1,1,75,0,1.053666," ","integrate(cos(d*x+c)^5*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{75 \, a d x + {\left(40 \, a \cos\left(d x + c\right)^{5} + 48 \, a \cos\left(d x + c\right)^{4} + 50 \, a \cos\left(d x + c\right)^{3} + 64 \, a \cos\left(d x + c\right)^{2} + 75 \, a \cos\left(d x + c\right) + 128 \, a\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(75*a*d*x + (40*a*cos(d*x + c)^5 + 48*a*cos(d*x + c)^4 + 50*a*cos(d*x + c)^3 + 64*a*cos(d*x + c)^2 + 75*a*cos(d*x + c) + 128*a)*sin(d*x + c))/d","A",0
2,1,64,0,1.817861," ","integrate(cos(d*x+c)^4*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{45 \, a d x + {\left(24 \, a \cos\left(d x + c\right)^{4} + 30 \, a \cos\left(d x + c\right)^{3} + 32 \, a \cos\left(d x + c\right)^{2} + 45 \, a \cos\left(d x + c\right) + 64 \, a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*a*d*x + (24*a*cos(d*x + c)^4 + 30*a*cos(d*x + c)^3 + 32*a*cos(d*x + c)^2 + 45*a*cos(d*x + c) + 64*a)*sin(d*x + c))/d","A",0
3,1,53,0,0.930598," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, a d x + {\left(6 \, a \cos\left(d x + c\right)^{3} + 8 \, a \cos\left(d x + c\right)^{2} + 9 \, a \cos\left(d x + c\right) + 16 \, a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(9*a*d*x + (6*a*cos(d*x + c)^3 + 8*a*cos(d*x + c)^2 + 9*a*cos(d*x + c) + 16*a)*sin(d*x + c))/d","A",0
4,1,42,0,0.811055," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a d x + {\left(2 \, a \cos\left(d x + c\right)^{2} + 3 \, a \cos\left(d x + c\right) + 4 \, a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*a*d*x + (2*a*cos(d*x + c)^2 + 3*a*cos(d*x + c) + 4*a)*sin(d*x + c))/d","A",0
5,1,29,0,2.334497," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{a d x + {\left(a \cos\left(d x + c\right) + 2 \, a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*d*x + (a*cos(d*x + c) + 2*a)*sin(d*x + c))/d","A",0
6,1,17,0,0.753170," ","integrate(a+a*cos(d*x+c),x, algorithm=""fricas"")","\frac{a d x + a \sin\left(d x + c\right)}{d}"," ",0,"(a*d*x + a*sin(d*x + c))/d","A",0
7,1,36,0,1.676403," ","integrate((a+a*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{2 \, a d x + a \log\left(\sin\left(d x + c\right) + 1\right) - a \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"1/2*(2*a*d*x + a*log(sin(d*x + c) + 1) - a*log(-sin(d*x + c) + 1))/d","B",0
8,1,60,0,1.007102," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - a \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, a \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(a*cos(d*x + c)*log(sin(d*x + c) + 1) - a*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*a*sin(d*x + c))/(d*cos(d*x + c))","B",0
9,1,74,0,1.633185," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^3,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 \, {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{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*(2*a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
10,1,88,0,1.233028," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, a \cos\left(d x + c\right)^{2} + 3 \, a \cos\left(d x + c\right) + 2 \, a\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*a*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*a*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(4*a*cos(d*x + c)^2 + 3*a*cos(d*x + c) + 2*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
11,1,99,0,0.871346," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{9 \, a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, a \cos\left(d x + c\right)^{3} + 9 \, a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) + 6 \, a\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(9*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 9*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*a*cos(d*x + c)^3 + 9*a*cos(d*x + c)^2 + 8*a*cos(d*x + c) + 6*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
12,1,110,0,1.219396," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{45 \, a \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 45 \, a \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(64 \, a \cos\left(d x + c\right)^{4} + 45 \, a \cos\left(d x + c\right)^{3} + 32 \, a \cos\left(d x + c\right)^{2} + 30 \, a \cos\left(d x + c\right) + 24 \, a\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(45*a*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 45*a*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(64*a*cos(d*x + c)^4 + 45*a*cos(d*x + c)^3 + 32*a*cos(d*x + c)^2 + 30*a*cos(d*x + c) + 24*a)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
13,1,89,0,1.644170," ","integrate(cos(d*x+c)^4*(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{165 \, a^{2} d x + {\left(40 \, a^{2} \cos\left(d x + c\right)^{5} + 96 \, a^{2} \cos\left(d x + c\right)^{4} + 110 \, a^{2} \cos\left(d x + c\right)^{3} + 128 \, a^{2} \cos\left(d x + c\right)^{2} + 165 \, a^{2} \cos\left(d x + c\right) + 256 \, a^{2}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(165*a^2*d*x + (40*a^2*cos(d*x + c)^5 + 96*a^2*cos(d*x + c)^4 + 110*a^2*cos(d*x + c)^3 + 128*a^2*cos(d*x + c)^2 + 165*a^2*cos(d*x + c) + 256*a^2)*sin(d*x + c))/d","A",0
14,1,76,0,1.460194," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, a^{2} d x + {\left(4 \, a^{2} \cos\left(d x + c\right)^{4} + 10 \, a^{2} \cos\left(d x + c\right)^{3} + 12 \, a^{2} \cos\left(d x + c\right)^{2} + 15 \, a^{2} \cos\left(d x + c\right) + 24 \, a^{2}\right)} \sin\left(d x + c\right)}{20 \, d}"," ",0,"1/20*(15*a^2*d*x + (4*a^2*cos(d*x + c)^4 + 10*a^2*cos(d*x + c)^3 + 12*a^2*cos(d*x + c)^2 + 15*a^2*cos(d*x + c) + 24*a^2)*sin(d*x + c))/d","A",0
15,1,63,0,1.563458," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{21 \, a^{2} d x + {\left(6 \, a^{2} \cos\left(d x + c\right)^{3} + 16 \, a^{2} \cos\left(d x + c\right)^{2} + 21 \, a^{2} \cos\left(d x + c\right) + 32 \, a^{2}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(21*a^2*d*x + (6*a^2*cos(d*x + c)^3 + 16*a^2*cos(d*x + c)^2 + 21*a^2*cos(d*x + c) + 32*a^2)*sin(d*x + c))/d","A",0
16,1,49,0,1.560685," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} d x + {\left(a^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} \cos\left(d x + c\right) + 5 \, a^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(3*a^2*d*x + (a^2*cos(d*x + c)^2 + 3*a^2*cos(d*x + c) + 5*a^2)*sin(d*x + c))/d","A",0
17,1,36,0,1.172764," ","integrate((a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} d x + {\left(a^{2} \cos\left(d x + c\right) + 4 \, a^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(3*a^2*d*x + (a^2*cos(d*x + c) + 4*a^2)*sin(d*x + c))/d","A",0
18,1,53,0,1.427849," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c),x, algorithm=""fricas"")","\frac{4 \, a^{2} d x + a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(4*a^2*d*x + a^2*log(sin(d*x + c) + 1) - a^2*log(-sin(d*x + c) + 1) + 2*a^2*sin(d*x + c))/d","A",0
19,1,76,0,1.613009," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{a^{2} d x \cos\left(d x + c\right) + a^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - a^{2} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + a^{2} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"(a^2*d*x*cos(d*x + c) + a^2*cos(d*x + c)*log(sin(d*x + c) + 1) - a^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + a^2*sin(d*x + c))/(d*cos(d*x + c))","B",0
20,1,83,0,1.338666," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, a^{2} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a^{2} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(3*a^2*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 3*a^2*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(4*a^2*cos(d*x + c) + a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
21,1,96,0,1.634714," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, a^{2} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a^{2} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(5 \, a^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(3*a^2*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*a^2*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(5*a^2*cos(d*x + c)^2 + 3*a^2*cos(d*x + c) + a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
22,1,111,0,1.894621," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{21 \, a^{2} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 21 \, a^{2} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(32 \, a^{2} \cos\left(d x + c\right)^{3} + 21 \, a^{2} \cos\left(d x + c\right)^{2} + 16 \, a^{2} \cos\left(d x + c\right) + 6 \, a^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(21*a^2*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 21*a^2*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(32*a^2*cos(d*x + c)^3 + 21*a^2*cos(d*x + c)^2 + 16*a^2*cos(d*x + c) + 6*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
23,1,89,0,0.879489," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{345 \, a^{3} d x + {\left(40 \, a^{3} \cos\left(d x + c\right)^{5} + 144 \, a^{3} \cos\left(d x + c\right)^{4} + 230 \, a^{3} \cos\left(d x + c\right)^{3} + 272 \, a^{3} \cos\left(d x + c\right)^{2} + 345 \, a^{3} \cos\left(d x + c\right) + 544 \, a^{3}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(345*a^3*d*x + (40*a^3*cos(d*x + c)^5 + 144*a^3*cos(d*x + c)^4 + 230*a^3*cos(d*x + c)^3 + 272*a^3*cos(d*x + c)^2 + 345*a^3*cos(d*x + c) + 544*a^3)*sin(d*x + c))/d","A",0
24,1,76,0,2.161315," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{195 \, a^{3} d x + {\left(24 \, a^{3} \cos\left(d x + c\right)^{4} + 90 \, a^{3} \cos\left(d x + c\right)^{3} + 152 \, a^{3} \cos\left(d x + c\right)^{2} + 195 \, a^{3} \cos\left(d x + c\right) + 304 \, a^{3}\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(195*a^3*d*x + (24*a^3*cos(d*x + c)^4 + 90*a^3*cos(d*x + c)^3 + 152*a^3*cos(d*x + c)^2 + 195*a^3*cos(d*x + c) + 304*a^3)*sin(d*x + c))/d","A",0
25,1,63,0,1.528043," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, a^{3} d x + {\left(2 \, a^{3} \cos\left(d x + c\right)^{3} + 8 \, a^{3} \cos\left(d x + c\right)^{2} + 15 \, a^{3} \cos\left(d x + c\right) + 24 \, a^{3}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(15*a^3*d*x + (2*a^3*cos(d*x + c)^3 + 8*a^3*cos(d*x + c)^2 + 15*a^3*cos(d*x + c) + 24*a^3)*sin(d*x + c))/d","A",0
26,1,50,0,1.968189," ","integrate((a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, a^{3} d x + {\left(2 \, a^{3} \cos\left(d x + c\right)^{2} + 9 \, a^{3} \cos\left(d x + c\right) + 22 \, a^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(15*a^3*d*x + (2*a^3*cos(d*x + c)^2 + 9*a^3*cos(d*x + c) + 22*a^3)*sin(d*x + c))/d","A",0
27,1,65,0,1.639068," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c),x, algorithm=""fricas"")","\frac{7 \, a^{3} d x + a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(a^{3} \cos\left(d x + c\right) + 6 \, a^{3}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(7*a^3*d*x + a^3*log(sin(d*x + c) + 1) - a^3*log(-sin(d*x + c) + 1) + (a^3*cos(d*x + c) + 6*a^3)*sin(d*x + c))/d","A",0
28,1,91,0,0.798206," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{6 \, a^{3} d x \cos\left(d x + c\right) + 3 \, a^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(6*a^3*d*x*cos(d*x + c) + 3*a^3*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*a^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(a^3*cos(d*x + c) + a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
29,1,98,0,1.054416," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, a^{3} d x \cos\left(d x + c\right)^{2} + 7 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 7 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*a^3*d*x*cos(d*x + c)^2 + 7*a^3*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 7*a^3*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(6*a^3*cos(d*x + c) + a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
30,1,98,0,0.664648," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{15 \, a^{3} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, a^{3} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(22 \, a^{3} \cos\left(d x + c\right)^{2} + 9 \, a^{3} \cos\left(d x + c\right) + 2 \, a^{3}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(15*a^3*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 15*a^3*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(22*a^3*cos(d*x + c)^2 + 9*a^3*cos(d*x + c) + 2*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
31,1,111,0,1.026283," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{15 \, a^{3} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, a^{3} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, a^{3} \cos\left(d x + c\right)^{3} + 15 \, a^{3} \cos\left(d x + c\right)^{2} + 8 \, a^{3} \cos\left(d x + c\right) + 2 \, a^{3}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(15*a^3*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 15*a^3*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(24*a^3*cos(d*x + c)^3 + 15*a^3*cos(d*x + c)^2 + 8*a^3*cos(d*x + c) + 2*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
32,1,124,0,0.974042," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{195 \, a^{3} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 195 \, a^{3} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(304 \, a^{3} \cos\left(d x + c\right)^{4} + 195 \, a^{3} \cos\left(d x + c\right)^{3} + 152 \, a^{3} \cos\left(d x + c\right)^{2} + 90 \, a^{3} \cos\left(d x + c\right) + 24 \, a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(195*a^3*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 195*a^3*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(304*a^3*cos(d*x + c)^4 + 195*a^3*cos(d*x + c)^3 + 152*a^3*cos(d*x + c)^2 + 90*a^3*cos(d*x + c) + 24*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
33,1,89,0,0.907547," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{735 \, a^{4} d x + {\left(40 \, a^{4} \cos\left(d x + c\right)^{5} + 192 \, a^{4} \cos\left(d x + c\right)^{4} + 410 \, a^{4} \cos\left(d x + c\right)^{3} + 576 \, a^{4} \cos\left(d x + c\right)^{2} + 735 \, a^{4} \cos\left(d x + c\right) + 1152 \, a^{4}\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(735*a^4*d*x + (40*a^4*cos(d*x + c)^5 + 192*a^4*cos(d*x + c)^4 + 410*a^4*cos(d*x + c)^3 + 576*a^4*cos(d*x + c)^2 + 735*a^4*cos(d*x + c) + 1152*a^4)*sin(d*x + c))/d","A",0
34,1,76,0,0.933344," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, a^{4} d x + {\left(6 \, a^{4} \cos\left(d x + c\right)^{4} + 30 \, a^{4} \cos\left(d x + c\right)^{3} + 68 \, a^{4} \cos\left(d x + c\right)^{2} + 105 \, a^{4} \cos\left(d x + c\right) + 166 \, a^{4}\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(105*a^4*d*x + (6*a^4*cos(d*x + c)^4 + 30*a^4*cos(d*x + c)^3 + 68*a^4*cos(d*x + c)^2 + 105*a^4*cos(d*x + c) + 166*a^4)*sin(d*x + c))/d","A",0
35,1,63,0,1.027354," ","integrate((a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, a^{4} d x + {\left(6 \, a^{4} \cos\left(d x + c\right)^{3} + 32 \, a^{4} \cos\left(d x + c\right)^{2} + 81 \, a^{4} \cos\left(d x + c\right) + 160 \, a^{4}\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(105*a^4*d*x + (6*a^4*cos(d*x + c)^3 + 32*a^4*cos(d*x + c)^2 + 81*a^4*cos(d*x + c) + 160*a^4)*sin(d*x + c))/d","A",0
36,1,80,0,0.811650," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c),x, algorithm=""fricas"")","\frac{36 \, a^{4} d x + 3 \, a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{4} \cos\left(d x + c\right)^{2} + 6 \, a^{4} \cos\left(d x + c\right) + 20 \, a^{4}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(36*a^4*d*x + 3*a^4*log(sin(d*x + c) + 1) - 3*a^4*log(-sin(d*x + c) + 1) + 2*(a^4*cos(d*x + c)^2 + 6*a^4*cos(d*x + c) + 20*a^4)*sin(d*x + c))/d","A",0
37,1,105,0,0.885436," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{13 \, a^{4} d x \cos\left(d x + c\right) + 4 \, a^{4} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, a^{4} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} \cos\left(d x + c\right) + 2 \, a^{4}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(13*a^4*d*x*cos(d*x + c) + 4*a^4*cos(d*x + c)*log(sin(d*x + c) + 1) - 4*a^4*cos(d*x + c)*log(-sin(d*x + c) + 1) + (a^4*cos(d*x + c)^2 + 8*a^4*cos(d*x + c) + 2*a^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
