8} - 112 \, a^{11} b^{10} + 70 \, a^{9} b^{12} - 28 \, a^{5} b^{16} + 16 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)^{4} + 7 \, {\left(3 \, a^{19} b^{2} - 11 \, a^{17} b^{4} - 4 \, a^{15} b^{6} + 84 \, a^{13} b^{8} - 182 \, a^{11} b^{10} + 182 \, a^{9} b^{12} - 84 \, a^{7} b^{14} + 4 \, a^{5} b^{16} + 11 \, a^{3} b^{18} - 3 \, a b^{20}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{21} + 14 \, a^{19} b^{2} - 91 \, a^{17} b^{4} + 168 \, a^{15} b^{6} - 14 \, a^{13} b^{8} - 364 \, a^{11} b^{10} + 546 \, a^{9} b^{12} - 344 \, a^{7} b^{14} + 77 \, a^{5} b^{16} + 14 \, a^{3} b^{18} - 7 \, a b^{20}\right)} d + {\left({\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)} d \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, a^{16} b^{5} - 48 \, a^{14} b^{7} + 140 \, a^{12} b^{9} - 224 \, a^{10} b^{11} + 210 \, a^{8} b^{13} - 112 \, a^{6} b^{15} + 28 \, a^{4} b^{17} - b^{21}\right)} d \cos\left(d x + c\right)^{4} + {\left(35 \, a^{18} b^{3} - 203 \, a^{16} b^{5} + 444 \, a^{14} b^{7} - 364 \, a^{12} b^{9} - 182 \, a^{10} b^{11} + 630 \, a^{8} b^{13} - 532 \, a^{6} b^{15} + 196 \, a^{4} b^{17} - 21 \, a^{2} b^{19} - 3 \, b^{21}\right)} d \cos\left(d x + c\right)^{2} - {\left(7 \, a^{20} b - 14 \, a^{18} b^{3} - 77 \, a^{16} b^{5} + 344 \, a^{14} b^{7} - 546 \, a^{12} b^{9} + 364 \, a^{10} b^{11} + 14 \, a^{8} b^{13} - 168 \, a^{6} b^{15} + 91 \, a^{4} b^{17} - 14 \, a^{2} b^{19} - b^{21}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/3360*(2*(40*a^8*b^5 + 1478*a^6*b^7 + 261*a^4*b^9 - 1651*a^2*b^11 - 128*b^13)*cos(d*x + c)^7 - 28*(60*a^10*b^3 + 1837*a^8*b^5 + 176*a^6*b^7 - 1680*a^4*b^9 - 361*a^2*b^11 - 32*b^13)*cos(d*x + c)^5 + 70*(40*a^12*b + 900*a^10*b^3 + 1111*a^8*b^5 - 501*a^6*b^7 - 1395*a^4*b^9 - 139*a^2*b^11 - 16*b^13)*cos(d*x + c)^3 + 105*(8*a^12 + 188*a^10*b^2 + 705*a^8*b^4 + 861*a^6*b^6 + 315*a^4*b^8 + 35*a^2*b^10 - 7*(8*a^6*b^6 + 20*a^4*b^8 + 5*a^2*b^10)*cos(d*x + c)^6 + 7*(40*a^8*b^4 + 124*a^6*b^6 + 85*a^4*b^8 + 15*a^2*b^10)*cos(d*x + c)^4 - 7*(24*a^10*b^2 + 140*a^8*b^4 + 239*a^6*b^6 + 110*a^4*b^8 + 15*a^2*b^10)*cos(d*x + c)^2 + (56*a^11*b + 420*a^9*b^3 + 903*a^7*b^5 + 603*a^5*b^7 + 125*a^3*b^9 + 5*a*b^11 - (8*a^5*b^7 + 20*a^3*b^9 + 5*a*b^11)*cos(d*x + c)^6 + 3*(56*a^7*b^5 + 148*a^5*b^7 + 55*a^3*b^9 + 5*a*b^11)*cos(d*x + c)^4 - (280*a^9*b^3 + 1036*a^7*b^5 + 1039*a^5*b^7 + 270*a^3*b^9 + 15*a*b^11)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 420*(24*a^12*b + 116*a^10*b^3 + 99*a^8*b^5 - 129*a^6*b^7 - 95*a^4*b^9 - 15*a^2*b^11)*cos(d*x + c) - 14*((40*a^9*b^4 + 1358*a^7*b^6 + 81*a^5*b^8 - 1426*a^3*b^10 - 53*a*b^12)*cos(d*x + c)^5 - 10*(20*a^11*b^2 + 535*a^9*b^4 + 147*a^7*b^6 - 407*a^5*b^8 - 283*a^3*b^10 - 12*a*b^12)*cos(d*x + c)^3 + 15*(8*a^13 + 132*a^11*b^2 + 285*a^9*b^4 - 42*a^7*b^6 - 288*a^5*b^8 - 90*a^3*b^10 - 5*a*b^12)*cos(d*x + c))*sin(d*x + c))/(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)*d*cos(d*x + c)^6 - 7*(5*a^17*b^4 - 32*a^15*b^6 + 84*a^13*b^8 - 112*a^11*b^10 + 70*a^9*b^12 - 28*a^5*b^16 + 16*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c)^4 + 7*(3*a^19*b^2 - 11*a^17*b^4 - 4*a^15*b^6 + 84*a^13*b^8 - 182*a^11*b^10 + 182*a^9*b^12 - 84*a^7*b^14 + 4*a^5*b^16 + 11*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c)^2 - (a^21 + 14*a^19*b^2 - 91*a^17*b^4 + 168*a^15*b^6 - 14*a^13*b^8 - 364*a^11*b^10 + 546*a^9*b^12 - 344*a^7*b^14 + 77*a^5*b^16 + 14*a^3*b^18 - 7*a*b^20)*d + ((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)*d*cos(d*x + c)^6 - 3*(7*a^16*b^5 - 48*a^14*b^7 + 140*a^12*b^9 - 224*a^10*b^11 + 210*a^8*b^13 - 112*a^6*b^15 + 28*a^4*b^17 - b^21)*d*cos(d*x + c)^4 + (35*a^18*b^3 - 203*a^16*b^5 + 444*a^14*b^7 - 364*a^12*b^9 - 182*a^10*b^11 + 630*a^8*b^13 - 532*a^6*b^15 + 196*a^4*b^17 - 21*a^2*b^19 - 3*b^21)*d*cos(d*x + c)^2 - (7*a^20*b - 14*a^18*b^3 - 77*a^16*b^5 + 344*a^14*b^7 - 546*a^12*b^9 + 364*a^10*b^11 + 14*a^8*b^13 - 168*a^6*b^15 + 91*a^4*b^17 - 14*a^2*b^19 - b^21)*d)*sin(d*x + c)), 1/1680*((40*a^8*b^5 + 1478*a^6*b^7 + 261*a^4*b^9 - 1651*a^2*b^11 - 128*b^13)*cos(d*x + c)^7 - 14*(60*a^10*b^3 + 1837*a^8*b^5 + 176*a^6*b^7 - 1680*a^4*b^9 - 361*a^2*b^11 - 32*b^13)*cos(d*x + c)^5 + 35*(40*a^12*b + 900*a^10*b^3 + 1111*a^8*b^5 - 501*a^6*b^7 - 1395*a^4*b^9 - 139*a^2*b^11 - 16*b^13)*cos(d*x + c)^3 + 105*(8*a^12 + 188*a^10*b^2 + 705*a^8*b^4 + 861*a^6*b^6 + 315*a^4*b^8 + 35*a^2*b^10 - 7*(8*a^6*b^6 + 20*a^4*b^8 + 5*a^2*b^10)*cos(d*x + c)^6 + 7*(40*a^8*b^4 + 124*a^6*b^6 + 85*a^4*b^8 + 15*a^2*b^10)*cos(d*x + c)^4 - 7*(24*a^10*b^2 + 140*a^8*b^4 + 239*a^6*b^6 + 110*a^4*b^8 + 15*a^2*b^10)*cos(d*x + c)^2 + (56*a^11*b + 420*a^9*b^3 + 903*a^7*b^5 + 603*a^5*b^7 + 125*a^3*b^9 + 5*a*b^11 - (8*a^5*b^7 + 20*a^3*b^9 + 5*a*b^11)*cos(d*x + c)^6 + 3*(56*a^7*b^5 + 148*a^5*b^7 + 55*a^3*b^9 + 5*a*b^11)*cos(d*x + c)^4 - (280*a^9*b^3 + 1036*a^7*b^5 + 1039*a^5*b^7 + 270*a^3*b^9 + 15*a*b^11)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 210*(24*a^12*b + 116*a^10*b^3 + 99*a^8*b^5 - 129*a^6*b^7 - 95*a^4*b^9 - 15*a^2*b^11)*cos(d*x + c) - 7*((40*a^9*b^4 + 1358*a^7*b^6 + 81*a^5*b^8 - 1426*a^3*b^10 - 53*a*b^12)*cos(d*x + c)^5 - 10*(20*a^11*b^2 + 535*a^9*b^4 + 147*a^7*b^6 - 407*a^5*b^8 - 283*a^3*b^10 - 12*a*b^12)*cos(d*x + c)^3 + 15*(8*a^13 + 132*a^11*b^2 + 285*a^9*b^4 - 42*a^7*b^6 - 288*a^5*b^8 - 90*a^3*b^10 - 5*a*b^12)*cos(d*x + c))*sin(d*x + c))/(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)*d*cos(d*x + c)^6 - 7*(5*a^17*b^4 - 32*a^15*b^6 + 84*a^13*b^8 - 112*a^11*b^10 + 70*a^9*b^12 - 28*a^5*b^16 + 16*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c)^4 + 7*(3*a^19*b^2 - 11*a^17*b^4 - 4*a^15*b^6 + 84*a^13*b^8 - 182*a^11*b^10 + 182*a^9*b^12 - 84*a^7*b^14 + 4*a^5*b^16 + 11*a^3*b^18 - 3*a*b^20)*d*cos(d*x + c)^2 - (a^21 + 14*a^19*b^2 - 91*a^17*b^4 + 168*a^15*b^6 - 14*a^13*b^8 - 364*a^11*b^10 + 546*a^9*b^12 - 344*a^7*b^14 + 77*a^5*b^16 + 14*a^3*b^18 - 7*a*b^20)*d + ((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)*d*cos(d*x + c)^6 - 3*(7*a^16*b^5 - 48*a^14*b^7 + 140*a^12*b^9 - 224*a^10*b^11 + 210*a^8*b^13 - 112*a^6*b^15 + 28*a^4*b^17 - b^21)*d*cos(d*x + c)^4 + (35*a^18*b^3 - 203*a^16*b^5 + 444*a^14*b^7 - 364*a^12*b^9 - 182*a^10*b^11 + 630*a^8*b^13 - 532*a^6*b^15 + 196*a^4*b^17 - 21*a^2*b^19 - 3*b^21)*d*cos(d*x + c)^2 - (7*a^20*b - 14*a^18*b^3 - 77*a^16*b^5 + 344*a^14*b^7 - 546*a^12*b^9 + 364*a^10*b^11 + 14*a^8*b^13 - 168*a^6*b^15 + 91*a^4*b^17 - 14*a^2*b^19 - b^21)*d)*sin(d*x + c))]","B",0
471,1,3882,0,2.224781," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\left[\frac{1120 \, a^{16} b - 8960 \, a^{14} b^{3} + 31360 \, a^{12} b^{5} - 62720 \, a^{10} b^{7} + 78400 \, a^{8} b^{9} - 62720 \, a^{6} b^{11} + 31360 \, a^{4} b^{13} - 8960 \, a^{2} b^{15} + 1120 \, b^{17} - 2 \, {\left(560 \, a^{10} b^{7} + 41912 \, a^{8} b^{9} + 83162 \, a^{6} b^{11} - 71123 \, a^{4} b^{13} - 52463 \, a^{2} b^{15} - 2048 \, b^{17}\right)} \cos\left(d x + c\right)^{8} + 28 \, {\left(840 \, a^{12} b^{5} + 53648 \, a^{10} b^{7} + 95441 \, a^{8} b^{9} - 77704 \, a^{6} b^{11} - 60644 \, a^{4} b^{13} - 11069 \, a^{2} b^{15} - 512 \, b^{17}\right)} \cos\left(d x + c\right)^{6} - 70 \, {\left(560 \, a^{14} b^{3} + 27440 \, a^{12} b^{5} + 71064 \, a^{10} b^{7} + 29927 \, a^{8} b^{9} - 81421 \, a^{6} b^{11} - 43131 \, a^{4} b^{13} - 4183 \, a^{2} b^{15} - 256 \, b^{17}\right)} \cos\left(d x + c\right)^{4} + 140 \, {\left(56 \, a^{16} b + 1400 \, a^{14} b^{3} + 13832 \, a^{12} b^{5} + 24080 \, a^{10} b^{7} - 4591 \, a^{8} b^{9} - 23443 \, a^{6} b^{11} - 10717 \, a^{4} b^{13} - 553 \, a^{2} b^{15} - 64 \, b^{17}\right)} \cos\left(d x + c\right)^{2} - 315 \, {\left(7 \, {\left(64 \, a^{8} b^{8} + 336 \, a^{6} b^{10} + 280 \, a^{4} b^{12} + 35 \, a^{2} b^{14}\right)} \cos\left(d x + c\right)^{7} - 7 \, {\left(320 \, a^{10} b^{6} + 1872 \, a^{8} b^{8} + 2408 \, a^{6} b^{10} + 1015 \, a^{4} b^{12} + 105 \, a^{2} b^{14}\right)} \cos\left(d x + c\right)^{5} + 7 \, {\left(192 \, a^{12} b^{4} + 1648 \, a^{10} b^{6} + 4392 \, a^{8} b^{8} + 3913 \, a^{6} b^{10} + 1190 \, a^{4} b^{12} + 105 \, a^{2} b^{14}\right)} \cos\left(d x + c\right)^{3} - {\left(64 \, a^{14} b^{2} + 1680 \, a^{12} b^{4} + 9576 \, a^{10} b^{6} + 18123 \, a^{8} b^{8} + 12887 \, a^{6} b^{10} + 3185 \, a^{4} b^{12} + 245 \, a^{2} b^{14}\right)} \cos\left(d x + c\right) + {\left({\left(64 \, a^{7} b^{9} + 336 \, a^{5} b^{11} + 280 \, a^{3} b^{13} + 35 \, a b^{15}\right)} \cos\left(d x + c\right)^{7} - 3 \, {\left(448 \, a^{9} b^{7} + 2416 \, a^{7} b^{9} + 2296 \, a^{5} b^{11} + 525 \, a^{3} b^{13} + 35 \, a b^{15}\right)} \cos\left(d x + c\right)^{5} + {\left(2240 \, a^{11} b^{5} + 14448 \, a^{9} b^{7} + 24104 \, a^{7} b^{9} + 13993 \, a^{5} b^{11} + 2310 \, a^{3} b^{13} + 105 \, a b^{15}\right)} \cos\left(d x + c\right)^{3} - {\left(448 \, a^{13} b^{3} + 4592 \, a^{11} b^{5} + 15064 \, a^{9} b^{7} + 17165 \, a^{7} b^{9} + 7441 \, a^{5} b^{11} + 1015 \, a^{3} b^{13} + 35 \, a b^{15}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 14 \, {\left(80 \, a^{17} - 640 \, a^{15} b^{2} + 2240 \, a^{13} b^{4} - 4480 \, a^{11} b^{6} + 5600 \, a^{9} b^{8} - 4480 \, a^{7} b^{10} + 2240 \, a^{5} b^{12} - 640 \, a^{3} b^{14} + 80 \, a b^{16} - {\left(560 \, a^{11} b^{6} + 39032 \, a^{9} b^{8} + 70922 \, a^{7} b^{10} - 68603 \, a^{5} b^{12} - 41438 \, a^{3} b^{14} - 473 \, a b^{16}\right)} \cos\left(d x + c\right)^{6} + 10 \, {\left(280 \, a^{13} b^{4} + 15960 \, a^{11} b^{6} + 29463 \, a^{9} b^{8} - 13541 \, a^{7} b^{10} - 23679 \, a^{5} b^{12} - 8391 \, a^{3} b^{14} - 92 \, a b^{16}\right)} \cos\left(d x + c\right)^{4} - 15 \, {\left(112 \, a^{15} b^{2} + 4256 \, a^{13} b^{4} + 13272 \, a^{11} b^{6} + 11977 \, a^{9} b^{8} - 15634 \, a^{7} b^{10} - 11088 \, a^{5} b^{12} - 2870 \, a^{3} b^{14} - 25 \, a b^{16}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{1120 \, {\left(7 \, {\left(a^{19} b^{6} - 9 \, a^{17} b^{8} + 36 \, a^{15} b^{10} - 84 \, a^{13} b^{12} + 126 \, a^{11} b^{14} - 126 \, a^{9} b^{16} + 84 \, a^{7} b^{18} - 36 \, a^{5} b^{20} + 9 \, a^{3} b^{22} - a b^{24}\right)} d \cos\left(d x + c\right)^{7} - 7 \, {\left(5 \, a^{21} b^{4} - 42 \, a^{19} b^{6} + 153 \, a^{17} b^{8} - 312 \, a^{15} b^{10} + 378 \, a^{13} b^{12} - 252 \, a^{11} b^{14} + 42 \, a^{9} b^{16} + 72 \, a^{7} b^{18} - 63 \, a^{5} b^{20} + 22 \, a^{3} b^{22} - 3 \, a b^{24}\right)} d \cos\left(d x + c\right)^{5} + 7 \, {\left(3 \, a^{23} b^{2} - 17 \, a^{21} b^{4} + 21 \, a^{19} b^{6} + 81 \, a^{17} b^{8} - 354 \, a^{15} b^{10} + 630 \, a^{13} b^{12} - 630 \, a^{11} b^{14} + 354 \, a^{9} b^{16} - 81 \, a^{7} b^{18} - 21 \, a^{5} b^{20} + 17 \, a^{3} b^{22} - 3 \, a b^{24}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{25} + 12 \, a^{23} b^{2} - 118 \, a^{21} b^{4} + 364 \, a^{19} b^{6} - 441 \, a^{17} b^{8} - 168 \, a^{15} b^{10} + 1260 \, a^{13} b^{12} - 1800 \, a^{11} b^{14} + 1311 \, a^{9} b^{16} - 484 \, a^{7} b^{18} + 42 \, a^{5} b^{20} + 28 \, a^{3} b^{22} - 7 \, a b^{24}\right)} d \cos\left(d x + c\right) + {\left({\left(a^{18} b^{7} - 9 \, a^{16} b^{9} + 36 \, a^{14} b^{11} - 84 \, a^{12} b^{13} + 126 \, a^{10} b^{15} - 126 \, a^{8} b^{17} + 84 \, a^{6} b^{19} - 36 \, a^{4} b^{21} + 9 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)^{7} - 3 \, {\left(7 \, a^{20} b^{5} - 62 \, a^{18} b^{7} + 243 \, a^{16} b^{9} - 552 \, a^{14} b^{11} + 798 \, a^{12} b^{13} - 756 \, a^{10} b^{15} + 462 \, a^{8} b^{17} - 168 \, a^{6} b^{19} + 27 \, a^{4} b^{21} + 2 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)^{5} + {\left(35 \, a^{22} b^{3} - 273 \, a^{20} b^{5} + 885 \, a^{18} b^{7} - 1455 \, a^{16} b^{9} + 990 \, a^{14} b^{11} + 630 \, a^{12} b^{13} - 1974 \, a^{10} b^{15} + 1890 \, a^{8} b^{17} - 945 \, a^{6} b^{19} + 235 \, a^{4} b^{21} - 15 \, a^{2} b^{23} - 3 \, b^{25}\right)} d \cos\left(d x + c\right)^{3} - {\left(7 \, a^{24} b - 28 \, a^{22} b^{3} - 42 \, a^{20} b^{5} + 484 \, a^{18} b^{7} - 1311 \, a^{16} b^{9} + 1800 \, a^{14} b^{11} - 1260 \, a^{12} b^{13} + 168 \, a^{10} b^{15} + 441 \, a^{8} b^{17} - 364 \, a^{6} b^{19} + 118 \, a^{4} b^{21} - 12 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}, \frac{560 \, a^{16} b - 4480 \, a^{14} b^{3} + 15680 \, a^{12} b^{5} - 31360 \, a^{10} b^{7} + 39200 \, a^{8} b^{9} - 31360 \, a^{6} b^{11} + 15680 \, a^{4} b^{13} - 4480 \, a^{2} b^{15} + 560 \, b^{17} - {\left(560 \, a^{10} b^{7} + 41912 \, a^{8} b^{9} + 83162 \, a^{6} b^{11} - 71123 \, a^{4} b^{13} - 52463 \, a^{2} b^{15} - 2048 \, b^{17}\right)} \cos\left(d x + c\right)^{8} + 14 \, {\left(840 \, a^{12} b^{5} + 53648 \, a^{10} b^{7} + 95441 \, a^{8} b^{9} - 77704 \, a^{6} b^{11} - 60644 \, a^{4} b^{13} - 11069 \, a^{2} b^{15} - 512 \, b^{17}\right)} \cos\left(d x + c\right)^{6} - 35 \, {\left(560 \, a^{14} b^{3} + 27440 \, a^{12} b^{5} + 71064 \, a^{10} b^{7} + 29927 \, a^{8} b^{9} - 81421 \, a^{6} b^{11} - 43131 \, a^{4} b^{13} - 4183 \, a^{2} b^{15} - 256 \, b^{17}\right)} \cos\left(d x + c\right)^{4} + 70 \, {\left(56 \, a^{16} b + 1400 \, a^{14} b^{3} + 13832 \, a^{12} b^{5} + 24080 \, a^{10} b^{7} - 4591 \, a^{8} b^{9} - 23443 \, a^{6} b^{11} - 10717 \, a^{4} b^{13} - 553 \, a^{2} b^{15} - 64 \, b^{17}\right)} \cos\left(d x + c\right)^{2} + 315 \, {\left(7 \, {\left(64 \, a^{8} b^{8} + 336 \, a^{6} b^{10} + 280 \, a^{4} b^{12} + 35 \, a^{2} b^{14}\right)} \cos\left(d x + c\right)^{7} - 7 \, {\left(320 \, a^{10} b^{6} + 1872 \, a^{8} b^{8} + 2408 \, a^{6} b^{10} + 1015 \, a^{4} b^{12} + 105 \, a^{2} b^{14}\right)} \cos\left(d x + c\right)^{5} + 7 \, {\left(192 \, a^{12} b^{4} + 1648 \, a^{10} b^{6} + 4392 \, a^{8} b^{8} + 3913 \, a^{6} b^{10} + 1190 \, a^{4} b^{12} + 105 \, a^{2} b^{14}\right)} \cos\left(d x + c\right)^{3} - {\left(64 \, a^{14} b^{2} + 1680 \, a^{12} b^{4} + 9576 \, a^{10} b^{6} + 18123 \, a^{8} b^{8} + 12887 \, a^{6} b^{10} + 3185 \, a^{4} b^{12} + 245 \, a^{2} b^{14}\right)} \cos\left(d x + c\right) + {\left({\left(64 \, a^{7} b^{9} + 336 \, a^{5} b^{11} + 280 \, a^{3} b^{13} + 35 \, a b^{15}\right)} \cos\left(d x + c\right)^{7} - 3 \, {\left(448 \, a^{9} b^{7} + 2416 \, a^{7} b^{9} + 2296 \, a^{5} b^{11} + 525 \, a^{3} b^{13} + 35 \, a b^{15}\right)} \cos\left(d x + c\right)^{5} + {\left(2240 \, a^{11} b^{5} + 14448 \, a^{9} b^{7} + 24104 \, a^{7} b^{9} + 13993 \, a^{5} b^{11} + 2310 \, a^{3} b^{13} + 105 \, a b^{15}\right)} \cos\left(d x + c\right)^{3} - {\left(448 \, a^{13} b^{3} + 4592 \, a^{11} b^{5} + 15064 \, a^{9} b^{7} + 17165 \, a^{7} b^{9} + 7441 \, a^{5} b^{11} + 1015 \, a^{3} b^{13} + 35 \, a b^{15}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 7 \, {\left(80 \, a^{17} - 640 \, a^{15} b^{2} + 2240 \, a^{13} b^{4} - 4480 \, a^{11} b^{6} + 5600 \, a^{9} b^{8} - 4480 \, a^{7} b^{10} + 2240 \, a^{5} b^{12} - 640 \, a^{3} b^{14} + 80 \, a b^{16} - {\left(560 \, a^{11} b^{6} + 39032 \, a^{9} b^{8} + 70922 \, a^{7} b^{10} - 68603 \, a^{5} b^{12} - 41438 \, a^{3} b^{14} - 473 \, a b^{16}\right)} \cos\left(d x + c\right)^{6} + 10 \, {\left(280 \, a^{13} b^{4} + 15960 \, a^{11} b^{6} + 29463 \, a^{9} b^{8} - 13541 \, a^{7} b^{10} - 23679 \, a^{5} b^{12} - 8391 \, a^{3} b^{14} - 92 \, a b^{16}\right)} \cos\left(d x + c\right)^{4} - 15 \, {\left(112 \, a^{15} b^{2} + 4256 \, a^{13} b^{4} + 13272 \, a^{11} b^{6} + 11977 \, a^{9} b^{8} - 15634 \, a^{7} b^{10} - 11088 \, a^{5} b^{12} - 2870 \, a^{3} b^{14} - 25 \, a b^{16}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{560 \, {\left(7 \, {\left(a^{19} b^{6} - 9 \, a^{17} b^{8} + 36 \, a^{15} b^{10} - 84 \, a^{13} b^{12} + 126 \, a^{11} b^{14} - 126 \, a^{9} b^{16} + 84 \, a^{7} b^{18} - 36 \, a^{5} b^{20} + 9 \, a^{3} b^{22} - a b^{24}\right)} d \cos\left(d x + c\right)^{7} - 7 \, {\left(5 \, a^{21} b^{4} - 42 \, a^{19} b^{6} + 153 \, a^{17} b^{8} - 312 \, a^{15} b^{10} + 378 \, a^{13} b^{12} - 252 \, a^{11} b^{14} + 42 \, a^{9} b^{16} + 72 \, a^{7} b^{18} - 63 \, a^{5} b^{20} + 22 \, a^{3} b^{22} - 3 \, a b^{24}\right)} d \cos\left(d x + c\right)^{5} + 7 \, {\left(3 \, a^{23} b^{2} - 17 \, a^{21} b^{4} + 21 \, a^{19} b^{6} + 81 \, a^{17} b^{8} - 354 \, a^{15} b^{10} + 630 \, a^{13} b^{12} - 630 \, a^{11} b^{14} + 354 \, a^{9} b^{16} - 81 \, a^{7} b^{18} - 21 \, a^{5} b^{20} + 17 \, a^{3} b^{22} - 3 \, a b^{24}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{25} + 12 \, a^{23} b^{2} - 118 \, a^{21} b^{4} + 364 \, a^{19} b^{6} - 441 \, a^{17} b^{8} - 168 \, a^{15} b^{10} + 1260 \, a^{13} b^{12} - 1800 \, a^{11} b^{14} + 1311 \, a^{9} b^{16} - 484 \, a^{7} b^{18} + 42 \, a^{5} b^{20} + 28 \, a^{3} b^{22} - 7 \, a b^{24}\right)} d \cos\left(d x + c\right) + {\left({\left(a^{18} b^{7} - 9 \, a^{16} b^{9} + 36 \, a^{14} b^{11} - 84 \, a^{12} b^{13} + 126 \, a^{10} b^{15} - 126 \, a^{8} b^{17} + 84 \, a^{6} b^{19} - 36 \, a^{4} b^{21} + 9 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)^{7} - 3 \, {\left(7 \, a^{20} b^{5} - 62 \, a^{18} b^{7} + 243 \, a^{16} b^{9} - 552 \, a^{14} b^{11} + 798 \, a^{12} b^{13} - 756 \, a^{10} b^{15} + 462 \, a^{8} b^{17} - 168 \, a^{6} b^{19} + 27 \, a^{4} b^{21} + 2 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)^{5} + {\left(35 \, a^{22} b^{3} - 273 \, a^{20} b^{5} + 885 \, a^{18} b^{7} - 1455 \, a^{16} b^{9} + 990 \, a^{14} b^{11} + 630 \, a^{12} b^{13} - 1974 \, a^{10} b^{15} + 1890 \, a^{8} b^{17} - 945 \, a^{6} b^{19} + 235 \, a^{4} b^{21} - 15 \, a^{2} b^{23} - 3 \, b^{25}\right)} d \cos\left(d x + c\right)^{3} - {\left(7 \, a^{24} b - 28 \, a^{22} b^{3} - 42 \, a^{20} b^{5} + 484 \, a^{18} b^{7} - 1311 \, a^{16} b^{9} + 1800 \, a^{14} b^{11} - 1260 \, a^{12} b^{13} + 168 \, a^{10} b^{15} + 441 \, a^{8} b^{17} - 364 \, a^{6} b^{19} + 118 \, a^{4} b^{21} - 12 \, a^{2} b^{23} - b^{25}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/1120*(1120*a^16*b - 8960*a^14*b^3 + 31360*a^12*b^5 - 62720*a^10*b^7 + 78400*a^8*b^9 - 62720*a^6*b^11 + 31360*a^4*b^13 - 8960*a^2*b^15 + 1120*b^17 - 2*(560*a^10*b^7 + 41912*a^8*b^9 + 83162*a^6*b^11 - 71123*a^4*b^13 - 52463*a^2*b^15 - 2048*b^17)*cos(d*x + c)^8 + 28*(840*a^12*b^5 + 53648*a^10*b^7 + 95441*a^8*b^9 - 77704*a^6*b^11 - 60644*a^4*b^13 - 11069*a^2*b^15 - 512*b^17)*cos(d*x + c)^6 - 70*(560*a^14*b^3 + 27440*a^12*b^5 + 71064*a^10*b^7 + 29927*a^8*b^9 - 81421*a^6*b^11 - 43131*a^4*b^13 - 4183*a^2*b^15 - 256*b^17)*cos(d*x + c)^4 + 140*(56*a^16*b + 1400*a^14*b^3 + 13832*a^12*b^5 + 24080*a^10*b^7 - 4591*a^8*b^9 - 23443*a^6*b^11 - 10717*a^4*b^13 - 553*a^2*b^15 - 64*b^17)*cos(d*x + c)^2 - 315*(7*(64*a^8*b^8 + 336*a^6*b^10 + 280*a^4*b^12 + 35*a^2*b^14)*cos(d*x + c)^7 - 7*(320*a^10*b^6 + 1872*a^8*b^8 + 2408*a^6*b^10 + 1015*a^4*b^12 + 105*a^2*b^14)*cos(d*x + c)^5 + 7*(192*a^12*b^4 + 1648*a^10*b^6 + 4392*a^8*b^8 + 3913*a^6*b^10 + 1190*a^4*b^12 + 105*a^2*b^14)*cos(d*x + c)^3 - (64*a^14*b^2 + 1680*a^12*b^4 + 9576*a^10*b^6 + 18123*a^8*b^8 + 12887*a^6*b^10 + 3185*a^4*b^12 + 245*a^2*b^14)*cos(d*x + c) + ((64*a^7*b^9 + 336*a^5*b^11 + 280*a^3*b^13 + 35*a*b^15)*cos(d*x + c)^7 - 3*(448*a^9*b^7 + 2416*a^7*b^9 + 2296*a^5*b^11 + 525*a^3*b^13 + 35*a*b^15)*cos(d*x + c)^5 + (2240*a^11*b^5 + 14448*a^9*b^7 + 24104*a^7*b^9 + 13993*a^5*b^11 + 2310*a^3*b^13 + 105*a*b^15)*cos(d*x + c)^3 - (448*a^13*b^3 + 4592*a^11*b^5 + 15064*a^9*b^7 + 17165*a^7*b^9 + 7441*a^5*b^11 + 1015*a^3*b^13 + 35*a*b^15)*cos(d*x + c))*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 14*(80*a^17 - 640*a^15*b^2 + 2240*a^13*b^4 - 4480*a^11*b^6 + 5600*a^9*b^8 - 4480*a^7*b^10 + 2240*a^5*b^12 - 640*a^3*b^14 + 80*a*b^16 - (560*a^11*b^6 + 39032*a^9*b^8 + 70922*a^7*b^10 - 68603*a^5*b^12 - 41438*a^3*b^14 - 473*a*b^16)*cos(d*x + c)^6 + 10*(280*a^13*b^4 + 15960*a^11*b^6 + 29463*a^9*b^8 - 13541*a^7*b^10 - 23679*a^5*b^12 - 8391*a^3*b^14 - 92*a*b^16)*cos(d*x + c)^4 - 15*(112*a^15*b^2 + 4256*a^13*b^4 + 13272*a^11*b^6 + 11977*a^9*b^8 - 15634*a^7*b^10 - 11088*a^5*b^12 - 2870*a^3*b^14 - 25*a*b^16)*cos(d*x + c)^2)*sin(d*x + c))/(7*(a^19*b^6 - 9*a^17*b^8 + 36*a^15*b^10 - 84*a^13*b^12 + 126*a^11*b^14 - 126*a^9*b^16 + 84*a^7*b^18 - 36*a^5*b^20 + 9*a^3*b^22 - a*b^24)*d*cos(d*x + c)^7 - 7*(5*a^21*b^4 - 42*a^19*b^6 + 153*a^17*b^8 - 312*a^15*b^10 + 378*a^13*b^12 - 252*a^11*b^14 + 42*a^9*b^16 + 72*a^7*b^18 - 63*a^5*b^20 + 22*a^3*b^22 - 3*a*b^24)*d*cos(d*x + c)^5 + 7*(3*a^23*b^2 - 17*a^21*b^4 + 21*a^19*b^6 + 81*a^17*b^8 - 354*a^15*b^10 + 630*a^13*b^12 - 630*a^11*b^14 + 354*a^9*b^16 - 81*a^7*b^18 - 21*a^5*b^20 + 17*a^3*b^22 - 3*a*b^24)*d*cos(d*x + c)^3 - (a^25 + 12*a^23*b^2 - 118*a^21*b^4 + 364*a^19*b^6 - 441*a^17*b^8 - 168*a^15*b^10 + 1260*a^13*b^12 - 1800*a^11*b^14 + 1311*a^9*b^16 - 484*a^7*b^18 + 42*a^5*b^20 + 28*a^3*b^22 - 7*a*b^24)*d*cos(d*x + c) + ((a^18*b^7 - 9*a^16*b^9 + 36*a^14*b^11 - 84*a^12*b^13 + 126*a^10*b^15 - 126*a^8*b^17 + 84*a^6*b^19 - 36*a^4*b^21 + 9*a^2*b^23 - b^25)*d*cos(d*x + c)^7 - 3*(7*a^20*b^5 - 62*a^18*b^7 + 243*a^16*b^9 - 552*a^14*b^11 + 798*a^12*b^13 - 756*a^10*b^15 + 462*a^8*b^17 - 168*a^6*b^19 + 27*a^4*b^21 + 2*a^2*b^23 - b^25)*d*cos(d*x + c)^5 + (35*a^22*b^3 - 273*a^20*b^5 + 885*a^18*b^7 - 1455*a^16*b^9 + 990*a^14*b^11 + 630*a^12*b^13 - 1974*a^10*b^15 + 1890*a^8*b^17 - 945*a^6*b^19 + 235*a^4*b^21 - 15*a^2*b^23 - 3*b^25)*d*cos(d*x + c)^3 - (7*a^24*b - 28*a^22*b^3 - 42*a^20*b^5 + 484*a^18*b^7 - 1311*a^16*b^9 + 1800*a^14*b^11 - 1260*a^12*b^13 + 168*a^10*b^15 + 441*a^8*b^17 - 364*a^6*b^19 + 118*a^4*b^21 - 12*a^2*b^23 - b^25)*d*cos(d*x + c))*sin(d*x + c)), 1/560*(560*a^16*b - 4480*a^14*b^3 + 15680*a^12*b^5 - 31360*a^10*b^7 + 39200*a^8*b^9 - 31360*a^6*b^11 + 15680*a^4*b^13 - 4480*a^2*b^15 + 560*b^17 - (560*a^10*b^7 + 41912*a^8*b^9 + 83162*a^6*b^11 - 71123*a^4*b^13 - 52463*a^2*b^15 - 2048*b^17)*cos(d*x + c)^8 + 14*(840*a^12*b^5 + 53648*a^10*b^7 + 95441*a^8*b^9 - 77704*a^6*b^11 - 60644*a^4*b^13 - 11069*a^2*b^15 - 512*b^17)*cos(d*x + c)^6 - 35*(560*a^14*b^3 + 27440*a^12*b^5 + 71064*a^10*b^7 + 29927*a^8*b^9 - 81421*a^6*b^11 - 43131*a^4*b^13 - 4183*a^2*b^15 - 256*b^17)*cos(d*x + c)^4 + 70*(56*a^16*b + 1400*a^14*b^3 + 13832*a^12*b^5 + 24080*a^10*b^7 - 4591*a^8*b^9 - 23443*a^6*b^11 - 10717*a^4*b^13 - 553*a^2*b^15 - 64*b^17)*cos(d*x + c)^2 + 315*(7*(64*a^8*b^8 + 336*a^6*b^10 + 280*a^4*b^12 + 35*a^2*b^14)*cos(d*x + c)^7 - 7*(320*a^10*b^6 + 1872*a^8*b^8 + 2408*a^6*b^10 + 1015*a^4*b^12 + 105*a^2*b^14)*cos(d*x + c)^5 + 7*(192*a^12*b^4 + 1648*a^10*b^6 + 4392*a^8*b^8 + 3913*a^6*b^10 + 1190*a^4*b^12 + 105*a^2*b^14)*cos(d*x + c)^3 - (64*a^14*b^2 + 1680*a^12*b^4 + 9576*a^10*b^6 + 18123*a^8*b^8 + 12887*a^6*b^10 + 3185*a^4*b^12 + 245*a^2*b^14)*cos(d*x + c) + ((64*a^7*b^9 + 336*a^5*b^11 + 280*a^3*b^13 + 35*a*b^15)*cos(d*x + c)^7 - 3*(448*a^9*b^7 + 2416*a^7*b^9 + 2296*a^5*b^11 + 525*a^3*b^13 + 35*a*b^15)*cos(d*x + c)^5 + (2240*a^11*b^5 + 14448*a^9*b^7 + 24104*a^7*b^9 + 13993*a^5*b^11 + 2310*a^3*b^13 + 105*a*b^15)*cos(d*x + c)^3 - (448*a^13*b^3 + 4592*a^11*b^5 + 15064*a^9*b^7 + 17165*a^7*b^9 + 7441*a^5*b^11 + 1015*a^3*b^13 + 35*a*b^15)*cos(d*x + c))*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 7*(80*a^17 - 640*a^15*b^2 + 2240*a^13*b^4 - 4480*a^11*b^6 + 5600*a^9*b^8 - 4480*a^7*b^10 + 2240*a^5*b^12 - 640*a^3*b^14 + 80*a*b^16 - (560*a^11*b^6 + 39032*a^9*b^8 + 70922*a^7*b^10 - 68603*a^5*b^12 - 41438*a^3*b^14 - 473*a*b^16)*cos(d*x + c)^6 + 10*(280*a^13*b^4 + 15960*a^11*b^6 + 29463*a^9*b^8 - 13541*a^7*b^10 - 23679*a^5*b^12 - 8391*a^3*b^14 - 92*a*b^16)*cos(d*x + c)^4 - 15*(112*a^15*b^2 + 4256*a^13*b^4 + 13272*a^11*b^6 + 11977*a^9*b^8 - 15634*a^7*b^10 - 11088*a^5*b^12 - 2870*a^3*b^14 - 25*a*b^16)*cos(d*x + c)^2)*sin(d*x + c))/(7*(a^19*b^6 - 9*a^17*b^8 + 36*a^15*b^10 - 84*a^13*b^12 + 126*a^11*b^14 - 126*a^9*b^16 + 84*a^7*b^18 - 36*a^5*b^20 + 9*a^3*b^22 - a*b^24)*d*cos(d*x + c)^7 - 7*(5*a^21*b^4 - 42*a^19*b^6 + 153*a^17*b^8 - 312*a^15*b^10 + 378*a^13*b^12 - 252*a^11*b^14 + 42*a^9*b^16 + 72*a^7*b^18 - 63*a^5*b^20 + 22*a^3*b^22 - 3*a*b^24)*d*cos(d*x + c)^5 + 7*(3*a^23*b^2 - 17*a^21*b^4 + 21*a^19*b^6 + 81*a^17*b^8 - 354*a^15*b^10 + 630*a^13*b^12 - 630*a^11*b^14 + 354*a^9*b^16 - 81*a^7*b^18 - 21*a^5*b^20 + 17*a^3*b^22 - 3*a*b^24)*d*cos(d*x + c)^3 - (a^25 + 12*a^23*b^2 - 118*a^21*b^4 + 364*a^19*b^6 - 441*a^17*b^8 - 168*a^15*b^10 + 1260*a^13*b^12 - 1800*a^11*b^14 + 1311*a^9*b^16 - 484*a^7*b^18 + 42*a^5*b^20 + 28*a^3*b^22 - 7*a*b^24)*d*cos(d*x + c) + ((a^18*b^7 - 9*a^16*b^9 + 36*a^14*b^11 - 84*a^12*b^13 + 126*a^10*b^15 - 126*a^8*b^17 + 84*a^6*b^19 - 36*a^4*b^21 + 9*a^2*b^23 - b^25)*d*cos(d*x + c)^7 - 3*(7*a^20*b^5 - 62*a^18*b^7 + 243*a^16*b^9 - 552*a^14*b^11 + 798*a^12*b^13 - 756*a^10*b^15 + 462*a^8*b^17 - 168*a^6*b^19 + 27*a^4*b^21 + 2*a^2*b^23 - b^25)*d*cos(d*x + c)^5 + (35*a^22*b^3 - 273*a^20*b^5 + 885*a^18*b^7 - 1455*a^16*b^9 + 990*a^14*b^11 + 630*a^12*b^13 - 1974*a^10*b^15 + 1890*a^8*b^17 - 945*a^6*b^19 + 235*a^4*b^21 - 15*a^2*b^23 - 3*b^25)*d*cos(d*x + c)^3 - (7*a^24*b - 28*a^22*b^3 - 42*a^20*b^5 + 484*a^18*b^7 - 1311*a^16*b^9 + 1800*a^14*b^11 - 1260*a^12*b^13 + 168*a^10*b^15 + 441*a^8*b^17 - 364*a^6*b^19 + 118*a^4*b^21 - 12*a^2*b^23 - b^25)*d*cos(d*x + c))*sin(d*x + c))]","B",0