38,1,111,0,1.713530," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{16 \, a^{4} d x \cos\left(d x + c\right)^{2} + 13 \, a^{4} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 13 \, a^{4} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(16*a^4*d*x*cos(d*x + c)^2 + 13*a^4*cos(d*x + c)^2*log(sin(d*x + c) + 1) - 13*a^4*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*a^4*cos(d*x + c)^2 + 8*a^4*cos(d*x + c) + a^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
39,1,110,0,0.962494," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, a^{4} d x \cos\left(d x + c\right)^{3} + 9 \, a^{4} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, a^{4} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(20 \, a^{4} \cos\left(d x + c\right)^{2} + 6 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/3*(3*a^4*d*x*cos(d*x + c)^3 + 9*a^4*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 9*a^4*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + (20*a^4*cos(d*x + c)^2 + 6*a^4*cos(d*x + c) + a^4)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
40,1,111,0,1.997767," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{105 \, a^{4} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, a^{4} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(160 \, a^{4} \cos\left(d x + c\right)^{3} + 81 \, a^{4} \cos\left(d x + c\right)^{2} + 32 \, a^{4} \cos\left(d x + c\right) + 6 \, a^{4}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(105*a^4*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 105*a^4*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(160*a^4*cos(d*x + c)^3 + 81*a^4*cos(d*x + c)^2 + 32*a^4*cos(d*x + c) + 6*a^4)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
41,1,124,0,0.758647," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{105 \, a^{4} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, a^{4} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(166 \, a^{4} \cos\left(d x + c\right)^{4} + 105 \, a^{4} \cos\left(d x + c\right)^{3} + 68 \, a^{4} \cos\left(d x + c\right)^{2} + 30 \, a^{4} \cos\left(d x + c\right) + 6 \, a^{4}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/60*(105*a^4*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 105*a^4*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(166*a^4*cos(d*x + c)^4 + 105*a^4*cos(d*x + c)^3 + 68*a^4*cos(d*x + c)^2 + 30*a^4*cos(d*x + c) + 6*a^4)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
42,1,137,0,0.779631," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{735 \, a^{4} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 735 \, a^{4} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(1152 \, a^{4} \cos\left(d x + c\right)^{5} + 735 \, a^{4} \cos\left(d x + c\right)^{4} + 576 \, a^{4} \cos\left(d x + c\right)^{3} + 410 \, a^{4} \cos\left(d x + c\right)^{2} + 192 \, a^{4} \cos\left(d x + c\right) + 40 \, a^{4}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(735*a^4*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 735*a^4*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(1152*a^4*cos(d*x + c)^5 + 735*a^4*cos(d*x + c)^4 + 576*a^4*cos(d*x + c)^3 + 410*a^4*cos(d*x + c)^2 + 192*a^4*cos(d*x + c) + 40*a^4)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
43,1,79,0,1.054038," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{45 \, d x \cos\left(d x + c\right) + 45 \, d x + {\left(6 \, \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} + 13 \, \cos\left(d x + c\right)^{2} - 19 \, \cos\left(d x + c\right) - 64\right)} \sin\left(d x + c\right)}{24 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/24*(45*d*x*cos(d*x + c) + 45*d*x + (6*cos(d*x + c)^4 - 2*cos(d*x + c)^3 + 13*cos(d*x + c)^2 - 19*cos(d*x + c) - 64)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
44,1,70,0,1.101106," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{9 \, d x \cos\left(d x + c\right) + 9 \, d x - {\left(2 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} + 7 \, \cos\left(d x + c\right) + 16\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"-1/6*(9*d*x*cos(d*x + c) + 9*d*x - (2*cos(d*x + c)^3 - cos(d*x + c)^2 + 7*cos(d*x + c) + 16)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
45,1,57,0,1.168554," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, d x \cos\left(d x + c\right) + 3 \, d x + {\left(\cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(3*d*x*cos(d*x + c) + 3*d*x + (cos(d*x + c)^2 - cos(d*x + c) - 4)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
46,1,46,0,0.998673," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{d x \cos\left(d x + c\right) + d x - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"-(d*x*cos(d*x + c) + d*x - (cos(d*x + c) + 2)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
47,1,37,0,0.894731," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{d x \cos\left(d x + c\right) + d x - \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"(d*x*cos(d*x + c) + d*x - sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
48,1,22,0,0.910079," ","integrate(1/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{\sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"sin(d*x + c)/(a*d*cos(d*x + c) + a*d)","A",0
49,1,65,0,0.927171," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(\cos\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(\cos\left(d x + c\right) + 1\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*((cos(d*x + c) + 1)*log(sin(d*x + c) + 1) - (cos(d*x + c) + 1)*log(-sin(d*x + c) + 1) - 2*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
50,1,97,0,1.100871," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/2*((cos(d*x + c)^2 + cos(d*x + c))*log(sin(d*x + c) + 1) - (cos(d*x + c)^2 + cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*cos(d*x + c) + 1)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
51,1,112,0,1.062270," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{3} + \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)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}{4 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/4*(3*(cos(d*x + c)^3 + cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*(cos(d*x + c)^3 + cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(4*cos(d*x + c)^2 + cos(d*x + c) - 1)*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
52,1,124,0,1.054840," ","integrate(sec(d*x+c)^4/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{9 \, {\left(\cos\left(d x + c\right)^{4} + \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, {\left(\cos\left(d x + c\right)^{4} + \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(16 \, \cos\left(d x + c\right)^{3} + 7 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{12 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/12*(9*(cos(d*x + c)^4 + cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 9*(cos(d*x + c)^4 + cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(16*cos(d*x + c)^3 + 7*cos(d*x + c)^2 - cos(d*x + c) + 2)*sin(d*x + c))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
53,1,108,0,1.075176," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{15 \, d x \cos\left(d x + c\right)^{2} + 30 \, d x \cos\left(d x + c\right) + 15 \, d x - {\left(\cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 33 \, \cos\left(d x + c\right) + 24\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/3*(15*d*x*cos(d*x + c)^2 + 30*d*x*cos(d*x + c) + 15*d*x - (cos(d*x + c)^4 - cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 33*cos(d*x + c) + 24)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
54,1,99,0,1.997951," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{21 \, d x \cos\left(d x + c\right)^{2} + 42 \, d x \cos\left(d x + c\right) + 21 \, d x + {\left(3 \, \cos\left(d x + c\right)^{3} - 6 \, \cos\left(d x + c\right)^{2} - 43 \, \cos\left(d x + c\right) - 32\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(21*d*x*cos(d*x + c)^2 + 42*d*x*cos(d*x + c) + 21*d*x + (3*cos(d*x + c)^3 - 6*cos(d*x + c)^2 - 43*cos(d*x + c) - 32)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
55,1,90,0,1.344719," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, d x \cos\left(d x + c\right)^{2} + 12 \, d x \cos\left(d x + c\right) + 6 \, d x - {\left(3 \, \cos\left(d x + c\right)^{2} + 14 \, \cos\left(d x + c\right) + 10\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/3*(6*d*x*cos(d*x + c)^2 + 12*d*x*cos(d*x + c) + 6*d*x - (3*cos(d*x + c)^2 + 14*cos(d*x + c) + 10)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
56,1,80,0,0.991407," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, d x \cos\left(d x + c\right)^{2} + 6 \, d x \cos\left(d x + c\right) + 3 \, d x - {\left(5 \, \cos\left(d x + c\right) + 4\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*d*x*cos(d*x + c)^2 + 6*d*x*cos(d*x + c) + 3*d*x - (5*cos(d*x + c) + 4)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
57,1,51,0,1.526531," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(2*cos(d*x + c) + 1)*sin(d*x + c)/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
58,1,49,0,1.064899," ","integrate(1/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(cos(d*x + c) + 2)*sin(d*x + c)/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
59,1,114,0,0.896288," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, \cos\left(d x + c\right) + 5\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*log(sin(d*x + c) + 1) - 3*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*log(-sin(d*x + c) + 1) - 2*(4*cos(d*x + c) + 5)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
60,1,146,0,0.680019," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(10 \, \cos\left(d x + c\right)^{2} + 14 \, \cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*log(sin(d*x + c) + 1) - 3*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*log(-sin(d*x + c) + 1) - (10*cos(d*x + c)^2 + 14*cos(d*x + c) + 3)*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","A",0
61,1,162,0,1.097793," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{21 \, {\left(\cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 21 \, {\left(\cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(32 \, \cos\left(d x + c\right)^{3} + 43 \, \cos\left(d x + c\right)^{2} + 6 \, \cos\left(d x + c\right) - 3\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*(21*(cos(d*x + c)^4 + 2*cos(d*x + c)^3 + cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 21*(cos(d*x + c)^4 + 2*cos(d*x + c)^3 + cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(32*cos(d*x + c)^3 + 43*cos(d*x + c)^2 + 6*cos(d*x + c) - 3)*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
62,1,172,0,0.955542," ","integrate(sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{15 \, {\left(\cos\left(d x + c\right)^{5} + 2 \, \cos\left(d x + c\right)^{4} + \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(\cos\left(d x + c\right)^{5} + 2 \, \cos\left(d x + c\right)^{4} + \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(24 \, \cos\left(d x + c\right)^{4} + 33 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} + 2 \, a^{2} d \cos\left(d x + c\right)^{4} + a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/6*(15*(cos(d*x + c)^5 + 2*cos(d*x + c)^4 + cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 15*(cos(d*x + c)^5 + 2*cos(d*x + c)^4 + cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(24*cos(d*x + c)^4 + 33*cos(d*x + c)^3 + 6*cos(d*x + c)^2 - cos(d*x + c) + 1)*sin(d*x + c))/(a^2*d*cos(d*x + c)^5 + 2*a^2*d*cos(d*x + c)^4 + a^2*d*cos(d*x + c)^3)","A",0
63,1,135,0,1.016357," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{195 \, d x \cos\left(d x + c\right)^{3} + 585 \, d x \cos\left(d x + c\right)^{2} + 585 \, d x \cos\left(d x + c\right) + 195 \, d x + {\left(15 \, \cos\left(d x + c\right)^{4} - 45 \, \cos\left(d x + c\right)^{3} - 479 \, \cos\left(d x + c\right)^{2} - 717 \, \cos\left(d x + c\right) - 304\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(195*d*x*cos(d*x + c)^3 + 585*d*x*cos(d*x + c)^2 + 585*d*x*cos(d*x + c) + 195*d*x + (15*cos(d*x + c)^4 - 45*cos(d*x + c)^3 - 479*cos(d*x + c)^2 - 717*cos(d*x + c) - 304)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
64,1,126,0,1.183578," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, d x \cos\left(d x + c\right)^{3} + 45 \, d x \cos\left(d x + c\right)^{2} + 45 \, d x \cos\left(d x + c\right) + 15 \, d x - {\left(5 \, \cos\left(d x + c\right)^{3} + 39 \, \cos\left(d x + c\right)^{2} + 57 \, \cos\left(d x + c\right) + 24\right)} \sin\left(d x + c\right)}{5 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/5*(15*d*x*cos(d*x + c)^3 + 45*d*x*cos(d*x + c)^2 + 45*d*x*cos(d*x + c) + 15*d*x - (5*cos(d*x + c)^3 + 39*cos(d*x + c)^2 + 57*cos(d*x + c) + 24)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
65,1,116,0,1.745929," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, d x \cos\left(d x + c\right)^{3} + 45 \, d x \cos\left(d x + c\right)^{2} + 45 \, d x \cos\left(d x + c\right) + 15 \, d x - {\left(32 \, \cos\left(d x + c\right)^{2} + 51 \, \cos\left(d x + c\right) + 22\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(15*d*x*cos(d*x + c)^3 + 45*d*x*cos(d*x + c)^2 + 45*d*x*cos(d*x + c) + 15*d*x - (32*cos(d*x + c)^2 + 51*cos(d*x + c) + 22)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
66,1,75,0,2.212235," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(7 \, \cos\left(d x + c\right)^{2} + 6 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(7*cos(d*x + c)^2 + 6*cos(d*x + c) + 2)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
67,1,73,0,0.764145," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(\cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{5 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/5*(cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
68,1,75,0,0.772487," ","integrate(1/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(d x + c\right)^{2} + 6 \, \cos\left(d x + c\right) + 7\right)} \sin\left(d x + c\right)}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/15*(2*cos(d*x + c)^2 + 6*cos(d*x + c) + 7)*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
69,1,158,0,1.206384," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(22 \, \cos\left(d x + c\right)^{2} + 51 \, \cos\left(d x + c\right) + 32\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/30*(15*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*log(sin(d*x + c) + 1) - 15*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*log(-sin(d*x + c) + 1) - 2*(22*cos(d*x + c)^2 + 51*cos(d*x + c) + 32)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
70,1,190,0,0.890852," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(\cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(\cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(24 \, \cos\left(d x + c\right)^{3} + 57 \, \cos\left(d x + c\right)^{2} + 39 \, \cos\left(d x + c\right) + 5\right)} \sin\left(d x + c\right)}{10 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/10*(15*(cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*log(sin(d*x + c) + 1) - 15*(cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(24*cos(d*x + c)^3 + 57*cos(d*x + c)^2 + 39*cos(d*x + c) + 5)*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","A",0
71,1,206,0,1.148865," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{195 \, {\left(\cos\left(d x + c\right)^{5} + 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 195 \, {\left(\cos\left(d x + c\right)^{5} + 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(304 \, \cos\left(d x + c\right)^{4} + 717 \, \cos\left(d x + c\right)^{3} + 479 \, \cos\left(d x + c\right)^{2} + 45 \, \cos\left(d x + c\right) - 15\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/60*(195*(cos(d*x + c)^5 + 3*cos(d*x + c)^4 + 3*cos(d*x + c)^3 + cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 195*(cos(d*x + c)^5 + 3*cos(d*x + c)^4 + 3*cos(d*x + c)^3 + cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(304*cos(d*x + c)^4 + 717*cos(d*x + c)^3 + 479*cos(d*x + c)^2 + 45*cos(d*x + c) - 15)*sin(d*x + c))/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2)","A",0
72,1,171,0,1.733023," ","integrate(cos(d*x+c)^6/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{735 \, d x \cos\left(d x + c\right)^{4} + 2940 \, d x \cos\left(d x + c\right)^{3} + 4410 \, d x \cos\left(d x + c\right)^{2} + 2940 \, d x \cos\left(d x + c\right) + 735 \, d x + {\left(35 \, \cos\left(d x + c\right)^{5} - 140 \, \cos\left(d x + c\right)^{4} - 2012 \, \cos\left(d x + c\right)^{3} - 4548 \, \cos\left(d x + c\right)^{2} - 3873 \, \cos\left(d x + c\right) - 1152\right)} \sin\left(d x + c\right)}{70 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/70*(735*d*x*cos(d*x + c)^4 + 2940*d*x*cos(d*x + c)^3 + 4410*d*x*cos(d*x + c)^2 + 2940*d*x*cos(d*x + c) + 735*d*x + (35*cos(d*x + c)^5 - 140*cos(d*x + c)^4 - 2012*cos(d*x + c)^3 - 4548*cos(d*x + c)^2 - 3873*cos(d*x + c) - 1152)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
73,1,162,0,0.654591," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","-\frac{420 \, d x \cos\left(d x + c\right)^{4} + 1680 \, d x \cos\left(d x + c\right)^{3} + 2520 \, d x \cos\left(d x + c\right)^{2} + 1680 \, d x \cos\left(d x + c\right) + 420 \, d x - {\left(105 \, \cos\left(d x + c\right)^{4} + 1184 \, \cos\left(d x + c\right)^{3} + 2636 \, \cos\left(d x + c\right)^{2} + 2236 \, \cos\left(d x + c\right) + 664\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/105*(420*d*x*cos(d*x + c)^4 + 1680*d*x*cos(d*x + c)^3 + 2520*d*x*cos(d*x + c)^2 + 1680*d*x*cos(d*x + c) + 420*d*x - (105*cos(d*x + c)^4 + 1184*cos(d*x + c)^3 + 2636*cos(d*x + c)^2 + 2236*cos(d*x + c) + 664)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
74,1,152,0,0.820211," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{21 \, d x \cos\left(d x + c\right)^{4} + 84 \, d x \cos\left(d x + c\right)^{3} + 126 \, d x \cos\left(d x + c\right)^{2} + 84 \, d x \cos\left(d x + c\right) + 21 \, d x - {\left(52 \, \cos\left(d x + c\right)^{3} + 124 \, \cos\left(d x + c\right)^{2} + 107 \, \cos\left(d x + c\right) + 32\right)} \sin\left(d x + c\right)}{21 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/21*(21*d*x*cos(d*x + c)^4 + 84*d*x*cos(d*x + c)^3 + 126*d*x*cos(d*x + c)^2 + 84*d*x*cos(d*x + c) + 21*d*x - (52*cos(d*x + c)^3 + 124*cos(d*x + c)^2 + 107*cos(d*x + c) + 32)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
75,1,99,0,0.594175," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(12 \, \cos\left(d x + c\right)^{3} + 13 \, \cos\left(d x + c\right)^{2} + 8 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{35 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/35*(12*cos(d*x + c)^3 + 13*cos(d*x + c)^2 + 8*cos(d*x + c) + 2)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
76,1,99,0,1.058075," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(13 \, \cos\left(d x + c\right)^{3} + 52 \, \cos\left(d x + c\right)^{2} + 32 \, \cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(13*cos(d*x + c)^3 + 52*cos(d*x + c)^2 + 32*cos(d*x + c) + 8)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
77,1,99,0,0.915428," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(8 \, \cos\left(d x + c\right)^{3} + 32 \, \cos\left(d x + c\right)^{2} + 52 \, \cos\left(d x + c\right) + 13\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/105*(8*cos(d*x + c)^3 + 32*cos(d*x + c)^2 + 52*cos(d*x + c) + 13)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
78,1,99,0,0.917202," ","integrate(1/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(d x + c\right)^{3} + 8 \, \cos\left(d x + c\right)^{2} + 13 \, \cos\left(d x + c\right) + 12\right)} \sin\left(d x + c\right)}{35 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/35*(2*cos(d*x + c)^3 + 8*cos(d*x + c)^2 + 13*cos(d*x + c) + 12)*sin(d*x + c)/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
79,1,202,0,1.038887," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{21 \, {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 21 \, {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(32 \, \cos\left(d x + c\right)^{3} + 107 \, \cos\left(d x + c\right)^{2} + 124 \, \cos\left(d x + c\right) + 52\right)} \sin\left(d x + c\right)}{42 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/42*(21*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*log(sin(d*x + c) + 1) - 21*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*log(-sin(d*x + c) + 1) - 2*(32*cos(d*x + c)^3 + 107*cos(d*x + c)^2 + 124*cos(d*x + c) + 52)*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
80,1,234,0,0.899529," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","-\frac{210 \, {\left(\cos\left(d x + c\right)^{5} + 4 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 210 \, {\left(\cos\left(d x + c\right)^{5} + 4 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(664 \, \cos\left(d x + c\right)^{4} + 2236 \, \cos\left(d x + c\right)^{3} + 2636 \, \cos\left(d x + c\right)^{2} + 1184 \, \cos\left(d x + c\right) + 105\right)} \sin\left(d x + c\right)}{105 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + 6 \, a^{4} d \cos\left(d x + c\right)^{3} + 4 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/105*(210*(cos(d*x + c)^5 + 4*cos(d*x + c)^4 + 6*cos(d*x + c)^3 + 4*cos(d*x + c)^2 + cos(d*x + c))*log(sin(d*x + c) + 1) - 210*(cos(d*x + c)^5 + 4*cos(d*x + c)^4 + 6*cos(d*x + c)^3 + 4*cos(d*x + c)^2 + cos(d*x + c))*log(-sin(d*x + c) + 1) - (664*cos(d*x + c)^4 + 2236*cos(d*x + c)^3 + 2636*cos(d*x + c)^2 + 1184*cos(d*x + c) + 105)*sin(d*x + c))/(a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + 6*a^4*d*cos(d*x + c)^3 + 4*a^4*d*cos(d*x + c)^2 + a^4*d*cos(d*x + c))","A",0
81,1,250,0,1.086896," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{735 \, {\left(\cos\left(d x + c\right)^{6} + 4 \, \cos\left(d x + c\right)^{5} + 6 \, \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 735 \, {\left(\cos\left(d x + c\right)^{6} + 4 \, \cos\left(d x + c\right)^{5} + 6 \, \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(1152 \, \cos\left(d x + c\right)^{5} + 3873 \, \cos\left(d x + c\right)^{4} + 4548 \, \cos\left(d x + c\right)^{3} + 2012 \, \cos\left(d x + c\right)^{2} + 140 \, \cos\left(d x + c\right) - 35\right)} \sin\left(d x + c\right)}{140 \, {\left(a^{4} d \cos\left(d x + c\right)^{6} + 4 \, a^{4} d \cos\left(d x + c\right)^{5} + 6 \, a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + a^{4} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/140*(735*(cos(d*x + c)^6 + 4*cos(d*x + c)^5 + 6*cos(d*x + c)^4 + 4*cos(d*x + c)^3 + cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 735*(cos(d*x + c)^6 + 4*cos(d*x + c)^5 + 6*cos(d*x + c)^4 + 4*cos(d*x + c)^3 + cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(1152*cos(d*x + c)^5 + 3873*cos(d*x + c)^4 + 4548*cos(d*x + c)^3 + 2012*cos(d*x + c)^2 + 140*cos(d*x + c) - 35)*sin(d*x + c))/(a^4*d*cos(d*x + c)^6 + 4*a^4*d*cos(d*x + c)^5 + 6*a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + a^4*d*cos(d*x + c)^2)","A",0
82,1,207,0,0.881914," ","integrate(cos(d*x+c)^7/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{9765 \, d x \cos\left(d x + c\right)^{5} + 48825 \, d x \cos\left(d x + c\right)^{4} + 97650 \, d x \cos\left(d x + c\right)^{3} + 97650 \, d x \cos\left(d x + c\right)^{2} + 48825 \, d x \cos\left(d x + c\right) + 9765 \, d x + {\left(315 \, \cos\left(d x + c\right)^{6} - 1575 \, \cos\left(d x + c\right)^{5} - 28828 \, \cos\left(d x + c\right)^{4} - 87440 \, \cos\left(d x + c\right)^{3} - 112119 \, \cos\left(d x + c\right)^{2} - 66875 \, \cos\left(d x + c\right) - 15328\right)} \sin\left(d x + c\right)}{630 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/630*(9765*d*x*cos(d*x + c)^5 + 48825*d*x*cos(d*x + c)^4 + 97650*d*x*cos(d*x + c)^3 + 97650*d*x*cos(d*x + c)^2 + 48825*d*x*cos(d*x + c) + 9765*d*x + (315*cos(d*x + c)^6 - 1575*cos(d*x + c)^5 - 28828*cos(d*x + c)^4 - 87440*cos(d*x + c)^3 - 112119*cos(d*x + c)^2 - 66875*cos(d*x + c) - 15328)*sin(d*x + c))/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
83,1,198,0,1.188470," ","integrate(cos(d*x+c)^6/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","-\frac{315 \, d x \cos\left(d x + c\right)^{5} + 1575 \, d x \cos\left(d x + c\right)^{4} + 3150 \, d x \cos\left(d x + c\right)^{3} + 3150 \, d x \cos\left(d x + c\right)^{2} + 1575 \, d x \cos\left(d x + c\right) + 315 \, d x - {\left(63 \, \cos\left(d x + c\right)^{5} + 946 \, \cos\left(d x + c\right)^{4} + 2840 \, \cos\left(d x + c\right)^{3} + 3633 \, \cos\left(d x + c\right)^{2} + 2165 \, \cos\left(d x + c\right) + 496\right)} \sin\left(d x + c\right)}{63 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"-1/63*(315*d*x*cos(d*x + c)^5 + 1575*d*x*cos(d*x + c)^4 + 3150*d*x*cos(d*x + c)^3 + 3150*d*x*cos(d*x + c)^2 + 1575*d*x*cos(d*x + c) + 315*d*x - (63*cos(d*x + c)^5 + 946*cos(d*x + c)^4 + 2840*cos(d*x + c)^3 + 3633*cos(d*x + c)^2 + 2165*cos(d*x + c) + 496)*sin(d*x + c))/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
84,1,188,0,0.706428," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{315 \, d x \cos\left(d x + c\right)^{5} + 1575 \, d x \cos\left(d x + c\right)^{4} + 3150 \, d x \cos\left(d x + c\right)^{3} + 3150 \, d x \cos\left(d x + c\right)^{2} + 1575 \, d x \cos\left(d x + c\right) + 315 \, d x - {\left(863 \, \cos\left(d x + c\right)^{4} + 2740 \, \cos\left(d x + c\right)^{3} + 3549 \, \cos\left(d x + c\right)^{2} + 2125 \, \cos\left(d x + c\right) + 488\right)} \sin\left(d x + c\right)}{315 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/315*(315*d*x*cos(d*x + c)^5 + 1575*d*x*cos(d*x + c)^4 + 3150*d*x*cos(d*x + c)^3 + 3150*d*x*cos(d*x + c)^2 + 1575*d*x*cos(d*x + c) + 315*d*x - (863*cos(d*x + c)^4 + 2740*cos(d*x + c)^3 + 3549*cos(d*x + c)^2 + 2125*cos(d*x + c) + 488)*sin(d*x + c))/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
85,1,123,0,1.022326," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{{\left(83 \, \cos\left(d x + c\right)^{4} + 100 \, \cos\left(d x + c\right)^{3} + 84 \, \cos\left(d x + c\right)^{2} + 40 \, \cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right)}{315 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/315*(83*cos(d*x + c)^4 + 100*cos(d*x + c)^3 + 84*cos(d*x + c)^2 + 40*cos(d*x + c) + 8)*sin(d*x + c)/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
86,1,123,0,0.855415," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{{\left(5 \, \cos\left(d x + c\right)^{4} + 25 \, \cos\left(d x + c\right)^{3} + 21 \, \cos\left(d x + c\right)^{2} + 10 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{63 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/63*(5*cos(d*x + c)^4 + 25*cos(d*x + c)^3 + 21*cos(d*x + c)^2 + 10*cos(d*x + c) + 2)*sin(d*x + c)/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
87,1,123,0,0.726014," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 21 \, \cos\left(d x + c\right)^{2} + 10 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{45 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/45*(2*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 21*cos(d*x + c)^2 + 10*cos(d*x + c) + 2)*sin(d*x + c)/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
88,1,123,0,0.580814," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 21 \, \cos\left(d x + c\right)^{2} + 25 \, \cos\left(d x + c\right) + 5\right)} \sin\left(d x + c\right)}{63 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/63*(2*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 21*cos(d*x + c)^2 + 25*cos(d*x + c) + 5)*sin(d*x + c)/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
89,1,123,0,1.080065," ","integrate(1/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{{\left(8 \, \cos\left(d x + c\right)^{4} + 40 \, \cos\left(d x + c\right)^{3} + 84 \, \cos\left(d x + c\right)^{2} + 100 \, \cos\left(d x + c\right) + 83\right)} \sin\left(d x + c\right)}{315 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/315*(8*cos(d*x + c)^4 + 40*cos(d*x + c)^3 + 84*cos(d*x + c)^2 + 100*cos(d*x + c) + 83)*sin(d*x + c)/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
90,1,246,0,1.244036," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{315 \, {\left(\cos\left(d x + c\right)^{5} + 5 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 315 \, {\left(\cos\left(d x + c\right)^{5} + 5 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right) + 1\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(488 \, \cos\left(d x + c\right)^{4} + 2125 \, \cos\left(d x + c\right)^{3} + 3549 \, \cos\left(d x + c\right)^{2} + 2740 \, \cos\left(d x + c\right) + 863\right)} \sin\left(d x + c\right)}{630 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/630*(315*(cos(d*x + c)^5 + 5*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 10*cos(d*x + c)^2 + 5*cos(d*x + c) + 1)*log(sin(d*x + c) + 1) - 315*(cos(d*x + c)^5 + 5*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 10*cos(d*x + c)^2 + 5*cos(d*x + c) + 1)*log(-sin(d*x + c) + 1) - 2*(488*cos(d*x + c)^4 + 2125*cos(d*x + c)^3 + 3549*cos(d*x + c)^2 + 2740*cos(d*x + c) + 863)*sin(d*x + c))/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
91,1,278,0,1.045171," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","-\frac{315 \, {\left(\cos\left(d x + c\right)^{6} + 5 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 5 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 315 \, {\left(\cos\left(d x + c\right)^{6} + 5 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 5 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(496 \, \cos\left(d x + c\right)^{5} + 2165 \, \cos\left(d x + c\right)^{4} + 3633 \, \cos\left(d x + c\right)^{3} + 2840 \, \cos\left(d x + c\right)^{2} + 946 \, \cos\left(d x + c\right) + 63\right)} \sin\left(d x + c\right)}{126 \, {\left(a^{5} d \cos\left(d x + c\right)^{6} + 5 \, a^{5} d \cos\left(d x + c\right)^{5} + 10 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 5 \, a^{5} d \cos\left(d x + c\right)^{2} + a^{5} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/126*(315*(cos(d*x + c)^6 + 5*cos(d*x + c)^5 + 10*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 5*cos(d*x + c)^2 + cos(d*x + c))*log(sin(d*x + c) + 1) - 315*(cos(d*x + c)^6 + 5*cos(d*x + c)^5 + 10*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 5*cos(d*x + c)^2 + cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(496*cos(d*x + c)^5 + 2165*cos(d*x + c)^4 + 3633*cos(d*x + c)^3 + 2840*cos(d*x + c)^2 + 946*cos(d*x + c) + 63)*sin(d*x + c))/(a^5*d*cos(d*x + c)^6 + 5*a^5*d*cos(d*x + c)^5 + 10*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 5*a^5*d*cos(d*x + c)^2 + a^5*d*cos(d*x + c))","A",0
92,1,294,0,1.143690," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^5,x, algorithm=""fricas"")","\frac{9765 \, {\left(\cos\left(d x + c\right)^{7} + 5 \, \cos\left(d x + c\right)^{6} + 10 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9765 \, {\left(\cos\left(d x + c\right)^{7} + 5 \, \cos\left(d x + c\right)^{6} + 10 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15328 \, \cos\left(d x + c\right)^{6} + 66875 \, \cos\left(d x + c\right)^{5} + 112119 \, \cos\left(d x + c\right)^{4} + 87440 \, \cos\left(d x + c\right)^{3} + 28828 \, \cos\left(d x + c\right)^{2} + 1575 \, \cos\left(d x + c\right) - 315\right)} \sin\left(d x + c\right)}{1260 \, {\left(a^{5} d \cos\left(d x + c\right)^{7} + 5 \, a^{5} d \cos\left(d x + c\right)^{6} + 10 \, a^{5} d \cos\left(d x + c\right)^{5} + 10 \, a^{5} d \cos\left(d x + c\right)^{4} + 5 \, a^{5} d \cos\left(d x + c\right)^{3} + a^{5} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/1260*(9765*(cos(d*x + c)^7 + 5*cos(d*x + c)^6 + 10*cos(d*x + c)^5 + 10*cos(d*x + c)^4 + 5*cos(d*x + c)^3 + cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 9765*(cos(d*x + c)^7 + 5*cos(d*x + c)^6 + 10*cos(d*x + c)^5 + 10*cos(d*x + c)^4 + 5*cos(d*x + c)^3 + cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(15328*cos(d*x + c)^6 + 66875*cos(d*x + c)^5 + 112119*cos(d*x + c)^4 + 87440*cos(d*x + c)^3 + 28828*cos(d*x + c)^2 + 1575*cos(d*x + c) - 315)*sin(d*x + c))/(a^5*d*cos(d*x + c)^7 + 5*a^5*d*cos(d*x + c)^6 + 10*a^5*d*cos(d*x + c)^5 + 10*a^5*d*cos(d*x + c)^4 + 5*a^5*d*cos(d*x + c)^3 + a^5*d*cos(d*x + c)^2)","A",0