472,1,4500,0,3.565971," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","\left[\frac{224 \, a^{18} b - 2016 \, a^{16} b^{3} + 8064 \, a^{14} b^{5} - 18816 \, a^{12} b^{7} + 28224 \, a^{10} b^{9} - 28224 \, a^{8} b^{11} + 18816 \, a^{6} b^{13} - 8064 \, a^{4} b^{15} + 2016 \, a^{2} b^{17} - 224 \, b^{19} - 2 \, {\left(224 \, a^{12} b^{7} - 6272 \, a^{10} b^{9} - 201284 \, a^{8} b^{11} - 205692 \, a^{6} b^{13} + 277535 \, a^{4} b^{15} + 131393 \, a^{2} b^{17} + 4096 \, b^{19}\right)} \cos\left(d x + c\right)^{10} + 28 \, {\left(336 \, a^{14} b^{5} - 9352 \, a^{12} b^{7} - 252014 \, a^{10} b^{9} - 230159 \, a^{8} b^{11} + 297312 \, a^{6} b^{13} + 165122 \, a^{4} b^{15} + 27731 \, a^{2} b^{17} + 1024 \, b^{19}\right)} \cos\left(d x + c\right)^{8} - 70 \, {\left(224 \, a^{16} b^{3} - 5936 \, a^{14} b^{5} - 126448 \, a^{12} b^{7} - 243082 \, a^{10} b^{9} - 29747 \, a^{8} b^{11} + 284285 \, a^{6} b^{13} + 109607 \, a^{4} b^{15} + 10585 \, a^{2} b^{17} + 512 \, b^{19}\right)} \cos\left(d x + c\right)^{6} + 28 \, {\left(112 \, a^{18} b - 2296 \, a^{16} b^{3} - 35224 \, a^{14} b^{5} - 308392 \, a^{12} b^{7} - 337750 \, a^{10} b^{9} + 149783 \, a^{8} b^{11} + 394751 \, a^{6} b^{13} + 130949 \, a^{4} b^{15} + 7427 \, a^{2} b^{17} + 640 \, b^{19}\right)} \cos\left(d x + c\right)^{4} - 224 \, {\left(7 \, a^{18} b - 46 \, a^{16} b^{3} + 116 \, a^{14} b^{5} - 112 \, a^{12} b^{7} - 70 \, a^{10} b^{9} + 308 \, a^{8} b^{11} - 364 \, a^{6} b^{13} + 224 \, a^{4} b^{15} - 73 \, a^{2} b^{17} + 10 \, b^{19}\right)} \cos\left(d x + c\right)^{2} + 3465 \, {\left(7 \, {\left(32 \, a^{8} b^{10} + 112 \, a^{6} b^{12} + 70 \, a^{4} b^{14} + 7 \, a^{2} b^{16}\right)} \cos\left(d x + c\right)^{9} - 7 \, {\left(160 \, a^{10} b^{8} + 656 \, a^{8} b^{10} + 686 \, a^{6} b^{12} + 245 \, a^{4} b^{14} + 21 \, a^{2} b^{16}\right)} \cos\left(d x + c\right)^{7} + 7 \, {\left(96 \, a^{12} b^{6} + 656 \, a^{10} b^{8} + 1426 \, a^{8} b^{10} + 1057 \, a^{6} b^{12} + 280 \, a^{4} b^{14} + 21 \, a^{2} b^{16}\right)} \cos\left(d x + c\right)^{5} - {\left(32 \, a^{14} b^{4} + 784 \, a^{12} b^{6} + 3542 \, a^{10} b^{8} + 5621 \, a^{8} b^{10} + 3381 \, a^{6} b^{12} + 735 \, a^{4} b^{14} + 49 \, a^{2} b^{16}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(32 \, a^{7} b^{11} + 112 \, a^{5} b^{13} + 70 \, a^{3} b^{15} + 7 \, a b^{17}\right)} \cos\left(d x + c\right)^{9} - 3 \, {\left(224 \, a^{9} b^{9} + 816 \, a^{7} b^{11} + 602 \, a^{5} b^{13} + 119 \, a^{3} b^{15} + 7 \, a b^{17}\right)} \cos\left(d x + c\right)^{7} + {\left(1120 \, a^{11} b^{7} + 5264 \, a^{9} b^{9} + 7250 \, a^{7} b^{11} + 3521 \, a^{5} b^{13} + 504 \, a^{3} b^{15} + 21 \, a b^{17}\right)} \cos\left(d x + c\right)^{5} - {\left(224 \, a^{13} b^{5} + 1904 \, a^{11} b^{7} + 5082 \, a^{9} b^{9} + 4883 \, a^{7} b^{11} + 1827 \, a^{5} b^{13} + 217 \, a^{3} b^{15} + 7 \, a b^{17}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 14 \, {\left(16 \, a^{19} - 144 \, a^{17} b^{2} + 576 \, a^{15} b^{4} - 1344 \, a^{13} b^{6} + 2016 \, a^{11} b^{8} - 2016 \, a^{9} b^{10} + 1344 \, a^{7} b^{12} - 576 \, a^{5} b^{14} + 144 \, a^{3} b^{16} - 16 \, a b^{18} - {\left(224 \, a^{13} b^{6} - 6272 \, a^{11} b^{8} - 185444 \, a^{9} b^{10} - 166092 \, a^{7} b^{12} + 256745 \, a^{5} b^{14} + 100208 \, a^{3} b^{16} + 631 \, a b^{18}\right)} \cos\left(d x + c\right)^{8} + 10 \, {\left(112 \, a^{15} b^{4} - 3080 \, a^{13} b^{6} - 73962 \, a^{11} b^{8} - 78323 \, a^{9} b^{10} + 60829 \, a^{7} b^{12} + 73923 \, a^{5} b^{14} + 20401 \, a^{3} b^{16} + 100 \, a b^{18}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(224 \, a^{17} b^{2} - 5712 \, a^{15} b^{4} - 95648 \, a^{13} b^{6} - 254254 \, a^{11} b^{8} - 120855 \, a^{9} b^{10} + 282886 \, a^{7} b^{12} + 157892 \, a^{5} b^{14} + 35448 \, a^{3} b^{16} + 19 \, a b^{18}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(2 \, a^{19} - 35 \, a^{17} b^{2} + 208 \, a^{15} b^{4} - 644 \, a^{13} b^{6} + 1204 \, a^{11} b^{8} - 1442 \, a^{9} b^{10} + 1120 \, a^{7} b^{12} - 548 \, a^{5} b^{14} + 154 \, a^{3} b^{16} - 19 \, a b^{18}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{672 \, {\left(7 \, {\left(a^{21} b^{6} - 10 \, a^{19} b^{8} + 45 \, a^{17} b^{10} - 120 \, a^{15} b^{12} + 210 \, a^{13} b^{14} - 252 \, a^{11} b^{16} + 210 \, a^{9} b^{18} - 120 \, a^{7} b^{20} + 45 \, a^{5} b^{22} - 10 \, a^{3} b^{24} + a b^{26}\right)} d \cos\left(d x + c\right)^{9} - 7 \, {\left(5 \, a^{23} b^{4} - 47 \, a^{21} b^{6} + 195 \, a^{19} b^{8} - 465 \, a^{17} b^{10} + 690 \, a^{15} b^{12} - 630 \, a^{13} b^{14} + 294 \, a^{11} b^{16} + 30 \, a^{9} b^{18} - 135 \, a^{7} b^{20} + 85 \, a^{5} b^{22} - 25 \, a^{3} b^{24} + 3 \, a b^{26}\right)} d \cos\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{25} b^{2} - 20 \, a^{23} b^{4} + 38 \, a^{21} b^{6} + 60 \, a^{19} b^{8} - 435 \, a^{17} b^{10} + 984 \, a^{15} b^{12} - 1260 \, a^{13} b^{14} + 984 \, a^{11} b^{16} - 435 \, a^{9} b^{18} + 60 \, a^{7} b^{20} + 38 \, a^{5} b^{22} - 20 \, a^{3} b^{24} + 3 \, a b^{26}\right)} d \cos\left(d x + c\right)^{5} - {\left(a^{27} + 11 \, a^{25} b^{2} - 130 \, a^{23} b^{4} + 482 \, a^{21} b^{6} - 805 \, a^{19} b^{8} + 273 \, a^{17} b^{10} + 1428 \, a^{15} b^{12} - 3060 \, a^{13} b^{14} + 3111 \, a^{11} b^{16} - 1795 \, a^{9} b^{18} + 526 \, a^{7} b^{20} - 14 \, a^{5} b^{22} - 35 \, a^{3} b^{24} + 7 \, a b^{26}\right)} d \cos\left(d x + c\right)^{3} + {\left({\left(a^{20} b^{7} - 10 \, a^{18} b^{9} + 45 \, a^{16} b^{11} - 120 \, a^{14} b^{13} + 210 \, a^{12} b^{15} - 252 \, a^{10} b^{17} + 210 \, a^{8} b^{19} - 120 \, a^{6} b^{21} + 45 \, a^{4} b^{23} - 10 \, a^{2} b^{25} + b^{27}\right)} d \cos\left(d x + c\right)^{9} - 3 \, {\left(7 \, a^{22} b^{5} - 69 \, a^{20} b^{7} + 305 \, a^{18} b^{9} - 795 \, a^{16} b^{11} + 1350 \, a^{14} b^{13} - 1554 \, a^{12} b^{15} + 1218 \, a^{10} b^{17} - 630 \, a^{8} b^{19} + 195 \, a^{6} b^{21} - 25 \, a^{4} b^{23} - 3 \, a^{2} b^{25} + b^{27}\right)} d \cos\left(d x + c\right)^{7} + {\left(35 \, a^{24} b^{3} - 308 \, a^{22} b^{5} + 1158 \, a^{20} b^{7} - 2340 \, a^{18} b^{9} + 2445 \, a^{16} b^{11} - 360 \, a^{14} b^{13} - 2604 \, a^{12} b^{15} + 3864 \, a^{10} b^{17} - 2835 \, a^{8} b^{19} + 1180 \, a^{6} b^{21} - 250 \, a^{4} b^{23} + 12 \, a^{2} b^{25} + 3 \, b^{27}\right)} d \cos\left(d x + c\right)^{5} - {\left(7 \, a^{26} b - 35 \, a^{24} b^{3} - 14 \, a^{22} b^{5} + 526 \, a^{20} b^{7} - 1795 \, a^{18} b^{9} + 3111 \, a^{16} b^{11} - 3060 \, a^{14} b^{13} + 1428 \, a^{12} b^{15} + 273 \, a^{10} b^{17} - 805 \, a^{8} b^{19} + 482 \, a^{6} b^{21} - 130 \, a^{4} b^{23} + 11 \, a^{2} b^{25} + b^{27}\right)} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}, \frac{112 \, a^{18} b - 1008 \, a^{16} b^{3} + 4032 \, a^{14} b^{5} - 9408 \, a^{12} b^{7} + 14112 \, a^{10} b^{9} - 14112 \, a^{8} b^{11} + 9408 \, a^{6} b^{13} - 4032 \, a^{4} b^{15} + 1008 \, a^{2} b^{17} - 112 \, b^{19} - {\left(224 \, a^{12} b^{7} - 6272 \, a^{10} b^{9} - 201284 \, a^{8} b^{11} - 205692 \, a^{6} b^{13} + 277535 \, a^{4} b^{15} + 131393 \, a^{2} b^{17} + 4096 \, b^{19}\right)} \cos\left(d x + c\right)^{10} + 14 \, {\left(336 \, a^{14} b^{5} - 9352 \, a^{12} b^{7} - 252014 \, a^{10} b^{9} - 230159 \, a^{8} b^{11} + 297312 \, a^{6} b^{13} + 165122 \, a^{4} b^{15} + 27731 \, a^{2} b^{17} + 1024 \, b^{19}\right)} \cos\left(d x + c\right)^{8} - 35 \, {\left(224 \, a^{16} b^{3} - 5936 \, a^{14} b^{5} - 126448 \, a^{12} b^{7} - 243082 \, a^{10} b^{9} - 29747 \, a^{8} b^{11} + 284285 \, a^{6} b^{13} + 109607 \, a^{4} b^{15} + 10585 \, a^{2} b^{17} + 512 \, b^{19}\right)} \cos\left(d x + c\right)^{6} + 14 \, {\left(112 \, a^{18} b - 2296 \, a^{16} b^{3} - 35224 \, a^{14} b^{5} - 308392 \, a^{12} b^{7} - 337750 \, a^{10} b^{9} + 149783 \, a^{8} b^{11} + 394751 \, a^{6} b^{13} + 130949 \, a^{4} b^{15} + 7427 \, a^{2} b^{17} + 640 \, b^{19}\right)} \cos\left(d x + c\right)^{4} - 112 \, {\left(7 \, a^{18} b - 46 \, a^{16} b^{3} + 116 \, a^{14} b^{5} - 112 \, a^{12} b^{7} - 70 \, a^{10} b^{9} + 308 \, a^{8} b^{11} - 364 \, a^{6} b^{13} + 224 \, a^{4} b^{15} - 73 \, a^{2} b^{17} + 10 \, b^{19}\right)} \cos\left(d x + c\right)^{2} - 3465 \, {\left(7 \, {\left(32 \, a^{8} b^{10} + 112 \, a^{6} b^{12} + 70 \, a^{4} b^{14} + 7 \, a^{2} b^{16}\right)} \cos\left(d x + c\right)^{9} - 7 \, {\left(160 \, a^{10} b^{8} + 656 \, a^{8} b^{10} + 686 \, a^{6} b^{12} + 245 \, a^{4} b^{14} + 21 \, a^{2} b^{16}\right)} \cos\left(d x + c\right)^{7} + 7 \, {\left(96 \, a^{12} b^{6} + 656 \, a^{10} b^{8} + 1426 \, a^{8} b^{10} + 1057 \, a^{6} b^{12} + 280 \, a^{4} b^{14} + 21 \, a^{2} b^{16}\right)} \cos\left(d x + c\right)^{5} - {\left(32 \, a^{14} b^{4} + 784 \, a^{12} b^{6} + 3542 \, a^{10} b^{8} + 5621 \, a^{8} b^{10} + 3381 \, a^{6} b^{12} + 735 \, a^{4} b^{14} + 49 \, a^{2} b^{16}\right)} \cos\left(d x + c\right)^{3} + {\left({\left(32 \, a^{7} b^{11} + 112 \, a^{5} b^{13} + 70 \, a^{3} b^{15} + 7 \, a b^{17}\right)} \cos\left(d x + c\right)^{9} - 3 \, {\left(224 \, a^{9} b^{9} + 816 \, a^{7} b^{11} + 602 \, a^{5} b^{13} + 119 \, a^{3} b^{15} + 7 \, a b^{17}\right)} \cos\left(d x + c\right)^{7} + {\left(1120 \, a^{11} b^{7} + 5264 \, a^{9} b^{9} + 7250 \, a^{7} b^{11} + 3521 \, a^{5} b^{13} + 504 \, a^{3} b^{15} + 21 \, a b^{17}\right)} \cos\left(d x + c\right)^{5} - {\left(224 \, a^{13} b^{5} + 1904 \, a^{11} b^{7} + 5082 \, a^{9} b^{9} + 4883 \, a^{7} b^{11} + 1827 \, a^{5} b^{13} + 217 \, a^{3} b^{15} + 7 \, a b^{17}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 7 \, {\left(16 \, a^{19} - 144 \, a^{17} b^{2} + 576 \, a^{15} b^{4} - 1344 \, a^{13} b^{6} + 2016 \, a^{11} b^{8} - 2016 \, a^{9} b^{10} + 1344 \, a^{7} b^{12} - 576 \, a^{5} b^{14} + 144 \, a^{3} b^{16} - 16 \, a b^{18} - {\left(224 \, a^{13} b^{6} - 6272 \, a^{11} b^{8} - 185444 \, a^{9} b^{10} - 166092 \, a^{7} b^{12} + 256745 \, a^{5} b^{14} + 100208 \, a^{3} b^{16} + 631 \, a b^{18}\right)} \cos\left(d x + c\right)^{8} + 10 \, {\left(112 \, a^{15} b^{4} - 3080 \, a^{13} b^{6} - 73962 \, a^{11} b^{8} - 78323 \, a^{9} b^{10} + 60829 \, a^{7} b^{12} + 73923 \, a^{5} b^{14} + 20401 \, a^{3} b^{16} + 100 \, a b^{18}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(224 \, a^{17} b^{2} - 5712 \, a^{15} b^{4} - 95648 \, a^{13} b^{6} - 254254 \, a^{11} b^{8} - 120855 \, a^{9} b^{10} + 282886 \, a^{7} b^{12} + 157892 \, a^{5} b^{14} + 35448 \, a^{3} b^{16} + 19 \, a b^{18}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(2 \, a^{19} - 35 \, a^{17} b^{2} + 208 \, a^{15} b^{4} - 644 \, a^{13} b^{6} + 1204 \, a^{11} b^{8} - 1442 \, a^{9} b^{10} + 1120 \, a^{7} b^{12} - 548 \, a^{5} b^{14} + 154 \, a^{3} b^{16} - 19 \, a b^{18}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{336 \, {\left(7 \, {\left(a^{21} b^{6} - 10 \, a^{19} b^{8} + 45 \, a^{17} b^{10} - 120 \, a^{15} b^{12} + 210 \, a^{13} b^{14} - 252 \, a^{11} b^{16} + 210 \, a^{9} b^{18} - 120 \, a^{7} b^{20} + 45 \, a^{5} b^{22} - 10 \, a^{3} b^{24} + a b^{26}\right)} d \cos\left(d x + c\right)^{9} - 7 \, {\left(5 \, a^{23} b^{4} - 47 \, a^{21} b^{6} + 195 \, a^{19} b^{8} - 465 \, a^{17} b^{10} + 690 \, a^{15} b^{12} - 630 \, a^{13} b^{14} + 294 \, a^{11} b^{16} + 30 \, a^{9} b^{18} - 135 \, a^{7} b^{20} + 85 \, a^{5} b^{22} - 25 \, a^{3} b^{24} + 3 \, a b^{26}\right)} d \cos\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{25} b^{2} - 20 \, a^{23} b^{4} + 38 \, a^{21} b^{6} + 60 \, a^{19} b^{8} - 435 \, a^{17} b^{10} + 984 \, a^{15} b^{12} - 1260 \, a^{13} b^{14} + 984 \, a^{11} b^{16} - 435 \, a^{9} b^{18} + 60 \, a^{7} b^{20} + 38 \, a^{5} b^{22} - 20 \, a^{3} b^{24} + 3 \, a b^{26}\right)} d \cos\left(d x + c\right)^{5} - {\left(a^{27} + 11 \, a^{25} b^{2} - 130 \, a^{23} b^{4} + 482 \, a^{21} b^{6} - 805 \, a^{19} b^{8} + 273 \, a^{17} b^{10} + 1428 \, a^{15} b^{12} - 3060 \, a^{13} b^{14} + 3111 \, a^{11} b^{16} - 1795 \, a^{9} b^{18} + 526 \, a^{7} b^{20} - 14 \, a^{5} b^{22} - 35 \, a^{3} b^{24} + 7 \, a b^{26}\right)} d \cos\left(d x + c\right)^{3} + {\left({\left(a^{20} b^{7} - 10 \, a^{18} b^{9} + 45 \, a^{16} b^{11} - 120 \, a^{14} b^{13} + 210 \, a^{12} b^{15} - 252 \, a^{10} b^{17} + 210 \, a^{8} b^{19} - 120 \, a^{6} b^{21} + 45 \, a^{4} b^{23} - 10 \, a^{2} b^{25} + b^{27}\right)} d \cos\left(d x + c\right)^{9} - 3 \, {\left(7 \, a^{22} b^{5} - 69 \, a^{20} b^{7} + 305 \, a^{18} b^{9} - 795 \, a^{16} b^{11} + 1350 \, a^{14} b^{13} - 1554 \, a^{12} b^{15} + 1218 \, a^{10} b^{17} - 630 \, a^{8} b^{19} + 195 \, a^{6} b^{21} - 25 \, a^{4} b^{23} - 3 \, a^{2} b^{25} + b^{27}\right)} d \cos\left(d x + c\right)^{7} + {\left(35 \, a^{24} b^{3} - 308 \, a^{22} b^{5} + 1158 \, a^{20} b^{7} - 2340 \, a^{18} b^{9} + 2445 \, a^{16} b^{11} - 360 \, a^{14} b^{13} - 2604 \, a^{12} b^{15} + 3864 \, a^{10} b^{17} - 2835 \, a^{8} b^{19} + 1180 \, a^{6} b^{21} - 250 \, a^{4} b^{23} + 12 \, a^{2} b^{25} + 3 \, b^{27}\right)} d \cos\left(d x + c\right)^{5} - {\left(7 \, a^{26} b - 35 \, a^{24} b^{3} - 14 \, a^{22} b^{5} + 526 \, a^{20} b^{7} - 1795 \, a^{18} b^{9} + 3111 \, a^{16} b^{11} - 3060 \, a^{14} b^{13} + 1428 \, a^{12} b^{15} + 273 \, a^{10} b^{17} - 805 \, a^{8} b^{19} + 482 \, a^{6} b^{21} - 130 \, a^{4} b^{23} + 11 \, a^{2} b^{25} + b^{27}\right)} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/672*(224*a^18*b - 2016*a^16*b^3 + 8064*a^14*b^5 - 18816*a^12*b^7 + 28224*a^10*b^9 - 28224*a^8*b^11 + 18816*a^6*b^13 - 8064*a^4*b^15 + 2016*a^2*b^17 - 224*b^19 - 2*(224*a^12*b^7 - 6272*a^10*b^9 - 201284*a^8*b^11 - 205692*a^6*b^13 + 277535*a^4*b^15 + 131393*a^2*b^17 + 4096*b^19)*cos(d*x + c)^10 + 28*(336*a^14*b^5 - 9352*a^12*b^7 - 252014*a^10*b^9 - 230159*a^8*b^11 + 297312*a^6*b^13 + 165122*a^4*b^15 + 27731*a^2*b^17 + 1024*b^19)*cos(d*x + c)^8 - 70*(224*a^16*b^3 - 5936*a^14*b^5 - 126448*a^12*b^7 - 243082*a^10*b^9 - 29747*a^8*b^11 + 284285*a^6*b^13 + 109607*a^4*b^15 + 10585*a^2*b^17 + 512*b^19)*cos(d*x + c)^6 + 28*(112*a^18*b - 2296*a^16*b^3 - 35224*a^14*b^5 - 308392*a^12*b^7 - 337750*a^10*b^9 + 149783*a^8*b^11 + 394751*a^6*b^13 + 130949*a^4*b^15 + 7427*a^2*b^17 + 640*b^19)*cos(d*x + c)^4 - 224*(7*a^18*b - 46*a^16*b^3 + 116*a^14*b^5 - 112*a^12*b^7 - 70*a^10*b^9 + 308*a^8*b^11 - 364*a^6*b^13 + 224*a^4*b^15 - 73*a^2*b^17 + 10*b^19)*cos(d*x + c)^2 + 3465*(7*(32*a^8*b^10 + 112*a^6*b^12 + 70*a^4*b^14 + 7*a^2*b^16)*cos(d*x + c)^9 - 7*(160*a^10*b^8 + 656*a^8*b^10 + 686*a^6*b^12 + 245*a^4*b^14 + 21*a^2*b^16)*cos(d*x + c)^7 + 7*(96*a^12*b^6 + 656*a^10*b^8 + 1426*a^8*b^10 + 1057*a^6*b^12 + 280*a^4*b^14 + 21*a^2*b^16)*cos(d*x + c)^5 - (32*a^14*b^4 + 784*a^12*b^6 + 3542*a^10*b^8 + 5621*a^8*b^10 + 3381*a^6*b^12 + 735*a^4*b^14 + 49*a^2*b^16)*cos(d*x + c)^3 + ((32*a^7*b^11 + 112*a^5*b^13 + 70*a^3*b^15 + 7*a*b^17)*cos(d*x + c)^9 - 3*(224*a^9*b^9 + 816*a^7*b^11 + 602*a^5*b^13 + 119*a^3*b^15 + 7*a*b^17)*cos(d*x + c)^7 + (1120*a^11*b^7 + 5264*a^9*b^9 + 7250*a^7*b^11 + 3521*a^5*b^13 + 504*a^3*b^15 + 21*a*b^17)*cos(d*x + c)^5 - (224*a^13*b^5 + 1904*a^11*b^7 + 5082*a^9*b^9 + 4883*a^7*b^11 + 1827*a^5*b^13 + 217*a^3*b^15 + 7*a*b^17)*cos(d*x + c)^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 14*(16*a^19 - 144*a^17*b^2 + 576*a^15*b^4 - 1344*a^13*b^6 + 2016*a^11*b^8 - 2016*a^9*b^10 + 1344*a^7*b^12 - 576*a^5*b^14 + 144*a^3*b^16 - 16*a*b^18 - (224*a^13*b^6 - 6272*a^11*b^8 - 