93,1,147,0,0.801219," ","integrate(cos(d*x+c)^5/(a+a*cos(d*x+c))^6,x, algorithm=""fricas"")","\frac{{\left(146 \, \cos\left(d x + c\right)^{5} + 183 \, \cos\left(d x + c\right)^{4} + 184 \, \cos\left(d x + c\right)^{3} + 124 \, \cos\left(d x + c\right)^{2} + 48 \, \cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right)}{693 \, {\left(a^{6} d \cos\left(d x + c\right)^{6} + 6 \, a^{6} d \cos\left(d x + c\right)^{5} + 15 \, a^{6} d \cos\left(d x + c\right)^{4} + 20 \, a^{6} d \cos\left(d x + c\right)^{3} + 15 \, a^{6} d \cos\left(d x + c\right)^{2} + 6 \, a^{6} d \cos\left(d x + c\right) + a^{6} d\right)}}"," ",0,"1/693*(146*cos(d*x + c)^5 + 183*cos(d*x + c)^4 + 184*cos(d*x + c)^3 + 124*cos(d*x + c)^2 + 48*cos(d*x + c) + 8)*sin(d*x + c)/(a^6*d*cos(d*x + c)^6 + 6*a^6*d*cos(d*x + c)^5 + 15*a^6*d*cos(d*x + c)^4 + 20*a^6*d*cos(d*x + c)^3 + 15*a^6*d*cos(d*x + c)^2 + 6*a^6*d*cos(d*x + c) + a^6*d)","A",0
94,1,147,0,0.843014," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^6,x, algorithm=""fricas"")","\frac{{\left(61 \, \cos\left(d x + c\right)^{5} + 366 \, \cos\left(d x + c\right)^{4} + 368 \, \cos\left(d x + c\right)^{3} + 248 \, \cos\left(d x + c\right)^{2} + 96 \, \cos\left(d x + c\right) + 16\right)} \sin\left(d x + c\right)}{1155 \, {\left(a^{6} d \cos\left(d x + c\right)^{6} + 6 \, a^{6} d \cos\left(d x + c\right)^{5} + 15 \, a^{6} d \cos\left(d x + c\right)^{4} + 20 \, a^{6} d \cos\left(d x + c\right)^{3} + 15 \, a^{6} d \cos\left(d x + c\right)^{2} + 6 \, a^{6} d \cos\left(d x + c\right) + a^{6} d\right)}}"," ",0,"1/1155*(61*cos(d*x + c)^5 + 366*cos(d*x + c)^4 + 368*cos(d*x + c)^3 + 248*cos(d*x + c)^2 + 96*cos(d*x + c) + 16)*sin(d*x + c)/(a^6*d*cos(d*x + c)^6 + 6*a^6*d*cos(d*x + c)^5 + 15*a^6*d*cos(d*x + c)^4 + 20*a^6*d*cos(d*x + c)^3 + 15*a^6*d*cos(d*x + c)^2 + 6*a^6*d*cos(d*x + c) + a^6*d)","A",0
95,1,72,0,0.721567," ","integrate(cos(d*x+c)^4*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{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)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*cos(d*x + c)^4 + 40*cos(d*x + c)^3 + 48*cos(d*x + c)^2 + 64*cos(d*x + c) + 128)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
96,1,62,0,0.681744," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{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)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{35 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/35*(5*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 8*cos(d*x + c) + 16)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
97,1,52,0,0.816202," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(3 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/15*sqrt(a*cos(d*x + c) + a)*(3*cos(d*x + c)^2 + 4*cos(d*x + c) + 8)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
98,1,40,0,1.129200," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/3*sqrt(a*cos(d*x + c) + a)*(cos(d*x + c) + 2)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
99,1,32,0,1.043981," ","integrate((a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"2*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
100,1,146,0,1.019326," ","integrate((a+a*cos(d*x+c))^(1/2)*sec(d*x+c),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, d}, \frac{\sqrt{-a} \arctan\left(\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{-a} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{d}\right]"," ",0,"[1/2*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2))/d, sqrt(-a)*arctan(2*sqrt(a*cos(d*x + c) + a)*sqrt(-a)*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a))/d]","A",0
101,1,140,0,1.278525," ","integrate((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(\cos\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)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","B",0
102,1,155,0,1.154639," ","integrate((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(3*(cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*(3*cos(d*x + c) + 2)*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
103,1,165,0,0.743183," ","integrate((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{15 \, {\left(\cos\left(d x + c\right)^{4} + \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(15 \, \cos\left(d x + c\right)^{2} + 10 \, \cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(15*(cos(d*x + c)^4 + cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*(15*cos(d*x + c)^2 + 10*cos(d*x + c) + 8)*sin(d*x + c))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
104,1,78,0,1.544854," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a \cos\left(d x + c\right)^{4} + 85 \, a \cos\left(d x + c\right)^{3} + 102 \, a \cos\left(d x + c\right)^{2} + 136 \, a \cos\left(d x + c\right) + 272 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*a*cos(d*x + c)^4 + 85*a*cos(d*x + c)^3 + 102*a*cos(d*x + c)^2 + 136*a*cos(d*x + c) + 272*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
105,1,67,0,0.989617," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, a \cos\left(d x + c\right)^{3} + 39 \, a \cos\left(d x + c\right)^{2} + 52 \, a \cos\left(d x + c\right) + 104 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/105*(15*a*cos(d*x + c)^3 + 39*a*cos(d*x + c)^2 + 52*a*cos(d*x + c) + 104*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
106,1,55,0,0.589054," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a \cos\left(d x + c\right)^{2} + 3 \, a \cos\left(d x + c\right) + 6 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{5 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/5*(a*cos(d*x + c)^2 + 3*a*cos(d*x + c) + 6*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
107,1,44,0,0.967770," ","integrate((a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a \cos\left(d x + c\right) + 5 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/3*(a*cos(d*x + c) + 5*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
108,1,127,0,1.683152," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} a \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/2*((a*cos(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*a*sin(d*x + c))/(d*cos(d*x + c) + d)","B",0
109,1,146,0,1.044891," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} a \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(3*(a*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*a*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","B",0
110,1,162,0,1.891862," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{7 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(7 \, a \cos\left(d x + c\right) + 2 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(7*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(7*a*cos(d*x + c) + 2*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
111,1,173,0,0.883012," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{33 \, {\left(a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(33 \, a \cos\left(d x + c\right)^{2} + 22 \, a \cos\left(d x + c\right) + 8 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(33*(a*cos(d*x + c)^4 + a*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(33*a*cos(d*x + c)^2 + 22*a*cos(d*x + c) + 8*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
112,1,101,0,0.981496," ","integrate(cos(d*x+c)^3*(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, a^{2} \cos\left(d x + c\right)^{5} + 224 \, a^{2} \cos\left(d x + c\right)^{4} + 355 \, a^{2} \cos\left(d x + c\right)^{3} + 426 \, a^{2} \cos\left(d x + c\right)^{2} + 568 \, a^{2} \cos\left(d x + c\right) + 1136 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{693 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/693*(63*a^2*cos(d*x + c)^5 + 224*a^2*cos(d*x + c)^4 + 355*a^2*cos(d*x + c)^3 + 426*a^2*cos(d*x + c)^2 + 568*a^2*cos(d*x + c) + 1136*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
113,1,88,0,0.732095," ","integrate(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a^{2} \cos\left(d x + c\right)^{4} + 130 \, a^{2} \cos\left(d x + c\right)^{3} + 219 \, a^{2} \cos\left(d x + c\right)^{2} + 292 \, a^{2} \cos\left(d x + c\right) + 584 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*a^2*cos(d*x + c)^4 + 130*a^2*cos(d*x + c)^3 + 219*a^2*cos(d*x + c)^2 + 292*a^2*cos(d*x + c) + 584*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
114,1,75,0,0.604666," ","integrate(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{3} + 12 \, a^{2} \cos\left(d x + c\right)^{2} + 23 \, a^{2} \cos\left(d x + c\right) + 46 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{21 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/21*(3*a^2*cos(d*x + c)^3 + 12*a^2*cos(d*x + c)^2 + 23*a^2*cos(d*x + c) + 46*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
115,1,62,0,0.920044," ","integrate((a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{2} + 14 \, a^{2} \cos\left(d x + c\right) + 43 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/15*(3*a^2*cos(d*x + c)^2 + 14*a^2*cos(d*x + c) + 43*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
116,1,147,0,1.223086," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(a^{2} \cos\left(d x + c\right) + 8 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/6*(3*(a^2*cos(d*x + c) + a^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(a^2*cos(d*x + c) + 8*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
117,1,164,0,1.199024," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{5 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(5*(a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(2*a^2*cos(d*x + c) + a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
118,1,170,0,0.674985," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{19 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(11 \, a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(19*(a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(11*a^2*cos(d*x + c) + 2*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
119,1,183,0,0.962589," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{75 \, {\left(a^{2} \cos\left(d x + c\right)^{4} + a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(75 \, a^{2} \cos\left(d x + c\right)^{2} + 34 \, a^{2} \cos\left(d x + c\right) + 8 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(75*(a^2*cos(d*x + c)^4 + a^2*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(75*a^2*cos(d*x + c)^2 + 34*a^2*cos(d*x + c) + 8*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
120,1,196,0,1.474502," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{489 \, {\left(a^{2} \cos\left(d x + c\right)^{5} + a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, {\left(489 \, a^{2} \cos\left(d x + c\right)^{3} + 326 \, a^{2} \cos\left(d x + c\right)^{2} + 184 \, a^{2} \cos\left(d x + c\right) + 48 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{768 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/768*(489*(a^2*cos(d*x + c)^5 + a^2*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(489*a^2*cos(d*x + c)^3 + 326*a^2*cos(d*x + c)^2 + 184*a^2*cos(d*x + c) + 48*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
121,1,75,0,0.700777," ","integrate((a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a^{3} \cos\left(d x + c\right)^{3} + 27 \, a^{3} \cos\left(d x + c\right)^{2} + 71 \, a^{3} \cos\left(d x + c\right) + 177 \, a^{3}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{35 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/35*(5*a^3*cos(d*x + c)^3 + 27*a^3*cos(d*x + c)^2 + 71*a^3*cos(d*x + c) + 177*a^3)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
122,1,153,0,1.293299," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(15 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} + 31 \, \cos\left(d x + c\right) - 43\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right) + \frac{105 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{210 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/210*(4*(15*cos(d*x + c)^3 - 3*cos(d*x + c)^2 + 31*cos(d*x + c) - 43)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c) + 105*sqrt(2)*(a*cos(d*x + c) + a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
123,1,143,0,0.680207," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(3 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 13\right)} \sin\left(d x + c\right) + \frac{15 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{30 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/30*(4*sqrt(a*cos(d*x + c) + a)*(3*cos(d*x + c)^2 - cos(d*x + c) + 13)*sin(d*x + c) + 15*sqrt(2)*(a*cos(d*x + c) + a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
124,1,131,0,1.144886," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + \frac{3 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/6*(4*sqrt(a*cos(d*x + c) + a)*(cos(d*x + c) - 1)*sin(d*x + c) + 3*sqrt(2)*(a*cos(d*x + c) + a)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
125,1,122,0,1.307541," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(sqrt(2)*(a*cos(d*x + c) + a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a) + 4*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
126,1,126,0,0.883485," ","integrate(1/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{2 \, \sqrt{a} d}, -\frac{\sqrt{2} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{-\frac{1}{a}}}{\sin\left(d x + c\right)}\right)}{d}\right]"," ",0,"[1/2*sqrt(2)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/(sqrt(a)*d), -sqrt(2)*sqrt(-1/a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(-1/a)/sin(d*x + c))/d]","A",0
127,1,164,0,0.734371," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, a d}"," ",0,"1/2*(sqrt(2)*sqrt(a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a*d)","B",0
128,1,236,0,0.899433," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\cos\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)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{2 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{4 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 2*sqrt(2)*(a*cos(d*x + c)^2 + a*cos(d*x + c))*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a) + 4*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","B",0
129,1,251,0,0.799949," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{7 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{8 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{16 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(7*(cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*sqrt(a*cos(d*x + c) + a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*sqrt(2)*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","B",0
130,1,263,0,0.848504," ","integrate(sec(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{27 \, {\left(\cos\left(d x + c\right)^{4} + \cos\left(d x + c\right)^{3}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(21 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 8\right)} \sin\left(d x + c\right) + \frac{48 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{\sqrt{a}}}{96 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/96*(27*(cos(d*x + c)^4 + cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*(21*cos(d*x + c)^2 - 2*cos(d*x + c) + 8)*sin(d*x + c) + 48*sqrt(2)*(a*cos(d*x + c)^4 + a*cos(d*x + c)^3)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/sqrt(a))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
131,1,184,0,0.979471," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{75 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left(4 \, \cos\left(d x + c\right)^{3} - 4 \, \cos\left(d x + c\right)^{2} + 36 \, \cos\left(d x + c\right) + 49\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{40 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/40*(75*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(4*cos(d*x + c)^3 - 4*cos(d*x + c)^2 + 36*cos(d*x + c) + 49)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
132,1,174,0,0.680025," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{33 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(4 \, \cos\left(d x + c\right)^{2} - 12 \, \cos\left(d x + c\right) - 19\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/24*(33*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt(a*cos(d*x + c) + a)*(4*cos(d*x + c)^2 - 12*cos(d*x + c) - 19)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
133,1,164,0,0.704545," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{7 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(4 \, \cos\left(d x + c\right) + 5\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/8*(7*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt(a*cos(d*x + c) + a)*(4*cos(d*x + c) + 5)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
134,1,154,0,0.877459," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/8*(3*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","B",0
135,1,153,0,1.782979," ","integrate(1/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/8*(sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","B",0
136,1,254,0,1.537237," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/8*(5*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","B",0
137,1,286,0,1.212193," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{9 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\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 \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 6 \, {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\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)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"1/8*(9*sqrt(2)*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 6*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*(3*cos(d*x + c) + 2)*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","B",0
138,1,302,0,1.625224," ","integrate(sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{26 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 19 \, {\left(\cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(7 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(26*sqrt(2)*(cos(d*x + c)^4 + 2*cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 19*(cos(d*x + c)^4 + 2*cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*sqrt(a*cos(d*x + c) + a)*(7*cos(d*x + c)^2 + 3*cos(d*x + c) - 2)*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
139,1,208,0,0.833721," ","integrate(cos(d*x+c)^4/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{489 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left(32 \, \cos\left(d x + c\right)^{3} - 160 \, \cos\left(d x + c\right)^{2} - 503 \, \cos\left(d x + c\right) - 299\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{192 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/192*(489*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(32*cos(d*x + c)^3 - 160*cos(d*x + c)^2 - 503*cos(d*x + c) - 299)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
140,1,198,0,1.119966," ","integrate(cos(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{75 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(32 \, \cos\left(d x + c\right)^{2} + 85 \, \cos\left(d x + c\right) + 49\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/64*(75*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt(a*cos(d*x + c) + a)*(32*cos(d*x + c)^2 + 85*cos(d*x + c) + 49)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
141,1,188,0,1.044283," ","integrate(cos(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{19 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(13 \, \cos\left(d x + c\right) + 9\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/64*(19*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*sqrt(a*cos(d*x + c) + a)*(13*cos(d*x + c) + 9)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
142,1,188,0,1.015431," ","integrate(cos(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(5 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/64*(5*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt(a*cos(d*x + c) + a)*(5*cos(d*x + c) + 1)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
143,1,188,0,1.195900," ","integrate(1/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(3 \, \cos\left(d x + c\right) + 7\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/64*(3*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt(a*cos(d*x + c) + a)*(3*cos(d*x + c) + 7)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
144,1,298,0,1.061863," ","integrate(sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{43 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(-\frac{a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 32 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(11 \, \cos\left(d x + c\right) + 15\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/64*(43*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*log(-(a*cos(d*x + c)^2 + 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 32*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*sqrt(a*cos(d*x + c) + a)*(11*cos(d*x + c) + 15)*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
145,1,330,0,1.985281," ","integrate(sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{115 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\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 \cos\left(d x + c\right) + a} \sqrt{a} \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - 3 \, a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 80 \, {\left(\cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\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)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(35 \, \cos\left(d x + c\right)^{2} + 55 \, \cos\left(d x + c\right) + 16\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"1/64*(115*sqrt(2)*(cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*log(-(a*cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 80*(cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*sqrt(a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) - 2)*sin(d*x + c) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt(a*cos(d*x + c) + a)*(35*cos(d*x + c)^2 + 55*cos(d*x + c) + 16)*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","B",0
146,0,0,0,0.852479," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
147,0,0,0,5.957852," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
148,0,0,0,0.984049," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
149,0,0,0,1.974897," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \cos\left(d x + c\right) + a}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
150,0,0,0,1.100608," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
151,0,0,0,1.869468," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
152,0,0,0,1.165672," ","integrate((a+a*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
153,0,0,0,2.067294," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
154,0,0,0,1.661628," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{3} + 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^3 + 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
155,0,0,0,0.823425," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sqrt(cos(d*x + c)), x)","F",0
156,0,0,0,2.031683," ","integrate((a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)/sqrt(cos(d*x + c)), x)","F",0
157,0,0,0,0.912748," ","integrate((a+a*cos(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)/cos(d*x + c)^(3/2), x)","F",0
158,0,0,0,0.875763," ","integrate((a+a*cos(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)/cos(d*x + c)^(5/2), x)","F",0
159,0,0,0,0.918468," ","integrate((a+a*cos(d*x+c))^2/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)/cos(d*x + c)^(7/2), x)","F",0
160,0,0,0,1.277483," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
161,0,0,0,0.546367," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sqrt(cos(d*x + c)), x)","F",0
162,0,0,0,1.406908," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)/sqrt(cos(d*x + c)), x)","F",0
163,0,0,0,0.752787," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^(3/2), x)","F",0
164,0,0,0,1.924211," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^(5/2), x)","F",0
165,0,0,0,2.021842," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^(7/2), x)","F",0
166,0,0,0,1.096512," ","integrate((a+a*cos(d*x+c))^3/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)/cos(d*x + c)^(9/2), x)","F",0
167,0,0,0,1.959162," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{5} + 4 \, a^{4} \cos\left(d x + c\right)^{4} + 6 \, a^{4} \cos\left(d x + c\right)^{3} + 4 \, a^{4} \cos\left(d x + c\right)^{2} + a^{4} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^5 + 4*a^4*cos(d*x + c)^4 + 6*a^4*cos(d*x + c)^3 + 4*a^4*cos(d*x + c)^2 + a^4*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
168,0,0,0,0.656307," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)*sqrt(cos(d*x + c)), x)","F",0
169,0,0,0,1.055844," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)/sqrt(cos(d*x + c)), x)","F",0
170,0,0,0,0.900624," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)/cos(d*x + c)^(3/2), x)","F",0
171,0,0,0,2.742801," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)/cos(d*x + c)^(5/2), x)","F",0
172,0,0,0,1.763500," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)/cos(d*x + c)^(7/2), x)","F",0
173,0,0,0,1.284156," ","integrate((a+a*cos(d*x+c))^4/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)/cos(d*x + c)^(9/2), x)","F",0
174,0,0,0,0.869350," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^(7/2)/(a*cos(d*x + c) + a), x)","F",0
175,0,0,0,1.138348," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
176,0,0,0,1.499306," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
177,0,0,0,0.992632," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
178,0,0,0,1.223698," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
179,0,0,0,0.919112," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*cos(d*x + c)^3 + a*cos(d*x + c)^2), x)","F",0
180,0,0,0,0.622519," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*cos(d*x + c)^4 + a*cos(d*x + c)^3), x)","F",0
181,0,0,0,1.165086," ","integrate(cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{9}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(cos(d*x + c)^(9/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
182,0,0,0,2.627120," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(cos(d*x + c)^(7/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
183,0,0,0,0.666932," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(cos(d*x + c)^(5/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
184,0,0,0,0.982809," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
185,0,0,0,0.965583," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
186,0,0,0,2.005987," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{3} + 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^3 + 2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c)), x)","F",0
187,0,0,0,0.906253," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{4} + 2 \, a^{2} \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^4 + 2*a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2), x)","F",0
188,0,0,0,1.031546," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{5} + 2 \, a^{2} \cos\left(d x + c\right)^{4} + a^{2} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^5 + 2*a^2*cos(d*x + c)^4 + a^2*cos(d*x + c)^3), x)","F",0
189,0,0,0,1.105520," ","integrate(cos(d*x+c)^(11/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{11}{2}}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(cos(d*x + c)^(11/2)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
190,0,0,0,1.643323," ","integrate(cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{9}{2}}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(cos(d*x + c)^(9/2)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
191,0,0,0,1.038048," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(cos(d*x + c)^(7/2)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
192,0,0,0,0.675326," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(cos(d*x + c)^(5/2)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
193,0,0,0,0.557683," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
194,0,0,0,1.797580," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
195,0,0,0,1.418808," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c)), x)","F",0
196,0,0,0,1.325801," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{5} + 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^5 + 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2), x)","F",0
197,0,0,0,2.880767," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{6} + 3 \, a^{3} \cos\left(d x + c\right)^{5} + 3 \, a^{3} \cos\left(d x + c\right)^{4} + a^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^6 + 3*a^3*cos(d*x + c)^5 + 3*a^3*cos(d*x + c)^4 + a^3*cos(d*x + c)^3), x)","F",0
198,1,108,0,0.981710," ","integrate(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} {\left(8 \, \cos\left(d x + c\right)^{2} + 10 \, \cos\left(d x + c\right) + 15\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 15 \, \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/24*(sqrt(a*cos(d*x + c) + a)*(8*cos(d*x + c)^2 + 10*cos(d*x + c) + 15)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
199,1,98,0,1.745001," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right) + 3\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/4*(sqrt(a*cos(d*x + c) + a)*(2*cos(d*x + c) + 3)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
200,1,88,0,0.890884," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"-(sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
201,1,119,0,1.966968," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{-a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right)}{d}, -\frac{2 \, \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d}\right]"," ",0,"[sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(a*cos(d*x + c) + a)*sqrt(-a)*sqrt(cos(d*x + c))*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1))/d, -2*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/d]","A",0
202,1,49,0,0.789760," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)}"," ",0,"2*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
203,1,61,0,0.899209," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"2/3*sqrt(a*cos(d*x + c) + a)*(2*cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
204,1,71,0,1.074323," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(8 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 3\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/15*sqrt(a*cos(d*x + c) + a)*(8*cos(d*x + c)^2 + 4*cos(d*x + c) + 3)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
205,1,81,0,0.993511," ","integrate((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, \cos\left(d x + c\right)^{3} + 8 \, \cos\left(d x + c\right)^{2} + 6 \, \cos\left(d x + c\right) + 5\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{35 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/35*(16*cos(d*x + c)^3 + 8*cos(d*x + c)^2 + 6*cos(d*x + c) + 5)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
206,1,114,0,2.230244," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(8 \, a \cos\left(d x + c\right)^{2} + 22 \, a \cos\left(d x + c\right) + 33 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 33 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/24*((8*a*cos(d*x + c)^2 + 22*a*cos(d*x + c) + 33*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 33*(a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
207,1,103,0,1.045430," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a \cos\left(d x + c\right) + 7 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/4*((2*a*cos(d*x + c) + 7*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*(a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
208,1,90,0,1.121757," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} a \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d \cos\left(d x + c\right) + d}"," ",0,"(sqrt(a*cos(d*x + c) + a)*a*sqrt(cos(d*x + c))*sin(d*x + c) - 3*(a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
209,1,109,0,1.411250," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{a \cos\left(d x + c\right) + a} a \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)\right)}}{d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)}"," ",0,"2*(sqrt(a*cos(d*x + c) + a)*a*sqrt(cos(d*x + c))*sin(d*x + c) - (a*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
210,1,62,0,5.661182," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a \cos\left(d x + c\right) + a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"2/3*(5*a*cos(d*x + c) + a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