185444*a^9*b^10 - 166092*a^7*b^12 + 256745*a^5*b^14 + 100208*a^3*b^16 + 631*a*b^18)*cos(d*x + c)^8 + 10*(112*a^15*b^4 - 3080*a^13*b^6 - 73962*a^11*b^8 - 78323*a^9*b^10 + 60829*a^7*b^12 + 73923*a^5*b^14 + 20401*a^3*b^16 + 100*a*b^18)*cos(d*x + c)^6 - 3*(224*a^17*b^2 - 5712*a^15*b^4 - 95648*a^13*b^6 - 254254*a^11*b^8 - 120855*a^9*b^10 + 282886*a^7*b^12 + 157892*a^5*b^14 + 35448*a^3*b^16 + 19*a*b^18)*cos(d*x + c)^4 + 16*(2*a^19 - 35*a^17*b^2 + 208*a^15*b^4 - 644*a^13*b^6 + 1204*a^11*b^8 - 1442*a^9*b^10 + 1120*a^7*b^12 - 548*a^5*b^14 + 154*a^3*b^16 - 19*a*b^18)*cos(d*x + c)^2)*sin(d*x + c))/(7*(a^21*b^6 - 10*a^19*b^8 + 45*a^17*b^10 - 120*a^15*b^12 + 210*a^13*b^14 - 252*a^11*b^16 + 210*a^9*b^18 - 120*a^7*b^20 + 45*a^5*b^22 - 10*a^3*b^24 + a*b^26)*d*cos(d*x + c)^9 - 7*(5*a^23*b^4 - 47*a^21*b^6 + 195*a^19*b^8 - 465*a^17*b^10 + 690*a^15*b^12 - 630*a^13*b^14 + 294*a^11*b^16 + 30*a^9*b^18 - 135*a^7*b^20 + 85*a^5*b^22 - 25*a^3*b^24 + 3*a*b^26)*d*cos(d*x + c)^7 + 7*(3*a^25*b^2 - 20*a^23*b^4 + 38*a^21*b^6 + 60*a^19*b^8 - 435*a^17*b^10 + 984*a^15*b^12 - 1260*a^13*b^14 + 984*a^11*b^16 - 435*a^9*b^18 + 60*a^7*b^20 + 38*a^5*b^22 - 20*a^3*b^24 + 3*a*b^26)*d*cos(d*x + c)^5 - (a^27 + 11*a^25*b^2 - 130*a^23*b^4 + 482*a^21*b^6 - 805*a^19*b^8 + 273*a^17*b^10 + 1428*a^15*b^12 - 3060*a^13*b^14 + 3111*a^11*b^16 - 1795*a^9*b^18 + 526*a^7*b^20 - 14*a^5*b^22 - 35*a^3*b^24 + 7*a*b^26)*d*cos(d*x + c)^3 + ((a^20*b^7 - 10*a^18*b^9 + 45*a^16*b^11 - 120*a^14*b^13 + 210*a^12*b^15 - 252*a^10*b^17 + 210*a^8*b^19 - 120*a^6*b^21 + 45*a^4*b^23 - 10*a^2*b^25 + b^27)*d*cos(d*x + c)^9 - 3*(7*a^22*b^5 - 69*a^20*b^7 + 305*a^18*b^9 - 795*a^16*b^11 + 1350*a^14*b^13 - 1554*a^12*b^15 + 1218*a^10*b^17 - 630*a^8*b^19 + 195*a^6*b^21 - 25*a^4*b^23 - 3*a^2*b^25 + b^27)*d*cos(d*x + c)^7 + (35*a^24*b^3 - 308*a^22*b^5 + 1158*a^20*b^7 - 2340*a^18*b^9 + 2445*a^16*b^11 - 360*a^14*b^13 - 2604*a^12*b^15 + 3864*a^10*b^17 - 2835*a^8*b^19 + 1180*a^6*b^21 - 250*a^4*b^23 + 12*a^2*b^25 + 3*b^27)*d*cos(d*x + c)^5 - (7*a^26*b - 35*a^24*b^3 - 14*a^22*b^5 + 526*a^20*b^7 - 1795*a^18*b^9 + 3111*a^16*b^11 - 3060*a^14*b^13 + 1428*a^12*b^15 + 273*a^10*b^17 - 805*a^8*b^19 + 482*a^6*b^21 - 130*a^4*b^23 + 11*a^2*b^25 + b^27)*d*cos(d*x + c)^3)*sin(d*x + c)), 1/336*(112*a^18*b - 1008*a^16*b^3 + 4032*a^14*b^5 - 9408*a^12*b^7 + 14112*a^10*b^9 - 14112*a^8*b^11 + 9408*a^6*b^13 - 4032*a^4*b^15 + 1008*a^2*b^17 - 112*b^19 - (224*a^12*b^7 - 6272*a^10*b^9 - 201284*a^8*b^11 - 205692*a^6*b^13 + 277535*a^4*b^15 + 131393*a^2*b^17 + 4096*b^19)*cos(d*x + c)^10 + 14*(336*a^14*b^5 - 9352*a^12*b^7 - 252014*a^10*b^9 - 230159*a^8*b^11 + 297312*a^6*b^13 + 165122*a^4*b^15 + 27731*a^2*b^17 + 1024*b^19)*cos(d*x + c)^8 - 35*(224*a^16*b^3 - 5936*a^14*b^5 - 126448*a^12*b^7 - 243082*a^10*b^9 - 29747*a^8*b^11 + 284285*a^6*b^13 + 109607*a^4*b^15 + 10585*a^2*b^17 + 512*b^19)*cos(d*x + c)^6 + 14*(112*a^18*b - 2296*a^16*b^3 - 35224*a^14*b^5 - 308392*a^12*b^7 - 337750*a^10*b^9 + 149783*a^8*b^11 + 394751*a^6*b^13 + 130949*a^4*b^15 + 7427*a^2*b^17 + 640*b^19)*cos(d*x + c)^4 - 112*(7*a^18*b - 46*a^16*b^3 + 116*a^14*b^5 - 112*a^12*b^7 - 70*a^10*b^9 + 308*a^8*b^11 - 364*a^6*b^13 + 224*a^4*b^15 - 73*a^2*b^17 + 10*b^19)*cos(d*x + c)^2 - 3465*(7*(32*a^8*b^10 + 112*a^6*b^12 + 70*a^4*b^14 + 7*a^2*b^16)*cos(d*x + c)^9 - 7*(160*a^10*b^8 + 656*a^8*b^10 + 686*a^6*b^12 + 245*a^4*b^14 + 21*a^2*b^16)*cos(d*x + c)^7 + 7*(96*a^12*b^6 + 656*a^10*b^8 + 1426*a^8*b^10 + 1057*a^6*b^12 + 280*a^4*b^14 + 21*a^2*b^16)*cos(d*x + c)^5 - (32*a^14*b^4 + 784*a^12*b^6 + 3542*a^10*b^8 + 5621*a^8*b^10 + 3381*a^6*b^12 + 735*a^4*b^14 + 49*a^2*b^16)*cos(d*x + c)^3 + ((32*a^7*b^11 + 112*a^5*b^13 + 70*a^3*b^15 + 7*a*b^17)*cos(d*x + c)^9 - 3*(224*a^9*b^9 + 816*a^7*b^11 + 602*a^5*b^13 + 119*a^3*b^15 + 7*a*b^17)*cos(d*x + c)^7 + (1120*a^11*b^7 + 5264*a^9*b^9 + 7250*a^7*b^11 + 3521*a^5*b^13 + 504*a^3*b^15 + 21*a*b^17)*cos(d*x + c)^5 - (224*a^13*b^5 + 1904*a^11*b^7 + 5082*a^9*b^9 + 4883*a^7*b^11 + 1827*a^5*b^13 + 217*a^3*b^15 + 7*a*b^17)*cos(d*x + c)^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 7*(16*a^19 - 144*a^17*b^2 + 576*a^15*b^4 - 1344*a^13*b^6 + 2016*a^11*b^8 - 2016*a^9*b^10 + 1344*a^7*b^12 - 576*a^5*b^14 + 144*a^3*b^16 - 16*a*b^18 - (224*a^13*b^6 - 6272*a^11*b^8 - 185444*a^9*b^10 - 166092*a^7*b^12 + 256745*a^5*b^14 + 100208*a^3*b^16 + 631*a*b^18)*cos(d*x + c)^8 + 10*(112*a^15*b^4 - 3080*a^13*b^6 - 73962*a^11*b^8 - 78323*a^9*b^10 + 60829*a^7*b^12 + 73923*a^5*b^14 + 20401*a^3*b^16 + 100*a*b^18)*cos(d*x + c)^6 - 3*(224*a^17*b^2 - 5712*a^15*b^4 - 95648*a^13*b^6 - 254254*a^11*b^8 - 120855*a^9*b^10 + 282886*a^7*b^12 + 157892*a^5*b^14 + 35448*a^3*b^16 + 19*a*b^18)*cos(d*x + c)^4 + 16*(2*a^19 - 35*a^17*b^2 + 208*a^15*b^4 - 644*a^13*b^6 + 1204*a^11*b^8 - 1442*a^9*b^10 + 1120*a^7*b^12 - 548*a^5*b^14 + 154*a^3*b^16 - 19*a*b^18)*cos(d*x + c)^2)*sin(d*x + c))/(7*(a^21*b^6 - 10*a^19*b^8 + 45*a^17*b^10 - 120*a^15*b^12 + 210*a^13*b^14 - 252*a^11*b^16 + 210*a^9*b^18 - 120*a^7*b^20 + 45*a^5*b^22 - 10*a^3*b^24 + a*b^26)*d*cos(d*x + c)^9 - 7*(5*a^23*b^4 - 47*a^21*b^6 + 195*a^19*b^8 - 465*a^17*b^10 + 690*a^15*b^12 - 630*a^13*b^14 + 294*a^11*b^16 + 30*a^9*b^18 - 135*a^7*b^20 + 85*a^5*b^22 - 25*a^3*b^24 + 3*a*b^26)*d*cos(d*x + c)^7 + 7*(3*a^25*b^2 - 20*a^23*b^4 + 38*a^21*b^6 + 60*a^19*b^8 - 435*a^17*b^10 + 984*a^15*b^12 - 1260*a^13*b^14 + 984*a^11*b^16 - 435*a^9*b^18 + 60*a^7*b^20 + 38*a^5*b^22 - 20*a^3*b^24 + 3*a*b^26)*d*cos(d*x + c)^5 - (a^27 + 11*a^25*b^2 - 130*a^23*b^4 + 482*a^21*b^6 - 805*a^19*b^8 + 273*a^17*b^10 + 1428*a^15*b^12 - 3060*a^13*b^14 + 3111*a^11*b^16 - 1795*a^9*b^18 + 526*a^7*b^20 - 14*a^5*b^22 - 35*a^3*b^24 + 7*a*b^26)*d*cos(d*x + c)^3 + ((a^20*b^7 - 10*a^18*b^9 + 45*a^16*b^11 - 120*a^14*b^13 + 210*a^12*b^15 - 252*a^10*b^17 + 210*a^8*b^19 - 120*a^6*b^21 + 45*a^4*b^23 - 10*a^2*b^25 + b^27)*d*cos(d*x + c)^9 - 3*(7*a^22*b^5 - 69*a^20*b^7 + 305*a^18*b^9 - 795*a^16*b^11 + 1350*a^14*b^13 - 1554*a^12*b^15 + 1218*a^10*b^17 - 630*a^8*b^19 + 195*a^6*b^21 - 25*a^4*b^23 - 3*a^2*b^25 + b^27)*d*cos(d*x + c)^7 + (35*a^24*b^3 - 308*a^22*b^5 + 1158*a^20*b^7 - 2340*a^18*b^9 + 2445*a^16*b^11 - 360*a^14*b^13 - 2604*a^12*b^15 + 3864*a^10*b^17 - 2835*a^8*b^19 + 1180*a^6*b^21 - 250*a^4*b^23 + 12*a^2*b^25 + 3*b^27)*d*cos(d*x + c)^5 - (7*a^26*b - 35*a^24*b^3 - 14*a^22*b^5 + 526*a^20*b^7 - 1795*a^18*b^9 + 3111*a^16*b^11 - 3060*a^14*b^13 + 1428*a^12*b^15 + 273*a^10*b^17 - 805*a^8*b^19 + 482*a^6*b^21 - 130*a^4*b^23 + 11*a^2*b^25 + b^27)*d*cos(d*x + c)^3)*sin(d*x + c))]","B",0
473,1,142,0,1.050169," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{5} - 480 \, a^{3} b^{2} + 992 \, a b^{4} - 16 \, {\left(3 \, a^{3} b^{2} - 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(315 \, b^{5} \cos\left(d x + c\right)^{4} - 64 \, a^{4} b + 224 \, a^{2} b^{3} + 480 \, b^{5} + 40 \, {\left(a^{2} b^{3} + 9 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{3465 \, b^{5} d}"," ",0,"2/3465*(35*a*b^4*cos(d*x + c)^4 + 128*a^5 - 480*a^3*b^2 + 992*a*b^4 - 16*(3*a^3*b^2 - 8*a*b^4)*cos(d*x + c)^2 + (315*b^5*cos(d*x + c)^4 - 64*a^4*b + 224*a^2*b^3 + 480*b^5 + 40*(a^2*b^3 + 9*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^5*d)","A",0
474,1,78,0,1.016165," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{3} + 32 \, a b^{2} + {\left(15 \, b^{3} \cos\left(d x + c\right)^{2} + 4 \, a^{2} b + 20 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{105 \, b^{3} d}"," ",0,"2/105*(3*a*b^2*cos(d*x + c)^2 - 8*a^3 + 32*a*b^2 + (15*b^3*cos(d*x + c)^2 + 4*a^2*b + 20*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^3*d)","A",0
475,1,20,0,0.876893," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\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
476,1,1729,0,1.851601," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + \sqrt{a - b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right)}{8 \, d}, -\frac{2 \, \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) - \sqrt{a - b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right)}{8 \, d}, -\frac{2 \, \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) - \sqrt{a + b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right)}{8 \, d}, -\frac{\sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) + \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right)}{4 \, d}\right]"," ",0,"[1/8*(sqrt(a + b)*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + sqrt(a - b)*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)))/d, -1/8*(2*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c))) - sqrt(a - b)*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)))/d, -1/8*(2*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c))) - sqrt(a + b)*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)))/d, -1/4*(sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c))) + sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c))))/d]","B",0
477,1,2101,0,2.253740," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a^{2} - a b - b^{2}\right)} \sqrt{a + b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - {\left(2 \, a^{2} + a b - b^{2}\right)} \sqrt{a - b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 16 \, {\left(a^{2} - b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a} \sin\left(d x + c\right)}{32 \, {\left(a^{2} - b^{2}\right)} d \cos\left(d x + c\right)^{2}}, -\frac{2 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} + a b - b^{2}\right)} \sqrt{a - b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(a^{2} - b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a} \sin\left(d x + c\right)}{32 \, {\left(a^{2} - b^{2}\right)} d \cos\left(d x + c\right)^{2}}, -\frac{2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} - {\left(2 \, a^{2} - a b - b^{2}\right)} \sqrt{a + b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(a^{2} - b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a} \sin\left(d x + c\right)}{32 \, {\left(a^{2} - b^{2}\right)} d \cos\left(d x + c\right)^{2}}, -\frac{{\left(2 \, a^{2} + a b - b^{2}\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} - a b - b^{2}\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} - 8 \, {\left(a^{2} - b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a} \sin\left(d x + c\right)}{16 \, {\left(a^{2} - b^{2}\right)} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/32*((2*a^2 - a*b - b^2)*sqrt(a + b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - (2*a^2 + a*b - b^2)*sqrt(a - b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 16*(a^2 - b^2)*sqrt(b*sin(d*x + c) + a)*sin(d*x + c))/((a^2 - b^2)*d*cos(d*x + c)^2), -1/32*(2*(2*a^2 - a*b - b^2)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 + (2*a^2 + a*b - b^2)*sqrt(a - b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(a^2 - b^2)*sqrt(b*sin(d*x + c) + a)*sin(d*x + c))/((a^2 - b^2)*d*cos(d*x + c)^2), -1/32*(2*(2*a^2 + a*b - b^2)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 - (2*a^2 - a*b - b^2)*sqrt(a + b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(a^2 - b^2)*sqrt(b*sin(d*x + c) + a)*sin(d*x + c))/((a^2 - b^2)*d*cos(d*x + c)^2), -1/16*((2*a^2 + a*b - b^2)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 + (2*a^2 - a*b - b^2)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 - 8*(a^2 - b^2)*sqrt(b*sin(d*x + c) + a)*sin(d*x + c))/((a^2 - b^2)*d*cos(d*x + c)^2)]","B",0
478,0,0,0,1.439801," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{5}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^5, x)","F",0
479,0,0,0,1.120125," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4, x)","F",0
480,0,0,0,1.103169," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
481,0,0,0,0.872933," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
482,0,0,0,1.039908," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
483,1,184,0,1.001071," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3465 \, b^{6} \cos\left(d x + c\right)^{6} - 384 \, a^{6} + 2144 \, a^{4} b^{2} - 8256 \, a^{2} b^{4} - 2464 \, b^{6} - 35 \, {\left(3 \, a^{2} b^{4} + 11 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(18 \, a^{4} b^{2} - 81 \, a^{2} b^{4} - 77 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2205 \, a b^{5} \cos\left(d x + c\right)^{4} - 96 \, a^{5} b + 512 \, a^{3} b^{3} + 4064 \, a b^{5} + 20 \, {\left(3 \, a^{3} b^{3} + 137 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{45045 \, b^{5} d}"," ",0,"-2/45045*(3465*b^6*cos(d*x + c)^6 - 384*a^6 + 2144*a^4*b^2 - 8256*a^2*b^4 - 2464*b^6 - 35*(3*a^2*b^4 + 11*b^6)*cos(d*x + c)^4 + 8*(18*a^4*b^2 - 81*a^2*b^4 - 77*b^6)*cos(d*x + c)^2 - 2*(2205*a*b^5*cos(d*x + c)^4 - 96*a^5*b + 512*a^3*b^3 + 4064*a*b^5 + 20*(3*a^3*b^3 + 137*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^5*d)","A",0
484,1,111,0,1.184260," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, b^{4} \cos\left(d x + c\right)^{4} + 8 \, a^{4} - 60 \, a^{2} b^{2} - 28 \, b^{4} - {\left(3 \, a^{2} b^{2} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(25 \, a b^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} b + 38 \, a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{315 \, b^{3} d}"," ",0,"-2/315*(35*b^4*cos(d*x + c)^4 + 8*a^4 - 60*a^2*b^2 - 28*b^4 - (3*a^2*b^2 + 7*b^4)*cos(d*x + c)^2 - 2*(25*a*b^3*cos(d*x + c)^2 + 2*a^3*b + 38*a*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^3*d)","A",0