211,1,73,0,2.163755," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, a \cos\left(d x + c\right)^{2} + 3 \, a \cos\left(d x + c\right) + a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{5 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/5*(6*a*cos(d*x + c)^2 + 3*a*cos(d*x + c) + a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
212,1,86,0,0.979997," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(104 \, a \cos\left(d x + c\right)^{3} + 52 \, a \cos\left(d x + c\right)^{2} + 39 \, a \cos\left(d x + c\right) + 15 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/105*(104*a*cos(d*x + c)^3 + 52*a*cos(d*x + c)^2 + 39*a*cos(d*x + c) + 15*a)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
213,1,137,0,2.615600," ","integrate(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(48 \, a^{2} \cos\left(d x + c\right)^{3} + 184 \, a^{2} \cos\left(d x + c\right)^{2} + 326 \, a^{2} \cos\left(d x + c\right) + 489 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 489 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/192*((48*a^2*cos(d*x + c)^3 + 184*a^2*cos(d*x + c)^2 + 326*a^2*cos(d*x + c) + 489*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 489*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
214,1,124,0,1.769629," ","integrate(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(8 \, a^{2} \cos\left(d x + c\right)^{2} + 34 \, a^{2} \cos\left(d x + c\right) + 75 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 75 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/24*((8*a^2*cos(d*x + c)^2 + 34*a^2*cos(d*x + c) + 75*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 75*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
215,1,111,0,2.009092," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} \cos\left(d x + c\right) + 11 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 19 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/4*((2*a^2*cos(d*x + c) + 11*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 19*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
216,1,127,0,1.033486," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 5 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)}"," ",0,"((a^2*cos(d*x + c) + 2*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 5*(a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
217,1,131,0,2.380634," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(8 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)\right)}}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"2/3*((8*a^2*cos(d*x + c) + a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*(a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
218,1,81,0,1.012600," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(43 \, a^{2} \cos\left(d x + c\right)^{2} + 14 \, a^{2} \cos\left(d x + c\right) + 3 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"2/15*(43*a^2*cos(d*x + c)^2 + 14*a^2*cos(d*x + c) + 3*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
219,1,94,0,3.810759," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(46 \, a^{2} \cos\left(d x + c\right)^{3} + 23 \, a^{2} \cos\left(d x + c\right)^{2} + 12 \, a^{2} \cos\left(d x + c\right) + 3 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{21 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"2/21*(46*a^2*cos(d*x + c)^3 + 23*a^2*cos(d*x + c)^2 + 12*a^2*cos(d*x + c) + 3*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
220,1,107,0,1.937092," ","integrate((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(584 \, a^{2} \cos\left(d x + c\right)^{4} + 292 \, a^{2} \cos\left(d x + c\right)^{3} + 219 \, a^{2} \cos\left(d x + c\right)^{2} + 130 \, a^{2} \cos\left(d x + c\right) + 35 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"2/315*(584*a^2*cos(d*x + c)^4 + 292*a^2*cos(d*x + c)^3 + 219*a^2*cos(d*x + c)^2 + 130*a^2*cos(d*x + c) + 35*a^2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^6 + d*cos(d*x + c)^5)","A",0
221,1,50,0,1.097398," ","integrate((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/4),x, algorithm=""fricas"")","\frac{4 \, \sqrt{a \cos\left(d x + c\right) + a} a \cos\left(d x + c\right)^{\frac{3}{4}} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)}"," ",0,"4*sqrt(a*cos(d*x + c) + a)*a*cos(d*x + c)^(3/4)*sin(d*x + c)/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
222,1,119,0,1.140530," ","integrate((a+a*cos(f*x+e))^(1/2)/cos(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{a \cos\left(f x + e\right) + a} \sqrt{-a} \sqrt{\cos\left(f x + e\right)} \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{f}, -\frac{2 \, \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(f x + e\right) + a} \sqrt{\cos\left(f x + e\right)}}{\sqrt{a} \sin\left(f x + e\right)}\right)}{f}\right]"," ",0,"[sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(a*cos(f*x + e) + a)*sqrt(-a)*sqrt(cos(f*x + e))*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1))/f, -2*sqrt(a)*arctan(sqrt(a*cos(f*x + e) + a)*sqrt(cos(f*x + e))/(sqrt(a)*sin(f*x + e)))/f]","A",0
223,1,164,0,0.838387," ","integrate((a-a*cos(f*x+e))^(1/2)/(-cos(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} \log\left(\frac{4 \, \sqrt{-a \cos\left(f x + e\right) + a} {\left(2 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) + 1\right)} \sqrt{-a} \sqrt{-\cos\left(f x + e\right)} - {\left(8 \, a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) + a\right)} \sin\left(f x + e\right)}{\sin\left(f x + e\right)}\right)}{2 \, f}, \frac{\sqrt{a} \arctan\left(\frac{\sqrt{-a \cos\left(f x + e\right) + a} \sqrt{-\cos\left(f x + e\right)} {\left(2 \, \cos\left(f x + e\right) + 1\right)}}{2 \, \sqrt{a} \cos\left(f x + e\right) \sin\left(f x + e\right)}\right)}{f}\right]"," ",0,"[1/2*sqrt(-a)*log((4*sqrt(-a*cos(f*x + e) + a)*(2*cos(f*x + e)^2 + 3*cos(f*x + e) + 1)*sqrt(-a)*sqrt(-cos(f*x + e)) - (8*a*cos(f*x + e)^2 + 8*a*cos(f*x + e) + a)*sin(f*x + e))/sin(f*x + e))/f, sqrt(a)*arctan(1/2*sqrt(-a*cos(f*x + e) + a)*sqrt(-cos(f*x + e))*(2*cos(f*x + e) + 1)/(sqrt(a)*cos(f*x + e)*sin(f*x + e)))/f]","A",0
224,1,155,0,1.700138," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right) - 1\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{4 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{4 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}"," ",0,"1/4*(sqrt(a*cos(d*x + c) + a)*(2*cos(d*x + c) - 1)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 4*sqrt(2)*(a*cos(d*x + c) + a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)","A",0
225,1,143,0,1.177150," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"(sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - sqrt(2)*(a*cos(d*x + c) + a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
226,1,89,0,1.102472," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{a d}"," ",0,"(sqrt(2)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a*d)","A",0
227,1,159,0,1.028173," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{2 \, d}, \frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a}}\right)}{\sqrt{a} d}\right]"," ",0,"[1/2*sqrt(2)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(-1/a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*cos(d*x + c)^2 - 2*cos(d*x + c) + 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/d, sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)))/(sqrt(a)*d)]","A",0
228,1,132,0,1.119437," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\frac{\sqrt{2} {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a}}\right)}{\sqrt{a}} - 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)}"," ",0,"-(sqrt(2)*(a*cos(d*x + c)^2 + a*cos(d*x + c))*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)))/sqrt(a) - 2*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
229,1,145,0,2.211953," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - 1\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{3 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a}}\right)}{\sqrt{a}}}{3 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/3*(2*sqrt(a*cos(d*x + c) + a)*(cos(d*x + c) - 1)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*sqrt(2)*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)))/sqrt(a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
230,1,157,0,2.008352," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(13 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 3\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \frac{15 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a}}\right)}{\sqrt{a}}}{15 \, {\left(a d \cos\left(d x + c\right)^{4} + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/15*(2*sqrt(a*cos(d*x + c) + a)*(13*cos(d*x + c)^2 - cos(d*x + c) + 3)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*sqrt(2)*(a*cos(d*x + c)^4 + a*cos(d*x + c)^3)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c)/((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)))/sqrt(a))/(a*d*cos(d*x + c)^4 + a*d*cos(d*x + c)^3)","A",0
231,1,135,0,1.986339," ","integrate(cos(d*x+c)^(5/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(d x + c\right) - 1\right)} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 4 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - 7 \, {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/4*((2*cos(d*x + c) - 1)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c) + 4*(sqrt(2)*cos(d*x + c) + sqrt(2))*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) - 7*(cos(d*x + c) + 1)*arctan(sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)))/(d*cos(d*x + c) + d)","A",0
232,1,125,0,1.473727," ","integrate(cos(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"-((sqrt(2)*cos(d*x + c) + sqrt(2))*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) - (cos(d*x + c) + 1)*arctan(sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) - sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
233,1,70,0,0.882891," ","integrate(cos(d*x+c)^(1/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - 2 \, \arctan\left(\frac{\sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right)}{d}"," ",0,"(sqrt(2)*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*arctan(sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)))/d","A",0
234,1,54,0,0.661419," ","integrate(1/cos(d*x+c)^(1/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)}}\right)}{d}"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c)/(cos(d*x + c)^2 + cos(d*x + c)))/d","B",0
235,1,121,0,2.125844," ","integrate(1/cos(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(\sqrt{2} \cos\left(d x + c\right)^{2} + \sqrt{2} \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)}"," ",0,"-((sqrt(2)*cos(d*x + c)^2 + sqrt(2)*cos(d*x + c))*arctan(1/2*sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c)/(cos(d*x + c)^2 + cos(d*x + c))) - 2*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","B",0
236,1,134,0,3.607585," ","integrate(1/cos(d*x+c)^(5/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\cos\left(d x + c\right) + 1} {\left(\cos\left(d x + c\right) - 1\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left(\sqrt{2} \cos\left(d x + c\right)^{3} + \sqrt{2} \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)}}\right)}{3 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/3*(2*sqrt(cos(d*x + c) + 1)*(cos(d*x + c) - 1)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*(sqrt(2)*cos(d*x + c)^3 + sqrt(2)*cos(d*x + c)^2)*arctan(1/2*sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c)/(cos(d*x + c)^2 + cos(d*x + c))))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
237,1,146,0,2.244191," ","integrate(1/cos(d*x+c)^(7/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(13 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 3\right)} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 15 \, {\left(\sqrt{2} \cos\left(d x + c\right)^{4} + \sqrt{2} \cos\left(d x + c\right)^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)}}\right)}{15 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/15*(2*(13*cos(d*x + c)^2 - cos(d*x + c) + 3)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c) - 15*(sqrt(2)*cos(d*x + c)^4 + sqrt(2)*cos(d*x + c)^3)*arctan(1/2*sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c)/(cos(d*x + c)^2 + cos(d*x + c))))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
238,1,192,0,1.740927," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{9 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right) + 3\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 12 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/4*(9*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(2*cos(d*x + c) + 3)*sqrt(cos(d*x + c))*sin(d*x + c) - 12*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
239,1,182,0,1.828371," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 8 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(5*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 8*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
240,1,145,0,3.327291," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
241,1,146,0,1.142875," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(3*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
242,1,171,0,1.189747," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{7 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(5 \, \cos\left(d x + c\right) + 4\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/4*(7*sqrt(2)*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(5*cos(d*x + c) + 4)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","A",0
243,1,185,0,1.266154," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{33 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(19 \, \cos\left(d x + c\right)^{2} + 12 \, \cos\left(d x + c\right) - 4\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*(33*sqrt(2)*(cos(d*x + c)^4 + 2*cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(19*cos(d*x + c)^2 + 12*cos(d*x + c) - 4)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^4 + 2*a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2)","A",0
244,1,236,0,1.780444," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{115 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(16 \, \cos\left(d x + c\right)^{2} + 55 \, \cos\left(d x + c\right) + 35\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 160 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(115*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(16*cos(d*x + c)^2 + 55*cos(d*x + c) + 35)*sqrt(cos(d*x + c))*sin(d*x + c) - 160*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
245,1,226,0,2.027118," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{43 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(15 \, \cos\left(d x + c\right) + 11\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 64 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(43*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(15*cos(d*x + c) + 11)*sqrt(cos(d*x + c))*sin(d*x + c) - 64*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
246,1,180,0,0.951717," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(7 \, \cos\left(d x + c\right) + 3\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(3*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(7*cos(d*x + c) + 3)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
247,1,178,0,1.232156," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 5\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(5*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(cos(d*x + c) + 5)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
248,1,180,0,1.119143," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{19 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(9 \, \cos\left(d x + c\right) + 13\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(19*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(9*cos(d*x + c) + 13)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
249,1,205,0,2.263080," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{75 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(49 \, \cos\left(d x + c\right)^{2} + 85 \, \cos\left(d x + c\right) + 32\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/32*(75*sqrt(2)*(cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(49*cos(d*x + c)^2 + 85*cos(d*x + c) + 32)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","A",0
250,1,219,0,1.781029," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{489 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} + 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left(299 \, \cos\left(d x + c\right)^{3} + 503 \, \cos\left(d x + c\right)^{2} + 160 \, \cos\left(d x + c\right) - 32\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/96*(489*sqrt(2)*(cos(d*x + c)^5 + 3*cos(d*x + c)^4 + 3*cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*(299*cos(d*x + c)^3 + 503*cos(d*x + c)^2 + 160*cos(d*x + c) - 32)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2)","A",0
251,1,280,0,3.853307," ","integrate(cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{1911 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left(192 \, \cos\left(d x + c\right)^{3} + 1099 \, \cos\left(d x + c\right)^{2} + 1442 \, \cos\left(d x + c\right) + 567\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2688 \, {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(1911*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(192*cos(d*x + c)^3 + 1099*cos(d*x + c)^2 + 1442*cos(d*x + c) + 567)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c) - 2688*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
252,1,270,0,3.503021," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{531 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(247 \, \cos\left(d x + c\right)^{2} + 362 \, \cos\left(d x + c\right) + 147\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 768 \, {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(531*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(247*cos(d*x + c)^2 + 362*cos(d*x + c) + 147)*sqrt(cos(d*x + c))*sin(d*x + c) - 768*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
253,1,214,0,1.429680," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(67 \, \cos\left(d x + c\right)^{2} + 50 \, \cos\left(d x + c\right) + 15\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(15*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(67*cos(d*x + c)^2 + 50*cos(d*x + c) + 15)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
254,1,214,0,1.153778," ","integrate(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{21 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(17 \, \cos\left(d x + c\right)^{2} + 70 \, \cos\left(d x + c\right) + 21\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(21*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(17*cos(d*x + c)^2 + 70*cos(d*x + c) + 21)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
255,1,214,0,1.134872," ","integrate(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{39 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(5 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 39\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(39*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(5*cos(d*x + c)^2 - 2*cos(d*x + c) - 39)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
256,1,214,0,1.162248," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{189 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(103 \, \cos\left(d x + c\right)^{2} + 266 \, \cos\left(d x + c\right) + 195\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(189*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(103*cos(d*x + c)^2 + 266*cos(d*x + c) + 195)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
257,1,239,0,0.999003," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{1089 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} + 4 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left(691 \, \cos\left(d x + c\right)^{3} + 1874 \, \cos\left(d x + c\right)^{2} + 1599 \, \cos\left(d x + c\right) + 384\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + 6 \, a^{4} d \cos\left(d x + c\right)^{3} + 4 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/384*(1089*sqrt(2)*(cos(d*x + c)^5 + 4*cos(d*x + c)^4 + 6*cos(d*x + c)^3 + 4*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*(691*cos(d*x + c)^3 + 1874*cos(d*x + c)^2 + 1599*cos(d*x + c) + 384)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + 6*a^4*d*cos(d*x + c)^3 + 4*a^4*d*cos(d*x + c)^2 + a^4*d*cos(d*x + c))","A",0
258,1,253,0,0.977479," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{3045 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{6} + 4 \, \cos\left(d x + c\right)^{5} + 6 \, \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) - 2 \, {\left(1887 \, \cos\left(d x + c\right)^{4} + 5082 \, \cos\left(d x + c\right)^{3} + 4251 \, \cos\left(d x + c\right)^{2} + 896 \, \cos\left(d x + c\right) - 128\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{6} + 4 \, a^{4} d \cos\left(d x + c\right)^{5} + 6 \, a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + a^{4} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/384*(3045*sqrt(2)*(cos(d*x + c)^6 + 4*cos(d*x + c)^5 + 6*cos(d*x + c)^4 + 4*cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) - 2*(1887*cos(d*x + c)^4 + 5082*cos(d*x + c)^3 + 4251*cos(d*x + c)^2 + 896*cos(d*x + c) - 128)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^4*d*cos(d*x + c)^6 + 4*a^4*d*cos(d*x + c)^5 + 6*a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + a^4*d*cos(d*x + c)^2)","A",0
259,1,248,0,2.031843," ","integrate(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} + 5 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, {\left(853 \, \cos\left(d x + c\right)^{3} + 819 \, \cos\left(d x + c\right)^{2} + 455 \, \cos\left(d x + c\right) + 105\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6144 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/6144*(105*sqrt(2)*(cos(d*x + c)^5 + 5*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 10*cos(d*x + c)^2 + 5*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*(853*cos(d*x + c)^3 + 819*cos(d*x + c)^2 + 455*cos(d*x + c) + 105)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
260,1,248,0,1.139220," ","integrate(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(9/2),x, algorithm=""fricas"")","\frac{45 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} + 5 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)}}\right) + 2 \, {\left(73 \, \cos\left(d x + c\right)^{3} + 351 \, \cos\left(d x + c\right)^{2} + 195 \, \cos\left(d x + c\right) + 45\right)} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2048 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"1/2048*(45*sqrt(2)*(cos(d*x + c)^5 + 5*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 10*cos(d*x + c)^2 + 5*cos(d*x + c) + 1)*sqrt(a)*arctan(1/2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(a)*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 + a*cos(d*x + c))) + 2*(73*cos(d*x + c)^3 + 351*cos(d*x + c)^2 + 195*cos(d*x + c) + 45)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
261,1,31,0,0.805672," ","integrate(1/cos(x)^(1/2)/(1+cos(x))^(1/2),x, algorithm=""fricas"")","\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(x\right) + 1} \sqrt{\cos\left(x\right)} \sin\left(x\right)}{2 \, {\left(\cos\left(x\right)^{2} + \cos\left(x\right)\right)}}\right)"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*sqrt(cos(x) + 1)*sqrt(cos(x))*sin(x)/(cos(x)^2 + cos(x)))","B",0
262,1,105,0,0.967925," ","integrate(1/cos(x)^(1/2)/(a+a*cos(x))^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{2} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{a \cos\left(x\right) + a} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(x\right)} \sin\left(x\right) - 3 \, \cos\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1}{\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\right), \frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(x\right) + a} \sqrt{\cos\left(x\right)} \sin\left(x\right)}{2 \, {\left(\cos\left(x\right)^{2} + \cos\left(x\right)\right)} \sqrt{a}}\right)}{\sqrt{a}}\right]"," ",0,"[1/2*sqrt(2)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt(a*cos(x) + a)*sqrt(-1/a)*sqrt(cos(x))*sin(x) - 3*cos(x)^2 - 2*cos(x) + 1)/(cos(x)^2 + 2*cos(x) + 1)), sqrt(2)*arctan(1/2*sqrt(2)*sqrt(a*cos(x) + a)*sqrt(cos(x))*sin(x)/((cos(x)^2 + cos(x))*sqrt(a)))/sqrt(a)]","A",0
263,1,155,0,0.613123," ","integrate(cos(d*x+c)^(3/2)*(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a} \log\left(\frac{4 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \sqrt{\cos\left(d x + c\right)} - {\left(8 \, a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 4 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 3\right)} \sqrt{\cos\left(d x + c\right)}}{16 \, d \sin\left(d x + c\right)}"," ",0,"1/16*(3*sqrt(a)*log((4*sqrt(-a*cos(d*x + c) + a)*(2*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*sqrt(cos(d*x + c)) - (8*a*cos(d*x + c)^2 + 8*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - 4*sqrt(-a*cos(d*x + c) + a)*(2*cos(d*x + c)^2 - cos(d*x + c) - 3)*sqrt(cos(d*x + c)))/(d*sin(d*x + c))","A",0
264,1,142,0,0.935467," ","integrate(cos(d*x+c)^(1/2)*(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a} \log\left(-\frac{4 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \sqrt{\cos\left(d x + c\right)} + {\left(8 \, a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 4 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{4 \, d \sin\left(d x + c\right)}"," ",0,"1/4*(sqrt(a)*log(-(4*sqrt(-a*cos(d*x + c) + a)*(2*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*sqrt(cos(d*x + c)) + (8*a*cos(d*x + c)^2 + 8*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - 4*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c)))/(d*sin(d*x + c))","A",0
265,1,155,0,0.951293," ","integrate((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{4 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \sqrt{\cos\left(d x + c\right)} - {\left(8 \, a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right)}{2 \, d}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{-a \cos\left(d x + c\right) + a} \sqrt{-a} {\left(2 \, \cos\left(d x + c\right) + 1\right)}}{2 \, a \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}\right)}{d}\right]"," ",0,"[1/2*sqrt(a)*log((4*sqrt(-a*cos(d*x + c) + a)*(2*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*sqrt(cos(d*x + c)) - (8*a*cos(d*x + c)^2 + 8*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))/d, sqrt(-a)*arctan(1/2*sqrt(-a*cos(d*x + c) + a)*sqrt(-a)*(2*cos(d*x + c) + 1)/(a*sqrt(cos(d*x + c))*sin(d*x + c)))/d]","A",0
266,1,42,0,2.316255," ","integrate((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)}}{d \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}"," ",0,"2*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)/(d*sqrt(cos(d*x + c))*sin(d*x + c))","A",0
267,1,52,0,2.979213," ","integrate((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) - 1\right)}}{3 \, d \cos\left(d x + c\right)^{\frac{3}{2}} \sin\left(d x + c\right)}"," ",0,"-2/3*sqrt(-a*cos(d*x + c) + a)*(2*cos(d*x + c)^2 + cos(d*x + c) - 1)/(d*cos(d*x + c)^(3/2)*sin(d*x + c))","A",0
268,1,64,0,0.693632," ","integrate((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 3\right)} \sqrt{-a \cos\left(d x + c\right) + a}}{15 \, d \cos\left(d x + c\right)^{\frac{5}{2}} \sin\left(d x + c\right)}"," ",0,"2/15*(8*cos(d*x + c)^3 + 4*cos(d*x + c)^2 - cos(d*x + c) + 3)*sqrt(-a*cos(d*x + c) + a)/(d*cos(d*x + c)^(5/2)*sin(d*x + c))","A",0
269,1,124,0,0.864556," ","integrate((1-cos(d*x+c))^(1/2)*cos(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 3\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - 3 \, \log\left(-\frac{2 \, {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right)}{8 \, d \sin\left(d x + c\right)}"," ",0,"-1/8*(2*(2*cos(d*x + c)^2 - cos(d*x + c) - 3)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - 3*log(-(2*(cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - (2*cos(d*x + c) + 1)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
270,1,111,0,0.792478," ","integrate((1-cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - \log\left(-\frac{2 \, {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} + {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right)}{2 \, d \sin\left(d x + c\right)}"," ",0,"-1/2*(2*(cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - log(-(2*(cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + (2*cos(d*x + c) + 1)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
271,1,64,0,0.867734," ","integrate((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(-\frac{2 \, {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right)}{d}"," ",0,"log(-(2*(cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - (2*cos(d*x + c) + 1)*sin(d*x + c))/sin(d*x + c))/d","A",0
272,1,41,0,0.739941," ","integrate((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1}}{d \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}"," ",0,"2*(cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)/(d*sqrt(cos(d*x + c))*sin(d*x + c))","A",0
273,1,51,0,2.046499," ","integrate((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) - 1\right)} \sqrt{-\cos\left(d x + c\right) + 1}}{3 \, d \cos\left(d x + c\right)^{\frac{3}{2}} \sin\left(d x + c\right)}"," ",0,"-2/3*(2*cos(d*x + c)^2 + cos(d*x + c) - 1)*sqrt(-cos(d*x + c) + 1)/(d*cos(d*x + c)^(3/2)*sin(d*x + c))","A",0
274,1,63,0,1.185759," ","integrate((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 3\right)} \sqrt{-\cos\left(d x + c\right) + 1}}{15 \, d \cos\left(d x + c\right)^{\frac{5}{2}} \sin\left(d x + c\right)}"," ",0,"2/15*(8*cos(d*x + c)^3 + 4*cos(d*x + c)^2 - cos(d*x + c) + 3)*sqrt(-cos(d*x + c) + 1)/(d*cos(d*x + c)^(5/2)*sin(d*x + c))","A",0
275,1,226,0,0.797100," ","integrate(cos(d*x+c)^(5/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 7 \, \sqrt{a} \log\left(-\frac{2 \, \sqrt{-a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)} + {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{8 \, a d \sin\left(d x + c\right)}"," ",0,"1/8*(4*sqrt(2)*sqrt(a)*log(-(2*sqrt(2)*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sqrt(a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 7*sqrt(a)*log(-(2*sqrt(-a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) + 2*sqrt(-a*cos(d*x + c) + a)*(2*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(cos(d*x + c)))/(a*d*sin(d*x + c))","A",0
276,1,212,0,0.774451," ","integrate(cos(d*x+c)^(3/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + \sqrt{a} \log\left(-\frac{2 \, \sqrt{-a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)} + {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{2 \, a d \sin\left(d x + c\right)}"," ",0,"1/2*(sqrt(2)*sqrt(a)*log(-(2*sqrt(2)*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sqrt(a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + sqrt(a)*log(-(2*sqrt(-a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c))*sin(d*x + c) + 2*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c)))/(a*d*sin(d*x + c))","A",0
277,1,162,0,0.915157," ","integrate(cos(d*x+c)^(1/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) + 2 \, \sqrt{a} \log\left(-\frac{2 \, \sqrt{-a \cos\left(d x + c\right) + a} \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)} + {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{\sin\left(d x + c\right)}\right)}{2 \, a d}"," ",0,"1/2*(sqrt(2)*sqrt(a)*log(-(2*sqrt(2)*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sqrt(a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c))) + 2*sqrt(a)*log(-(2*sqrt(-a*cos(d*x + c) + a)*sqrt(a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c)))/(a*d)","A",0
278,1,144,0,1.325044," ","integrate(1/cos(d*x+c)^(1/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right)}{2 \, \sqrt{a} d}, \frac{\sqrt{2} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{-a \cos\left(d x + c\right) + a} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right)}{d}\right]"," ",0,"[1/2*sqrt(2)*log(-(2*sqrt(2)*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sqrt(a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))/(sqrt(a)*d), sqrt(2)*sqrt(-1/a)*arctan(sqrt(2)*sqrt(-a*cos(d*x + c) + a)*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c))/d]","A",0