485,1,53,0,0.860753," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}}{5 \, b d}"," ",0,"-2/5*(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(b*sin(d*x + c) + a)/(b*d)","B",0
486,0,0,0,2.594915," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) \sin\left(d x + c\right) + a \sec\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)*sin(d*x + c) + a*sec(d*x + c))*sqrt(b*sin(d*x + c) + a), x)","F",0
487,1,1969,0,1.896971," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a - b\right)} \sqrt{a + b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - {\left(2 \, a + b\right)} \sqrt{a - b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(a \sin\left(d x + c\right) + b\right)} \sqrt{b \sin\left(d x + c\right) + a}}{32 \, d \cos\left(d x + c\right)^{2}}, -\frac{2 \, {\left(2 \, a - b\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} - {\left(2 \, a + b\right)} \sqrt{a - b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(a \sin\left(d x + c\right) + b\right)} \sqrt{b \sin\left(d x + c\right) + a}}{32 \, d \cos\left(d x + c\right)^{2}}, -\frac{2 \, {\left(2 \, a + b\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sqrt{a + b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(a \sin\left(d x + c\right) + b\right)} \sqrt{b \sin\left(d x + c\right) + a}}{32 \, d \cos\left(d x + c\right)^{2}}, -\frac{{\left(2 \, a + b\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} + {\left(2 \, a - b\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} - 8 \, {\left(a \sin\left(d x + c\right) + b\right)} \sqrt{b \sin\left(d x + c\right) + a}}{16 \, d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[-1/32*((2*a - b)*sqrt(a + b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - (2*a + b)*sqrt(a - b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(a*sin(d*x + c) + b)*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^2), -1/32*(2*(2*a - b)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 - (2*a + b)*sqrt(a - b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(a*sin(d*x + c) + b)*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^2), -1/32*(2*(2*a + b)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 + (2*a - b)*sqrt(a + b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(a*sin(d*x + c) + b)*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^2), -1/16*((2*a + b)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 + (2*a - b)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 - 8*(a*sin(d*x + c) + b)*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^2)]","B",0
488,0,0,0,1.199259," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{5} \sin\left(d x + c\right) + a \sec\left(d x + c\right)^{5}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)^5*sin(d*x + c) + a*sec(d*x + c)^5)*sqrt(b*sin(d*x + c) + a), x)","F",0
489,0,0,0,0.738830," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + a \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*cos(d*x + c)^4*sin(d*x + c) + a*cos(d*x + c)^4)*sqrt(b*sin(d*x + c) + a), x)","F",0
490,0,0,0,1.135480," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*cos(d*x + c)^2*sin(d*x + c) + a*cos(d*x + c)^2)*sqrt(b*sin(d*x + c) + a), x)","F",0
491,0,0,0,1.434857," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{2} \sin\left(d x + c\right) + a \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)^2*sin(d*x + c) + a*sec(d*x + c)^2)*sqrt(b*sin(d*x + c) + a), x)","F",0
492,0,0,0,1.408857," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{4} \sin\left(d x + c\right) + a \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)^4*sin(d*x + c) + a*sec(d*x + c)^4)*sqrt(b*sin(d*x + c) + a), x)","F",0
493,0,0,0,1.498442," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{6} \sin\left(d x + c\right) + a \sec\left(d x + c\right)^{6}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)^6*sin(d*x + c) + a*sec(d*x + c)^6)*sqrt(b*sin(d*x + c) + a), x)","F",0
494,1,224,0,1.128051," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7161 \, a b^{6} \cos\left(d x + c\right)^{6} - 128 \, a^{7} + 992 \, a^{5} b^{2} - 6080 \, a^{3} b^{4} - 5536 \, a b^{6} - 7 \, {\left(5 \, a^{3} b^{4} + 79 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(3 \, a^{5} b^{2} - 20 \, a^{3} b^{4} - 67 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(3003 \, b^{7} \cos\left(d x + c\right)^{6} + 64 \, a^{6} b - 480 \, a^{4} b^{3} - 9088 \, a^{2} b^{5} - 1248 \, b^{7} - 63 \, {\left(71 \, a^{2} b^{5} + 13 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(5 \, a^{4} b^{3} + 718 \, a^{2} b^{5} + 117 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{45045 \, b^{5} d}"," ",0,"-2/45045*(7161*a*b^6*cos(d*x + c)^6 - 128*a^7 + 992*a^5*b^2 - 6080*a^3*b^4 - 5536*a*b^6 - 7*(5*a^3*b^4 + 79*a*b^6)*cos(d*x + c)^4 + 16*(3*a^5*b^2 - 20*a^3*b^4 - 67*a*b^6)*cos(d*x + c)^2 + (3003*b^7*cos(d*x + c)^6 + 64*a^6*b - 480*a^4*b^3 - 9088*a^2*b^5 - 1248*b^7 - 63*(71*a^2*b^5 + 13*b^7)*cos(d*x + c)^4 - 8*(5*a^4*b^3 + 718*a^2*b^5 + 117*b^7)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^5*d)","A",0
495,1,143,0,1.205051," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(161 \, a b^{4} \cos\left(d x + c\right)^{4} + 8 \, a^{5} - 96 \, a^{3} b^{2} - 136 \, a b^{4} - {\left(3 \, a^{3} b^{2} + 25 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(63 \, b^{5} \cos\left(d x + c\right)^{4} - 4 \, a^{4} b - 184 \, a^{2} b^{3} - 36 \, b^{5} - {\left(113 \, a^{2} b^{3} + 27 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{693 \, b^{3} d}"," ",0,"-2/693*(161*a*b^4*cos(d*x + c)^4 + 8*a^5 - 96*a^3*b^2 - 136*a*b^4 - (3*a^3*b^2 + 25*a*b^4)*cos(d*x + c)^2 + (63*b^5*cos(d*x + c)^4 - 4*a^4*b - 184*a^2*b^3 - 36*b^5 - (113*a^2*b^3 + 27*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^3*d)","B",0
496,1,77,0,1.039539," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{7 \, b d}"," ",0,"-2/7*(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b*d)","B",0
497,1,1937,0,4.813174," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a + b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a - b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(b^{2} \sin\left(d x + c\right) + 7 \, a b\right)} \sqrt{b \sin\left(d x + c\right) + a}}{24 \, d}, -\frac{6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{a - b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 16 \, {\left(b^{2} \sin\left(d x + c\right) + 7 \, a b\right)} \sqrt{b \sin\left(d x + c\right) + a}}{24 \, d}, -\frac{6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a + b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 16 \, {\left(b^{2} \sin\left(d x + c\right) + 7 \, a b\right)} \sqrt{b \sin\left(d x + c\right) + a}}{24 \, d}, -\frac{3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) + 8 \, {\left(b^{2} \sin\left(d x + c\right) + 7 \, a b\right)} \sqrt{b \sin\left(d x + c\right) + a}}{12 \, d}\right]"," ",0,"[1/24*(3*(a^2 + 2*a*b + b^2)*sqrt(a + b)*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 3*(a^2 - 2*a*b + b^2)*sqrt(a - b)*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(b^2*sin(d*x + c) + 7*a*b)*sqrt(b*sin(d*x + c) + a))/d, -1/24*(6*(a^2 + 2*a*b + b^2)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c))) - 3*(a^2 - 2*a*b + b^2)*sqrt(a - b)*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 16*(b^2*sin(d*x + c) + 7*a*b)*sqrt(b*sin(d*x + c) + a))/d, -1/24*(6*(a^2 - 2*a*b + b^2)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c))) - 3*(a^2 + 2*a*b + b^2)*sqrt(a + b)*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 16*(b^2*sin(d*x + c) + 7*a*b)*sqrt(b*sin(d*x + c) + a))/d, -1/12*(3*(a^2 - 2*a*b + b^2)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c))) + 3*(a^2 + 2*a*b + b^2)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c))) + 8*(b^2*sin(d*x + c) + 7*a*b)*sqrt(b*sin(d*x + c) + a))/d]","B",0
498,1,2071,0,2.910832," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \sqrt{a + b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + {\left(2 \, a^{2} + a b - 3 \, b^{2}\right)} \sqrt{a - b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(2 \, a b + {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{32 \, d \cos\left(d x + c\right)^{2}}, -\frac{2 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} + a b - 3 \, b^{2}\right)} \sqrt{a - b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(2 \, a b + {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{32 \, d \cos\left(d x + c\right)^{2}}, -\frac{2 \, {\left(2 \, a^{2} + a b - 3 \, b^{2}\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \sqrt{a + b} \cos\left(d x + c\right)^{2} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(2 \, a b + {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{32 \, d \cos\left(d x + c\right)^{2}}, -\frac{{\left(2 \, a^{2} + a b - 3 \, b^{2}\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{2} - 8 \, {\left(2 \, a b + {\left(a^{2} + b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{16 \, d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[-1/32*((2*a^2 - a*b - 3*b^2)*sqrt(a + b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + (2*a^2 + a*b - 3*b^2)*sqrt(a - b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(2*a*b + (a^2 + b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^2), -1/32*(2*(2*a^2 - a*b - 3*b^2)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 + (2*a^2 + a*b - 3*b^2)*sqrt(a - b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(2*a*b + (a^2 + b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^2), -1/32*(2*(2*a^2 + a*b - 3*b^2)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 + (2*a^2 - a*b - 3*b^2)*sqrt(a + b)*cos(d*x + c)^2*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(2*a*b + (a^2 + b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^2), -1/16*((2*a^2 + a*b - 3*b^2)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 + (2*a^2 - a*b - 3*b^2)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^2 - 8*(2*a*b + (a^2 + b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^2)]","B",0
499,1,2229,0,2.087572," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(4 \, a^{2} - 2 \, a b - b^{2}\right)} \sqrt{a + b} \cos\left(d x + c\right)^{4} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 3 \, {\left(4 \, a^{2} + 2 \, a b - b^{2}\right)} \sqrt{a - b} \cos\left(d x + c\right)^{4} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 16 \, {\left(a b \cos\left(d x + c\right)^{2} - 8 \, a b - {\left(3 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, a^{2} + 4 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{256 \, d \cos\left(d x + c\right)^{4}}, -\frac{6 \, {\left(4 \, a^{2} - 2 \, a b - b^{2}\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{4} + 3 \, {\left(4 \, a^{2} + 2 \, a b - b^{2}\right)} \sqrt{a - b} \cos\left(d x + c\right)^{4} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 16 \, {\left(a b \cos\left(d x + c\right)^{2} - 8 \, a b - {\left(3 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, a^{2} + 4 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{256 \, d \cos\left(d x + c\right)^{4}}, -\frac{6 \, {\left(4 \, a^{2} + 2 \, a b - b^{2}\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{4} + 3 \, {\left(4 \, a^{2} - 2 \, a b - b^{2}\right)} \sqrt{a + b} \cos\left(d x + c\right)^{4} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 16 \, {\left(a b \cos\left(d x + c\right)^{2} - 8 \, a b - {\left(3 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, a^{2} + 4 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{256 \, d \cos\left(d x + c\right)^{4}}, -\frac{3 \, {\left(4 \, a^{2} + 2 \, a b - b^{2}\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{4} + 3 \, {\left(4 \, a^{2} - 2 \, a b - b^{2}\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) \cos\left(d x + c\right)^{4} + 8 \, {\left(a b \cos\left(d x + c\right)^{2} - 8 \, a b - {\left(3 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, a^{2} + 4 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{128 \, d \cos\left(d x + c\right)^{4}}\right]"," ",0,"[-1/256*(3*(4*a^2 - 2*a*b - b^2)*sqrt(a + b)*cos(d*x + c)^4*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 3*(4*a^2 + 2*a*b - b^2)*sqrt(a - b)*cos(d*x + c)^4*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 16*(a*b*cos(d*x + c)^2 - 8*a*b - (3*(2*a^2 - b^2)*cos(d*x + c)^2 + 4*a^2 + 4*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^4), -1/256*(6*(4*a^2 - 2*a*b - b^2)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^4 + 3*(4*a^2 + 2*a*b - b^2)*sqrt(a - b)*cos(d*x + c)^4*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 16*(a*b*cos(d*x + c)^2 - 8*a*b - (3*(2*a^2 - b^2)*cos(d*x + c)^2 + 4*a^2 + 4*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^4), -1/256*(6*(4*a^2 + 2*a*b - b^2)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^4 + 3*(4*a^2 - 2*a*b - b^2)*sqrt(a + b)*cos(d*x + c)^4*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 16*(a*b*cos(d*x + c)^2 - 8*a*b - (3*(2*a^2 - b^2)*cos(d*x + c)^2 + 4*a^2 + 4*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^4), -1/128*(3*(4*a^2 + 2*a*b - b^2)*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^4 + 3*(4*a^2 - 2*a*b - b^2)*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c)))*cos(d*x + c)^4 + 8*(a*b*cos(d*x + c)^2 - 8*a*b - (3*(2*a^2 - b^2)*cos(d*x + c)^2 + 4*a^2 + 4*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/(d*cos(d*x + c)^4)]","B",0
500,0,0,0,1.516009," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{6} - 2 \, a b \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^6 - 2*a*b*cos(d*x + c)^4*sin(d*x + c) - (a^2 + b^2)*cos(d*x + c)^4)*sqrt(b*sin(d*x + c) + a), x)","F",0
501,0,0,0,1.160396," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{4} - 2 \, a b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^4 - 2*a*b*cos(d*x + c)^2*sin(d*x + c) - (a^2 + b^2)*cos(d*x + c)^2)*sqrt(b*sin(d*x + c) + a), x)","F",0
502,0,0,0,0.928821," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a b \sec\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((2*a*b*sec(d*x + c)^2*sin(d*x + c) - (b^2*cos(d*x + c)^2 - a^2 - b^2)*sec(d*x + c)^2)*sqrt(b*sin(d*x + c) + a), x)","F",0
503,0,0,0,1.257677," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a b \sec\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((2*a*b*sec(d*x + c)^4*sin(d*x + c) - (b^2*cos(d*x + c)^2 - a^2 - b^2)*sec(d*x + c)^4)*sqrt(b*sin(d*x + c) + a), x)","F",0
504,0,0,0,1.492922," ","integrate(sec(d*x+c)^6*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a b \sec\left(d x + c\right)^{6} \sin\left(d x + c\right) - {\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \sec\left(d x + c\right)^{6}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((2*a*b*sec(d*x + c)^6*sin(d*x + c) - (b^2*cos(d*x + c)^2 - a^2 - b^2)*sec(d*x + c)^6)*sqrt(b*sin(d*x + c) + a), x)","F",0
505,0,0,0,1.531634," ","integrate(sec(d*x+c)^8*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a b \sec\left(d x + c\right)^{8} \sin\left(d x + c\right) - {\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \sec\left(d x + c\right)^{8}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((2*a*b*sec(d*x + c)^8*sin(d*x + c) - (b^2*cos(d*x + c)^2 - a^2 - b^2)*sec(d*x + c)^8)*sqrt(b*sin(d*x + c) + a), x)","F",0
506,1,111,0,1.235694," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 288 \, a^{2} b^{2} + 224 \, b^{4} - 8 \, {\left(6 \, a^{2} b^{2} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(5 \, a b^{3} \cos\left(d x + c\right)^{2} - 8 \, a^{3} b + 16 \, a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{315 \, b^{5} d}"," ",0,"2/315*(35*b^4*cos(d*x + c)^4 + 128*a^4 - 288*a^2*b^2 + 224*b^4 - 8*(6*a^2*b^2 - 7*b^4)*cos(d*x + c)^2 + 8*(5*a*b^3*cos(d*x + c)^2 - 8*a^3*b + 16*a*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^5*d)","A",0
507,1,54,0,1.384721," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} \cos\left(d x + c\right)^{2} + 4 \, a b \sin\left(d x + c\right) - 8 \, a^{2} + 12 \, b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}}{15 \, b^{3} d}"," ",0,"2/15*(3*b^2*cos(d*x + c)^2 + 4*a*b*sin(d*x + c) - 8*a^2 + 12*b^2)*sqrt(b*sin(d*x + c) + a)/(b^3*d)","A",0
508,1,20,0,1.359734," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\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
509,0,0,0,1.628052," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
510,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (residue poly has multiple non-linear factors)","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=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (residue poly has multiple non-linear factors)","F(-2)",0
512,0,0,0,1.283683," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^4/sqrt(b*sin(d*x + c) + a), x)","F",0
513,0,0,0,0.897555," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
514,0,0,0,1.254799," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
515,0,0,0,1.023858," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^4/sqrt(b*sin(d*x + c) + a), x)","F",0
516,1,125,0,1.411055," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{4} \cos\left(d x + c\right)^{4} - 384 \, a^{4} + 608 \, a^{2} b^{2} - 160 \, b^{4} - 8 \, {\left(6 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(3 \, a b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{3} b + 32 \, a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{105 \, {\left(b^{6} d \sin\left(d x + c\right) + a b^{5} d\right)}}"," ",0,"2/105*(15*b^4*cos(d*x + c)^4 - 384*a^4 + 608*a^2*b^2 - 160*b^4 - 8*(6*a^2*b^2 - 5*b^4)*cos(d*x + c)^2 + 8*(3*a*b^3*cos(d*x + c)^2 - 24*a^3*b + 32*a*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^6*d*sin(d*x + c) + a*b^5*d)","A",0
517,1,67,0,1.377602," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} \cos\left(d x + c\right)^{2} + 4 \, a b \sin\left(d x + c\right) + 8 \, a^{2} - 4 \, b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}}{3 \, {\left(b^{4} d \sin\left(d x + c\right) + a b^{3} d\right)}}"," ",0,"2/3*(b^2*cos(d*x + c)^2 + 4*a*b*sin(d*x + c) + 8*a^2 - 4*b^2)*sqrt(b*sin(d*x + c) + a)/(b^4*d*sin(d*x + c) + a*b^3*d)","A",0
518,1,32,0,1.142114," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b \sin\left(d x + c\right) + a}}{b^{2} d \sin\left(d x + c\right) + a b d}"," ",0,"-2*sqrt(b*sin(d*x + c) + a)/(b^2*d*sin(d*x + c) + a*b*d)","A",0
519,0,0,0,1.525016," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*sec(d*x + c)/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
520,-2,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (residue poly has multiple non-linear factors)","F(-2)",0
521,0,0,0,2.846470," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{5}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^5/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
522,0,0,0,1.639967," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{6}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^6/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
523,0,0,0,1.445642," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
524,0,0,0,1.352196," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^2/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
525,0,0,0,1.295652," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^2/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
526,0,0,0,1.533514," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^4/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
527,1,147,0,1.439775," ","integrate(cos(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 32 \, a^{2} b^{2} - 32 \, b^{4} - 24 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} + 24 \, a^{3} b - 16 \, a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{15 \, {\left(b^{7} d \cos\left(d x + c\right)^{2} - 2 \, a b^{6} d \sin\left(d x + c\right) - {\left(a^{2} b^{5} + b^{7}\right)} d\right)}}"," ",0,"-2/15*(3*b^4*cos(d*x + c)^4 + 128*a^4 - 32*a^2*b^2 - 32*b^4 - 24*(2*a^2*b^2 - b^4)*cos(d*x + c)^2 + 8*(a*b^3*cos(d*x + c)^2 + 24*a^3*b - 16*a*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)/(b^7*d*cos(d*x + c)^2 - 2*a*b^6*d*sin(d*x + c) - (a^2*b^5 + b^7)*d)","A",0
528,1,91,0,1.273823," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{2} \cos\left(d x + c\right)^{2} - 12 \, a b \sin\left(d x + c\right) - 8 \, a^{2} - 4 \, b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}}{3 \, {\left(b^{5} d \cos\left(d x + c\right)^{2} - 2 \, a b^{4} d \sin\left(d x + c\right) - {\left(a^{2} b^{3} + b^{5}\right)} d\right)}}"," ",0,"-2/3*(3*b^2*cos(d*x + c)^2 - 12*a*b*sin(d*x + c) - 8*a^2 - 4*b^2)*sqrt(b*sin(d*x + c) + a)/(b^5*d*cos(d*x + c)^2 - 2*a*b^4*d*sin(d*x + c) - (a^2*b^3 + b^5)*d)","A",0
529,1,55,0,1.191710," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b \sin\left(d x + c\right) + a}}{3 \, {\left(b^{3} d \cos\left(d x + c\right)^{2} - 2 \, a b^{2} d \sin\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} d\right)}}"," ",0,"2/3*sqrt(b*sin(d*x + c) + a)/(b^3*d*cos(d*x + c)^2 - 2*a*b^2*d*sin(d*x + c) - (a^2*b + b^3)*d)","B",0
530,1,3225,0,3.097317," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a^{5} - 3 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{a + b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 3 \, {\left(a^{5} + 3 \, a^{4} b + 4 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} - {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{a - b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) + 16 \, {\left(7 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5} + 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{24 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\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)} d \sin\left(d x + c\right) - {\left(a^{8} - 2 \, a^{6} b^{2} + 2 \, a^{2} b^{6} - b^{8}\right)} d\right)}}, \frac{6 \, {\left(a^{5} - 3 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) - 3 \, {\left(a^{5} + 3 \, a^{4} b + 4 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} - {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{a - b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} - 256 \, a^{3} b + 320 \, a^{2} b^{2} - 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} - 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 20 \, a b^{2} - 8 \, b^{3} - {\left(10 \, a b^{2} - 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b + 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a - b} + 4 \, {\left(64 \, a^{3} b - 112 \, a^{2} b^{2} + 64 \, a b^{3} - 14 \, b^{4} - {\left(8 \, a b^{3} - 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(7 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5} + 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{24 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\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)} d \sin\left(d x + c\right) - {\left(a^{8} - 2 \, a^{6} b^{2} + 2 \, a^{2} b^{6} - b^{8}\right)} d\right)}}, \frac{6 \, {\left(a^{5} + 3 \, a^{4} b + 4 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} - {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) - 3 \, {\left(a^{5} - 3 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{a + b} \log\left(\frac{b^{4} \cos\left(d x + c\right)^{4} + 128 \, a^{4} + 256 \, a^{3} b + 320 \, a^{2} b^{2} + 256 \, a b^{3} + 72 \, b^{4} - 8 \, {\left(20 \, a^{2} b^{2} + 28 \, a b^{3} + 9 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3} - {\left(10 \, a b^{2} + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(b^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{2} b - 28 \, a b^{2} - 8 \, b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{a + b} + 4 \, {\left(64 \, a^{3} b + 112 \, a^{2} b^{2} + 64 \, a b^{3} + 14 \, b^{4} - {\left(8 \, a b^{3} + 7 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 8}\right) - 16 \, {\left(7 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5} + 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{24 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\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)} d \sin\left(d x + c\right) - {\left(a^{8} - 2 \, a^{6} b^{2} + 2 \, a^{2} b^{6} - b^{8}\right)} d\right)}}, \frac{3 \, {\left(a^{5} + 3 \, a^{4} b + 4 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} - {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a + b} \arctan\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} + 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a + b}}{4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - b^{3} - {\left(a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) + 3 \, {\left(a^{5} - 3 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a - b} \arctan\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 8 \, a b - 2 \, b^{2} - 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a} \sqrt{-a - b}}{4 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} \sin\left(d x + c\right)\right)}}\right) - 8 \, {\left(7 \, a^{4} b - 8 \, a^{2} b^{3} + b^{5} + 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}}{12 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\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)} d \sin\left(d x + c\right) - {\left(a^{8} - 2 \, a^{6} b^{2} + 2 \, a^{2} b^{6} - b^{8}\right)} d\right)}}\right]"," ",0,"[-1/24*(3*(a^5 - 3*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 + 3*a*b^4 - b^5 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(d*x + c)^2 + 2*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*sin(d*x + c))*sqrt(a + b)*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 3*(a^5 + 3*a^4*b + 4*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4 + b^5 - (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cos(d*x + c)^2 + 2*(a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*sin(d*x + c))*sqrt(a - b)*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) + 16*(7*a^4*b - 8*a^2*b^3 + b^5 + 6*(a^3*b^2 - a*b^4)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*sin(d*x + c) - (a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8)*d), 1/24*(6*(a^5 - 3*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 + 3*a*b^4 - b^5 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(d*x + c)^2 + 2*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*sin(d*x + c))*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c))) - 3*(a^5 + 3*a^4*b + 4*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4 + b^5 - (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cos(d*x + c)^2 + 2*(a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*sin(d*x + c))*sqrt(a - b)*log((b^4*cos(d*x + c)^4 + 128*a^4 - 256*a^3*b + 320*a^2*b^2 - 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 - 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 - 8*(16*a^3 - 24*a^2*b + 20*a*b^2 - 8*b^3 - (10*a*b^2 - 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b + 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a - b) + 4*(64*a^3*b - 112*a^2*b^2 + 64*a*b^3 - 14*b^4 - (8*a*b^3 - 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(7*a^4*b - 8*a^2*b^3 + b^5 + 6*(a^3*b^2 - a*b^4)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*sin(d*x + c) - (a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8)*d), 1/24*(6*(a^5 + 3*a^4*b + 4*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4 + b^5 - (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cos(d*x + c)^2 + 2*(a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*sin(d*x + c))*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c))) - 3*(a^5 - 3*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 + 3*a*b^4 - b^5 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(d*x + c)^2 + 2*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*sin(d*x + c))*sqrt(a + b)*log((b^4*cos(d*x + c)^4 + 128*a^4 + 256*a^3*b + 320*a^2*b^2 + 256*a*b^3 + 72*b^4 - 8*(20*a^2*b^2 + 28*a*b^3 + 9*b^4)*cos(d*x + c)^2 + 8*(16*a^3 + 24*a^2*b + 20*a*b^2 + 8*b^3 - (10*a*b^2 + 7*b^3)*cos(d*x + c)^2 - (b^3*cos(d*x + c)^2 - 24*a^2*b - 28*a*b^2 - 8*b^3)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(a + b) + 4*(64*a^3*b + 112*a^2*b^2 + 64*a*b^3 + 14*b^4 - (8*a*b^3 + 7*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(cos(d*x + c)^4 - 8*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 8)) - 16*(7*a^4*b - 8*a^2*b^3 + b^5 + 6*(a^3*b^2 - a*b^4)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*sin(d*x + c) - (a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8)*d), 1/12*(3*(a^5 + 3*a^4*b + 4*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4 + b^5 - (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cos(d*x + c)^2 + 2*(a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*sin(d*x + c))*sqrt(-a + b)*arctan(1/4*(b^2*cos(d*x + c)^2 - 8*a^2 + 8*a*b - 2*b^2 - 2*(4*a*b - 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a + b)/(2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - (a*b^2 - b^3)*cos(d*x + c)^2 + (3*a^2*b - 4*a*b^2 + b^3)*sin(d*x + c))) + 3*(a^5 - 3*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 + 3*a*b^4 - b^5 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*cos(d*x + c)^2 + 2*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*sin(d*x + c))*sqrt(-a - b)*arctan(-1/4*(b^2*cos(d*x + c)^2 - 8*a^2 - 8*a*b - 2*b^2 - 2*(4*a*b + 3*b^2)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a)*sqrt(-a - b)/(2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 - (a*b^2 + b^3)*cos(d*x + c)^2 + (3*a^2*b + 4*a*b^2 + b^3)*sin(d*x + c))) - 8*(7*a^4*b - 8*a^2*b^3 + b^5 + 6*(a^3*b^2 - a*b^4)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^2 - 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*sin(d*x + c) - (a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8)*d)]","B",0
531,0,0,0,2.183282," ","integrate(sec(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^3/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
532,0,0,0,3.528619," ","integrate(sec(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{5}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^5/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
533,0,0,0,1.976603," ","integrate(cos(d*x+c)^8/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{8}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^8/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
534,0,0,0,1.739456," ","integrate(cos(d*x+c)^6/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{6}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^6/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
535,0,0,0,1.356806," ","integrate(cos(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
536,0,0,0,1.226477," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^2/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
537,0,0,0,1.477619," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^2/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
538,0,0,0,1.749686," ","integrate(sec(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*sec(d*x + c)^4/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
539,0,0,0,1.364601," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b e^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a e^{3} \cos\left(d x + c\right)^{3}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*e^3*cos(d*x + c)^3*sin(d*x + c) + a*e^3*cos(d*x + c)^3)*sqrt(e*cos(d*x + c)), x)","F",0
540,0,0,0,0.887965," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b e^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a e^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*e^2*cos(d*x + c)^2*sin(d*x + c) + a*e^2*cos(d*x + c)^2)*sqrt(e*cos(d*x + c)), x)","F",0
541,0,0,0,1.334526," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b e \cos\left(d x + c\right) \sin\left(d x + c\right) + a e \cos\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*e*cos(d*x + c)*sin(d*x + c) + a*e*cos(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
542,0,0,0,1.262197," ","integrate((a+b*sin(d*x+c))*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a), x)","F",0
543,0,0,0,1.189679," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)/(e*cos(d*x + c)), x)","F",0
544,0,0,0,1.359322," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)/(e^2*cos(d*x + c)^2), x)","F",0
545,0,0,0,1.457227," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)/(e^3*cos(d*x + c)^3), x)","F",0
546,0,0,0,1.535872," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}}{e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)/(e^4*cos(d*x + c)^4), x)","F",0
547,0,0,0,0.868142," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} e^{3} \cos\left(d x + c\right)^{5} - 2 \, a b e^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - {\left(a^{2} + b^{2}\right)} e^{3} \cos\left(d x + c\right)^{3}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(b^2*e^3*cos(d*x + c)^5 - 2*a*b*e^3*cos(d*x + c)^3*sin(d*x + c) - (a^2 + b^2)*e^3*cos(d*x + c)^3)*sqrt(e*cos(d*x + c)), x)","F",0
548,0,0,0,1.368232," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} e^{2} \cos\left(d x + c\right)^{4} - 2 \, a b e^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(a^{2} + b^{2}\right)} e^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(b^2*e^2*cos(d*x + c)^4 - 2*a*b*e^2*cos(d*x + c)^2*sin(d*x + c) - (a^2 + b^2)*e^2*cos(d*x + c)^2)*sqrt(e*cos(d*x + c)), x)","F",0
549,0,0,0,1.347947," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} e \cos\left(d x + c\right)^{3} - 2 \, a b e \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} + b^{2}\right)} e \cos\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(b^2*e*cos(d*x + c)^3 - 2*a*b*e*cos(d*x + c)*sin(d*x + c) - (a^2 + b^2)*e*cos(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
550,0,0,0,1.317678," ","integrate((a+b*sin(d*x+c))^2*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(e*cos(d*x + c)), x)","F",0
551,0,0,0,1.422525," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(e*cos(d*x + c))/(e*cos(d*x + c)), x)","F",0
552,0,0,0,1.046786," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(e*cos(d*x + c))/(e^2*cos(d*x + c)^2), x)","F",0
553,0,0,0,1.313247," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(e*cos(d*x + c))/(e^3*cos(d*x + c)^3), x)","F",0
554,0,0,0,1.408311," ","integrate((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(e*cos(d*x + c))/(e^4*cos(d*x + c)^4), x)","F",0
555,0,0,0,1.438276," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a b^{2} e^{3} \cos\left(d x + c\right)^{5} - {\left(a^{3} + 3 \, a b^{2}\right)} e^{3} \cos\left(d x + c\right)^{3} + {\left(b^{3} e^{3} \cos\left(d x + c\right)^{5} - {\left(3 \, a^{2} b + b^{3}\right)} e^{3} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a*b^2*e^3*cos(d*x + c)^5 - (a^3 + 3*a*b^2)*e^3*cos(d*x + c)^3 + (b^3*e^3*cos(d*x + c)^5 - (3*a^2*b + b^3)*e^3*cos(d*x + c)^3)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
556,0,0,0,1.408476," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a b^{2} e^{2} \cos\left(d x + c\right)^{4} - {\left(a^{3} + 3 \, a b^{2}\right)} e^{2} \cos\left(d x + c\right)^{2} + {\left(b^{3} e^{2} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{2} b + b^{3}\right)} e^{2} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a*b^2*e^2*cos(d*x + c)^4 - (a^3 + 3*a*b^2)*e^2*cos(d*x + c)^2 + (b^3*e^2*cos(d*x + c)^4 - (3*a^2*b + b^3)*e^2*cos(d*x + c)^2)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
557,0,0,0,1.477520," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a b^{2} e \cos\left(d x + c\right)^{3} - {\left(a^{3} + 3 \, a b^{2}\right)} e \cos\left(d x + c\right) + {\left(b^{3} e \cos\left(d x + c\right)^{3} - {\left(3 \, a^{2} b + b^{3}\right)} e \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a*b^2*e*cos(d*x + c)^3 - (a^3 + 3*a*b^2)*e*cos(d*x + c) + (b^3*e*cos(d*x + c)^3 - (3*a^2*b + b^3)*e*cos(d*x + c))*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
558,0,0,0,1.439276," ","integrate((a+b*sin(d*x+c))^3*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
559,0,0,0,0.735966," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e*cos(d*x + c)), x)","F",0
560,0,0,0,1.406401," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^2*cos(d*x + c)^2), x)","F",0
561,0,0,0,1.408096," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^3*cos(d*x + c)^3), x)","F",0
562,0,0,0,1.191902," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^4*cos(d*x + c)^4), x)","F",0
563,0,0,0,0.749434," ","integrate((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{5} \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^5*cos(d*x + c)^5), x)","F",0
564,0,0,0,1.491405," ","integrate((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{4} e^{3} \cos\left(d x + c\right)^{7} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} e^{3} \cos\left(d x + c\right)^{5} + {\left(a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} e^{3} \cos\left(d x + c\right)^{3} - 4 \, {\left(a b^{3} e^{3} \cos\left(d x + c\right)^{5} - {\left(a^{3} b + a b^{3}\right)} e^{3} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^4*e^3*cos(d*x + c)^7 - 2*(3*a^2*b^2 + b^4)*e^3*cos(d*x + c)^5 + (a^4 + 6*a^2*b^2 + b^4)*e^3*cos(d*x + c)^3 - 4*(a*b^3*e^3*cos(d*x + c)^5 - (a^3*b + a*b^3)*e^3*cos(d*x + c)^3)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
565,0,0,0,1.300483," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{4} e^{2} \cos\left(d x + c\right)^{6} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} e^{2} \cos\left(d x + c\right)^{4} + {\left(a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} e^{2} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} e^{2} \cos\left(d x + c\right)^{4} - {\left(a^{3} b + a b^{3}\right)} e^{2} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^4*e^2*cos(d*x + c)^6 - 2*(3*a^2*b^2 + b^4)*e^2*cos(d*x + c)^4 + (a^4 + 6*a^2*b^2 + b^4)*e^2*cos(d*x + c)^2 - 4*(a*b^3*e^2*cos(d*x + c)^4 - (a^3*b + a*b^3)*e^2*cos(d*x + c)^2)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
566,0,0,0,1.008528," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{4} e \cos\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} e \cos\left(d x + c\right)^{3} + {\left(a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} e \cos\left(d x + c\right) - 4 \, {\left(a b^{3} e \cos\left(d x + c\right)^{3} - {\left(a^{3} b + a b^{3}\right)} e \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^4*e*cos(d*x + c)^5 - 2*(3*a^2*b^2 + b^4)*e*cos(d*x + c)^3 + (a^4 + 6*a^2*b^2 + b^4)*e*cos(d*x + c) - 4*(a*b^3*e*cos(d*x + c)^3 - (a^3*b + a*b^3)*e*cos(d*x + c))*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
567,0,0,0,1.309252," ","integrate((a+b*sin(d*x+c))^4*(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c)), x)","F",0
568,0,0,0,1.246833," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e*cos(d*x + c)), x)","F",0
569,0,0,0,1.303200," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^2*cos(d*x + c)^2), x)","F",0
570,0,0,0,1.029316," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^3*cos(d*x + c)^3), x)","F",0
571,0,0,0,1.502912," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^4*cos(d*x + c)^4), x)","F",0
572,0,0,0,1.422697," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{5} \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral((b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^5*cos(d*x + c)^5), x)","F",0
573,0,0,0,1.043758," ","integrate((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{e \cos\left(d x + c\right)}}{e^{6} \cos\left(d x + c\right)^{6}}, x\right)"," ",0,"integral((b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c))*sqrt(e*cos(d*x + c))/(e^6*cos(d*x + c)^6), x)","F",0
574,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""fricas"")","\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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,0,0,0,1.566494," ","integrate(1/(c*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \cos\left(f x + e\right)} \sqrt{b \sin\left(f x + e\right) + a}}{b c \cos\left(f x + e\right) \sin\left(f x + e\right) + a c \cos\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(c*cos(f*x + e))*sqrt(b*sin(f*x + e) + a)/(b*c*cos(f*x + e)*sin(f*x + e) + a*c*cos(f*x + e)), x)","F",0
616,0,0,0,1.654932," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))*(e*cos(d*x + c))^p, x)","F",0
617,0,0,0,1.368152," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*(e*cos(d*x + c))^p, x)","F",0
618,0,0,0,1.220582," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
619,0,0,0,1.595988," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((e*cos(d*x + c))^p/(b*sin(d*x + c) + a), x)","F",0
620,0,0,0,1.646585," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(e*cos(d*x + c))^p/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
621,0,0,0,1.511188," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(e*cos(d*x + c))^p/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
622,0,0,0,1.893073," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{b^{8} \cos\left(d x + c\right)^{8} + a^{8} + 28 \, a^{6} b^{2} + 70 \, a^{4} b^{4} + 28 \, a^{2} b^{6} + b^{8} - 4 \, {\left(7 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(35 \, a^{4} b^{4} + 42 \, a^{2} b^{6} + 3 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(7 \, a^{6} b^{2} + 35 \, a^{4} b^{4} + 21 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(a b^{7} \cos\left(d x + c\right)^{6} - a^{7} b - 7 \, a^{5} b^{3} - 7 \, a^{3} b^{5} - a b^{7} - {\left(7 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral((e*cos(d*x + c))^p/(b^8*cos(d*x + c)^8 + a^8 + 28*a^6*b^2 + 70*a^4*b^4 + 28*a^2*b^6 + b^8 - 4*(7*a^2*b^6 + b^8)*cos(d*x + c)^6 + 2*(35*a^4*b^4 + 42*a^2*b^6 + 3*b^8)*cos(d*x + c)^4 - 4*(7*a^6*b^2 + 35*a^4*b^4 + 21*a^2*b^6 + b^8)*cos(d*x + c)^2 - 8*(a*b^7*cos(d*x + c)^6 - a^7*b - 7*a^5*b^3 - 7*a^3*b^5 - a*b^7 - (7*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^4 + (7*a^5*b^3 + 14*a^3*b^5 + 3*a*b^7)*cos(d*x + c)^2)*sin(d*x + c)), x)","F",0
623,0,0,0,1.575014," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)*sqrt(b*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
624,0,0,0,1.546493," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^(3/2)*(e*cos(d*x + c))^p, x)","F",0
625,0,0,0,1.368376," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*(e*cos(d*x + c))^p, x)","F",0
626,0,0,0,1.640918," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e \cos\left(d x + c\right)\right)^{p}}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral((e*cos(d*x + c))^p/sqrt(b*sin(d*x + c) + a), x)","F",0
627,0,0,0,1.203046," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*(e*cos(d*x + c))^p/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
628,0,0,0,1.634018," ","integrate((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{p}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*(e*cos(d*x + c))^p/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
629,0,0,0,1.452718," ","integrate((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{p} {\left(b \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^p*(b*sin(d*x + c) + a)^m, x)","F",0
630,1,814,0,1.867006," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","-\frac{{\left(720 \, a^{7} - 3024 \, a^{5} b^{2} + 5040 \, a^{3} b^{4} - 5040 \, a b^{6} - {\left(a b^{6} m^{6} + 15 \, a b^{6} m^{5} + 85 \, a b^{6} m^{4} + 225 \, a b^{6} m^{3} + 274 \, a b^{6} m^{2} + 120 \, a b^{6} m\right)} \cos\left(d x + c\right)^{6} - 6 \, {\left(2 \, a b^{6} m^{5} - {\left(5 \, a^{3} b^{4} - 23 \, a b^{6}\right)} m^{4} - 2 \, {\left(15 \, a^{3} b^{4} - 44 \, a b^{6}\right)} m^{3} - {\left(55 \, a^{3} b^{4} - 133 \, a b^{6}\right)} m^{2} - 6 \, {\left(5 \, a^{3} b^{4} - 11 \, a b^{6}\right)} m\right)} \cos\left(d x + c\right)^{4} - 192 \, {\left(a^{3} b^{4} + a b^{6}\right)} m^{3} + 288 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} - 7 \, a b^{6}\right)} m^{2} - 24 \, {\left({\left(a^{3} b^{4} + 3 \, a b^{6}\right)} m^{4} - 6 \, {\left(a^{3} b^{4} - 5 \, a b^{6}\right)} m^{3} + {\left(15 \, a^{5} b^{2} - 55 \, a^{3} b^{4} + 84 \, a b^{6}\right)} m^{2} + 3 \, {\left(5 \, a^{5} b^{2} - 16 \, a^{3} b^{4} + 19 \, a b^{6}\right)} m\right)} \cos\left(d x + c\right)^{2} - 192 \, {\left(3 \, a^{5} b^{2} - 13 \, a^{3} b^{4} + 32 \, a b^{6}\right)} m - {\left(2304 \, b^{7} + {\left(b^{7} m^{6} + 21 \, b^{7} m^{5} + 175 \, b^{7} m^{4} + 735 \, b^{7} m^{3} + 1624 \, b^{7} m^{2} + 1764 \, b^{7} m + 720 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(144 \, b^{7} + {\left(a^{2} b^{5} + b^{7}\right)} m^{5} + 2 \, {\left(5 \, a^{2} b^{5} + 8 \, b^{7}\right)} m^{4} + 5 \, {\left(7 \, a^{2} b^{5} + 19 \, b^{7}\right)} m^{3} + 10 \, {\left(5 \, a^{2} b^{5} + 26 \, b^{7}\right)} m^{2} + 12 \, {\left(2 \, a^{2} b^{5} + 27 \, b^{7}\right)} m\right)} \cos\left(d x + c\right)^{4} + 48 \, {\left(a^{4} b^{3} + 6 \, a^{2} b^{5} + b^{7}\right)} m^{3} - 576 \, {\left(a^{4} b^{3} - 4 \, a^{2} b^{5} - b^{7}\right)} m^{2} + 24 \, {\left(48 \, b^{7} + {\left(3 \, a^{2} b^{5} + b^{7}\right)} m^{4} - {\left(5 \, a^{4} b^{3} - 24 \, a^{2} b^{5} - 13 \, b^{7}\right)} m^{3} - {\left(15 \, a^{4} b^{3} - 51 \, a^{2} b^{5} - 56 \, b^{7}\right)} m^{2} - 2 \, {\left(5 \, a^{4} b^{3} - 15 \, a^{2} b^{5} - 46 \, b^{7}\right)} m\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left(15 \, a^{6} b - 58 \, a^{4} b^{3} + 87 \, a^{2} b^{5} + 44 \, b^{7}\right)} m\right)} \sin\left(d x + c\right)\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{b^{7} d m^{7} + 28 \, b^{7} d m^{6} + 322 \, b^{7} d m^{5} + 1960 \, b^{7} d m^{4} + 6769 \, b^{7} d m^{3} + 13132 \, b^{7} d m^{2} + 13068 \, b^{7} d m + 5040 \, b^{7} d}"," ",0,"-(720*a^7 - 3024*a^5*b^2 + 5040*a^3*b^4 - 5040*a*b^6 - (a*b^6*m^6 + 15*a*b^6*m^5 + 85*a*b^6*m^4 + 225*a*b^6*m^3 + 274*a*b^6*m^2 + 120*a*b^6*m)*cos(d*x + c)^6 - 6*(2*a*b^6*m^5 - (5*a^3*b^4 - 23*a*b^6)*m^4 - 2*(15*a^3*b^4 - 44*a*b^6)*m^3 - (55*a^3*b^4 - 133*a*b^6)*m^2 - 6*(5*a^3*b^4 - 11*a*b^6)*m)*cos(d*x + c)^4 - 192*(a^3*b^4 + a*b^6)*m^3 + 288*(a^5*b^2 - 2*a^3*b^4 - 7*a*b^6)*m^2 - 24*((a^3*b^4 + 3*a*b^6)*m^4 - 6*(a^3*b^4 - 5*a*b^6)*m^3 + (15*a^5*b^2 - 55*a^3*b^4 + 84*a*b^6)*m^2 + 3*(5*a^5*b^2 - 16*a^3*b^4 + 19*a*b^6)*m)*cos(d*x + c)^2 - 192*(3*a^5*b^2 - 13*a^3*b^4 + 32*a*b^6)*m - (2304*b^7 + (b^7*m^6 + 21*b^7*m^5 + 175*b^7*m^4 + 735*b^7*m^3 + 1624*b^7*m^2 + 1764*b^7*m + 720*b^7)*cos(d*x + c)^6 + 6*(144*b^7 + (a^2*b^5 + b^7)*m^5 + 2*(5*a^2*b^5 + 8*b^7)*m^4 + 5*(7*a^2*b^5 + 19*b^7)*m^3 + 10*(5*a^2*b^5 + 26*b^7)*m^2 + 12*(2*a^2*b^5 + 27*b^7)*m)*cos(d*x + c)^4 + 48*(a^4*b^3 + 6*a^2*b^5 + b^7)*m^3 - 576*(a^4*b^3 - 4*a^2*b^5 - b^7)*m^2 + 24*(48*b^7 + (3*a^2*b^5 + b^7)*m^4 - (5*a^4*b^3 - 24*a^2*b^5 - 13*b^7)*m^3 - (15*a^4*b^3 - 51*a^2*b^5 - 56*b^7)*m^2 - 2*(5*a^4*b^3 - 15*a^2*b^5 - 46*b^7)*m)*cos(d*x + c)^2 + 48*(15*a^6*b - 58*a^4*b^3 + 87*a^2*b^5 + 44*b^7)*m)*sin(d*x + c))*(b*sin(d*x + c) + a)^m/(b^7*d*m^7 + 28*b^7*d*m^6 + 322*b^7*d*m^5 + 1960*b^7*d*m^4 + 6769*b^7*d*m^3 + 13132*b^7*d*m^2 + 13068*b^7*d*m + 5040*b^7*d)","B",0
631,1,381,0,1.529729," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left(24 \, a^{5} - 80 \, a^{3} b^{2} + 120 \, a b^{4} + {\left(a b^{4} m^{4} + 6 \, a b^{4} m^{3} + 11 \, a b^{4} m^{2} + 6 \, a b^{4} m\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(a^{3} b^{2} + 3 \, a b^{4}\right)} m^{2} + 4 \, {\left(2 \, a b^{4} m^{3} - 3 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} m^{2} - {\left(3 \, a^{3} b^{2} - 7 \, a b^{4}\right)} m\right)} \cos\left(d x + c\right)^{2} - 24 \, {\left(a^{3} b^{2} - 5 \, a b^{4}\right)} m + {\left(64 \, b^{5} + {\left(b^{5} m^{4} + 10 \, b^{5} m^{3} + 35 \, b^{5} m^{2} + 50 \, b^{5} m + 24 \, b^{5}\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{2} b^{3} + b^{5}\right)} m^{2} + 4 \, {\left(8 \, b^{5} + {\left(a^{2} b^{3} + b^{5}\right)} m^{3} + {\left(3 \, a^{2} b^{3} + 7 \, b^{5}\right)} m^{2} + 2 \, {\left(a^{2} b^{3} + 7 \, b^{5}\right)} m\right)} \cos\left(d x + c\right)^{2} - 24 \, {\left(a^{4} b - 3 \, a^{2} b^{3} - 2 \, b^{5}\right)} m\right)} \sin\left(d x + c\right)\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{b^{5} d m^{5} + 15 \, b^{5} d m^{4} + 85 \, b^{5} d m^{3} + 225 \, b^{5} d m^{2} + 274 \, b^{5} d m + 120 \, b^{5} d}"," ",0,"(24*a^5 - 80*a^3*b^2 + 120*a*b^4 + (a*b^4*m^4 + 6*a*b^4*m^3 + 11*a*b^4*m^2 + 6*a*b^4*m)*cos(d*x + c)^4 + 8*(a^3*b^2 + 3*a*b^4)*m^2 + 4*(2*a*b^4*m^3 - 3*(a^3*b^2 - 3*a*b^4)*m^2 - (3*a^3*b^2 - 7*a*b^4)*m)*cos(d*x + c)^2 - 24*(a^3*b^2 - 5*a*b^4)*m + (64*b^5 + (b^5*m^4 + 10*b^5*m^3 + 35*b^5*m^2 + 50*b^5*m + 24*b^5)*cos(d*x + c)^4 + 8*(3*a^2*b^3 + b^5)*m^2 + 4*(8*b^5 + (a^2*b^3 + b^5)*m^3 + (3*a^2*b^3 + 7*b^5)*m^2 + 2*(a^2*b^3 + 7*b^5)*m)*cos(d*x + c)^2 - 24*(a^4*b - 3*a^2*b^3 - 2*b^5)*m)*sin(d*x + c))*(b*sin(d*x + c) + a)^m/(b^5*d*m^5 + 15*b^5*d*m^4 + 85*b^5*d*m^3 + 225*b^5*d*m^2 + 274*b^5*d*m + 120*b^5*d)","B",0
632,1,142,0,1.245027," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left(4 \, a b^{2} m - 2 \, a^{3} + 6 \, a b^{2} + {\left(a b^{2} m^{2} + a b^{2} m\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, b^{3} + {\left(b^{3} m^{2} + 3 \, b^{3} m + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} m\right)} \sin\left(d x + c\right)\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{b^{3} d m^{3} + 6 \, b^{3} d m^{2} + 11 \, b^{3} d m + 6 \, b^{3} d}"," ",0,"(4*a*b^2*m - 2*a^3 + 6*a*b^2 + (a*b^2*m^2 + a*b^2*m)*cos(d*x + c)^2 + (4*b^3 + (b^3*m^2 + 3*b^3*m + 2*b^3)*cos(d*x + c)^2 + 2*(a^2*b + b^3)*m)*sin(d*x + c))*(b*sin(d*x + c) + a)^m/(b^3*d*m^3 + 6*b^3*d*m^2 + 11*b^3*d*m + 6*b^3*d)","A",0
633,1,33,0,1.315742," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left(b \sin\left(d x + c\right) + a\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{b d m + b d}"," ",0,"(b*sin(d*x + c) + a)*(b*sin(d*x + c) + a)^m/(b*d*m + b*d)","A",0
634,0,0,0,1.356652," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right), x\right)"," ",0,"integral((b*sin(d*x + c) + a)^m*sec(d*x + c), x)","F",0
635,0,0,0,1.361499," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^m*sec(d*x + c)^3, x)","F",0
636,0,0,0,1.589241," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{5}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^m*sec(d*x + c)^5, x)","F",0
637,0,0,0,1.311979," ","integrate(cos(d*x+c)^4*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^m*cos(d*x + c)^4, x)","F",0
638,0,0,0,1.335607," ","integrate(cos(d*x+c)^2*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^m*cos(d*x + c)^2, x)","F",0
639,0,0,0,1.125650," ","integrate(sec(d*x+c)^2*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^m*sec(d*x + c)^2, x)","F",0
640,0,0,0,1.285185," ","integrate(sec(d*x+c)^4*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{m} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^m*sec(d*x + c)^4, x)","F",0
641,0,0,0,1.530925," ","integrate((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m} e^{2} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^m*e^2*cos(d*x + c)^2, x)","F",0
642,0,0,0,1.291047," ","integrate((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m} e \cos\left(d x + c\right), x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^m*e*cos(d*x + c), x)","F",0
643,0,0,0,1.522141," ","integrate((e*cos(d*x+c))^(1/2)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^m, x)","F",0
644,0,0,0,1.328228," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{e \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^m/(e*cos(d*x + c)), x)","F",0
645,0,0,0,1.447618," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{e^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^m/(e^2*cos(d*x + c)^2), x)","F",0
646,0,0,0,1.400997," ","integrate((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e \cos\left(d x + c\right)} {\left(b \sin\left(d x + c\right) + a\right)}^{m}}{e^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(e*cos(d*x + c))*(b*sin(d*x + c) + a)^m/(e^3*cos(d*x + c)^3), x)","F",0
647,0,0,0,1.127582," ","integrate((e*cos(d*x+c))^(-4-m)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-m - 4} {\left(b \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-m - 4)*(b*sin(d*x + c) + a)^m, x)","F",0
648,0,0,0,1.676178," ","integrate((e*cos(d*x+c))^(-3-m)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-m - 3} {\left(b \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-m - 3)*(b*sin(d*x + c) + a)^m, x)","F",0
649,0,0,0,1.600322," ","integrate((e*cos(d*x+c))^(-2-m)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-m - 2} {\left(b \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-m - 2)*(b*sin(d*x + c) + a)^m, x)","F",0
650,0,0,0,1.551615," ","integrate((e*cos(d*x+c))^(-1-m)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-m - 1} {\left(b \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-m - 1)*(b*sin(d*x + c) + a)^m, x)","F",0
651,0,0,0,1.431716," ","integrate((a+b*sin(d*x+c))^m/((e*cos(d*x+c))^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sin\left(d x + c\right) + a\right)}^{m}}{\left(e \cos\left(d x + c\right)\right)^{m}}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^m/(e*cos(d*x + c))^m, x)","F",0
652,0,0,0,1.427070," ","integrate((e*cos(d*x+c))^(1-m)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-m + 1} {\left(b \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-m + 1)*(b*sin(d*x + c) + a)^m, x)","F",0
653,0,0,0,1.086719," ","integrate((e*cos(d*x+c))^(2-m)*(a+b*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e \cos\left(d x + c\right)\right)^{-m + 2} {\left(b \sin\left(d x + c\right) + a\right)}^{m}, x\right)"," ",0,"integral((e*cos(d*x + c))^(-m + 2)*(b*sin(d*x + c) + a)^m, x)","F",0