279,1,152,0,0.580943," ","integrate(1/cos(d*x+c)^(3/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \cos\left(d x + c\right) \log\left(-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{2 \, a d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"1/2*(sqrt(2)*sqrt(a)*cos(d*x + c)*log(-(2*sqrt(2)*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sqrt(a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 4*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)*sin(d*x + c))","A",0
280,1,165,0,1.025088," ","integrate(1/cos(d*x+c)^(5/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \sqrt{a} \cos\left(d x + c\right)^{2} \log\left(-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{6 \, a d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)}"," ",0,"1/6*(3*sqrt(2)*sqrt(a)*cos(d*x + c)^2*log(-(2*sqrt(2)*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sqrt(a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 4*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^2*sin(d*x + c))","A",0
281,1,177,0,0.907692," ","integrate(1/cos(d*x+c)^(7/2)/(a-a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} \sqrt{a} \cos\left(d x + c\right)^{3} \log\left(-\frac{\frac{2 \, \sqrt{2} \sqrt{-a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a}} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, {\left(13 \, \cos\left(d x + c\right)^{3} + 14 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 3\right)} \sqrt{-a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{30 \, a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)}"," ",0,"1/30*(15*sqrt(2)*sqrt(a)*cos(d*x + c)^3*log(-(2*sqrt(2)*sqrt(-a*cos(d*x + c) + a)*(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sqrt(a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 4*(13*cos(d*x + c)^3 + 14*cos(d*x + c)^2 + 4*cos(d*x + c) + 3)*sqrt(-a*cos(d*x + c) + a)*sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^3*sin(d*x + c))","A",0
282,1,239,0,0.932191," ","integrate(cos(d*x+c)^(5/2)/(1-cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} \log\left(-\frac{2 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} + 7 \, \log\left(\frac{2 \, {\left(\sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 7 \, \log\left(\frac{2 \, {\left(\sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right)}{8 \, d \sin\left(d x + c\right)}"," ",0,"1/8*(4*sqrt(2)*log(-(2*(sqrt(2)*cos(d*x + c) + sqrt(2))*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 2*(2*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + 7*log(2*(sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - 7*log(2*(sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - sin(d*x + c))/sin(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
283,1,225,0,1.292933," ","integrate(cos(d*x+c)^(3/2)/(1-cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{2 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 2 \, {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} + \log\left(\frac{2 \, {\left(\sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - \log\left(\frac{2 \, {\left(\sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)}\right) \sin\left(d x + c\right)}{2 \, d \sin\left(d x + c\right)}"," ",0,"1/2*(sqrt(2)*log(-(2*(sqrt(2)*cos(d*x + c) + sqrt(2))*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 2*(cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + log(2*(sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + sin(d*x + c))/sin(d*x + c))*sin(d*x + c) - log(2*(sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - sin(d*x + c))/sin(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","B",0
284,1,170,0,1.203430," ","integrate(cos(d*x+c)^(1/2)/(1-cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{2 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) + 2 \, \log\left(\frac{2 \, {\left(\sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} + \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)}\right) - 2 \, \log\left(\frac{2 \, {\left(\sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)}\right)}{2 \, d}"," ",0,"1/2*(sqrt(2)*log(-(2*(sqrt(2)*cos(d*x + c) + sqrt(2))*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c))) + 2*log(2*(sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) + sin(d*x + c))/sin(d*x + c)) - 2*log(2*(sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - sin(d*x + c))/sin(d*x + c)))/d","B",0
285,1,84,0,0.817441," ","integrate(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{2 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right)}{2 \, d}"," ",0,"1/2*sqrt(2)*log(-(2*(sqrt(2)*cos(d*x + c) + sqrt(2))*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))/d","B",0
286,1,144,0,0.840692," ","integrate(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \cos\left(d x + c\right) \log\left(-\frac{2 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, {\left(\cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{2 \, d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"1/2*(sqrt(2)*cos(d*x + c)*log(-(2*(sqrt(2)*cos(d*x + c) + sqrt(2))*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 4*(cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)))/(d*cos(d*x + c)*sin(d*x + c))","A",0
287,1,157,0,0.886038," ","integrate(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \cos\left(d x + c\right)^{2} \log\left(-\frac{2 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} - {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{{\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) + 4 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{6 \, d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)}"," ",0,"1/6*(3*sqrt(2)*cos(d*x + c)^2*log(-(2*(sqrt(2)*cos(d*x + c) + sqrt(2))*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))*sin(d*x + c) + 4*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-cos(d*x + c) + 1)*sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2*sin(d*x + c))","A",0
288,0,0,0,1.010895," ","integrate(cos(d*x+c)^(4/3)*(a+a*cos(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}} \cos\left(d x + c\right)^{\frac{4}{3}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)^(1/3)*cos(d*x + c)^(4/3), x)","F",0
289,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(4/3)*(a+a*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,0,0,0,1.451542," ","integrate(cos(d*x+c)^(5/3)*(a+a*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}} \cos\left(d x + c\right)^{\frac{5}{3}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)^(2/3)*cos(d*x + c)^(5/3), x)","F",0
291,0,0,0,1.410189," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
292,0,0,0,1.075340," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
293,0,0,0,2.622846," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
294,0,0,0,0.794064," ","integrate((a+a*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
295,0,0,0,1.955739," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \cos\left(d x + c\right) + a}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
296,0,0,0,0.948791," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \cos\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
297,0,0,0,4.012377," ","integrate((a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \cos\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
298,0,0,0,0.688761," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(7/2), x)","F",0
299,0,0,0,1.890050," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(5/2), x)","F",0
300,0,0,0,1.062372," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(3/2), x)","F",0
301,0,0,0,2.125618," ","integrate((a+a*cos(d*x+c))^2*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sqrt(sec(d*x + c)), x)","F",0
302,0,0,0,1.474979," ","integrate((a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)/sqrt(sec(d*x + c)), x)","F",0
303,0,0,0,2.202527," ","integrate((a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)/sec(d*x + c)^(3/2), x)","F",0
304,0,0,0,1.145070," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(9/2), x)","F",0
305,0,0,0,0.942732," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(7/2), x)","F",0
306,0,0,0,1.968619," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(5/2), x)","F",0
307,0,0,0,2.241616," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(3/2), x)","F",0
308,0,0,0,1.134326," ","integrate((a+a*cos(d*x+c))^3*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sqrt(sec(d*x + c)), x)","F",0
309,0,0,0,0.897145," ","integrate((a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)/sqrt(sec(d*x + c)), x)","F",0
310,0,0,0,1.110540," ","integrate((a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)/sec(d*x + c)^(3/2), x)","F",0
311,0,0,0,1.038386," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)*sec(d*x + c)^(9/2), x)","F",0
312,0,0,0,1.560439," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)*sec(d*x + c)^(7/2), x)","F",0
313,0,0,0,1.451249," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)*sec(d*x + c)^(5/2), x)","F",0
314,0,0,0,1.932912," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)*sec(d*x + c)^(3/2), x)","F",0
315,0,0,0,1.445070," ","integrate((a+a*cos(d*x+c))^4*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)*sqrt(sec(d*x + c)), x)","F",0
316,0,0,0,0.959567," ","integrate((a+a*cos(d*x+c))^4/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)/sqrt(sec(d*x + c)), x)","F",0
317,0,0,0,0.956874," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(sec(d*x + c)^(5/2)/(a*cos(d*x + c) + a), x)","F",0
318,0,0,0,1.090336," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(sec(d*x + c)^(3/2)/(a*cos(d*x + c) + a), x)","F",0
319,0,0,0,1.165890," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a*cos(d*x + c) + a), x)","F",0
320,0,0,0,1.092899," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(1/((a*cos(d*x + c) + a)*sqrt(sec(d*x + c))), x)","F",0
321,0,0,0,0.983884," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(1/((a*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
322,0,0,0,0.883426," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(1/((a*cos(d*x + c) + a)*sec(d*x + c)^(5/2)), x)","F",0
323,0,0,0,1.038508," ","integrate(1/(a+a*cos(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral(1/((a*cos(d*x + c) + a)*sec(d*x + c)^(7/2)), x)","F",0
324,0,0,0,1.020154," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sec(d*x + c)^(5/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
325,0,0,0,1.024979," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sec(d*x + c)^(3/2)/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
326,0,0,0,1.497128," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
327,0,0,0,0.928299," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(1/((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sqrt(sec(d*x + c))), x)","F",0
328,0,0,0,1.467908," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(1/((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(3/2)), x)","F",0
329,0,0,0,1.029865," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(1/((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(5/2)), x)","F",0
330,0,0,0,0.729114," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral(1/((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(7/2)), x)","F",0
331,0,0,0,1.490893," ","integrate(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral(1/((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*sec(d*x + c)^(9/2)), x)","F",0
332,0,0,0,1.083840," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sec(d*x + c)^(3/2)/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
333,0,0,0,0.985714," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3), x)","F",0
334,0,0,0,0.709098," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(1/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sqrt(sec(d*x + c))), x)","F",0
335,0,0,0,0.974833," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(1/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(3/2)), x)","F",0
336,0,0,0,1.107069," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(1/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(5/2)), x)","F",0
337,0,0,0,1.066153," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral(1/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(7/2)), x)","F",0
338,0,0,0,1.448481," ","integrate(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral(1/((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*sec(d*x + c)^(9/2)), x)","F",0
339,1,81,0,0.983986," ","integrate(sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, \cos\left(d x + c\right)^{3} + 8 \, \cos\left(d x + c\right)^{2} + 6 \, \cos\left(d x + c\right) + 5\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{35 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/35*(16*cos(d*x + c)^3 + 8*cos(d*x + c)^2 + 6*cos(d*x + c) + 5)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^4 + d*cos(d*x + c)^3)*sqrt(cos(d*x + c)))","A",0
340,1,71,0,1.033323," ","integrate(sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(8 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/15*sqrt(a*cos(d*x + c) + a)*(8*cos(d*x + c)^2 + 4*cos(d*x + c) + 3)*sin(d*x + c)/((d*cos(d*x + c)^3 + d*cos(d*x + c)^2)*sqrt(cos(d*x + c)))","A",0
341,1,59,0,0.791310," ","integrate(sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3*sqrt(a*cos(d*x + c) + a)*(2*cos(d*x + c) + 1)*sin(d*x + c)/((d*cos(d*x + c)^2 + d*cos(d*x + c))*sqrt(cos(d*x + c)))","A",0
342,1,40,0,0.999732," ","integrate(sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{{\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
343,1,119,0,1.197159," ","integrate(sec(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{-a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right) + 1}\right)}{d}, -\frac{2 \, \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d}\right]"," ",0,"[sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(a*cos(d*x + c) + a)*sqrt(-a)*sqrt(cos(d*x + c))*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1))/d, -2*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/d]","A",0
344,1,88,0,0.754991," ","integrate((a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"-(sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
345,1,108,0,1.224748," ","integrate((a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{\sqrt{a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/4*(3*sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - sqrt(a*cos(d*x + c) + a)*(2*cos(d*x + c)^2 + 3*cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
346,1,86,0,0.656082," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(104 \, a \cos\left(d x + c\right)^{3} + 52 \, a \cos\left(d x + c\right)^{2} + 39 \, a \cos\left(d x + c\right) + 15 \, a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/105*(104*a*cos(d*x + c)^3 + 52*a*cos(d*x + c)^2 + 39*a*cos(d*x + c) + 15*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^4 + d*cos(d*x + c)^3)*sqrt(cos(d*x + c)))","A",0
347,1,73,0,0.691794," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, a \cos\left(d x + c\right)^{2} + 3 \, a \cos\left(d x + c\right) + a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{5 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/5*(6*a*cos(d*x + c)^2 + 3*a*cos(d*x + c) + a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^3 + d*cos(d*x + c)^2)*sqrt(cos(d*x + c)))","A",0
348,1,60,0,0.896282," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a \cos\left(d x + c\right) + a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3*(5*a*cos(d*x + c) + a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^2 + d*cos(d*x + c))*sqrt(cos(d*x + c)))","A",0
349,1,91,0,1.165919," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{\sqrt{a \cos\left(d x + c\right) + a} a \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\right)}}{d \cos\left(d x + c\right) + d}"," ",0,"-2*((a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - sqrt(a*cos(d*x + c) + a)*a*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
350,1,90,0,1.067939," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \cos\left(d x + c\right) + a} a \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d \cos\left(d x + c\right) + d}"," ",0,"(sqrt(a*cos(d*x + c) + a)*a*sqrt(cos(d*x + c))*sin(d*x + c) - 3*(a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)","A",0
351,1,112,0,1.140691," ","integrate((a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{7 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(2 \, a \cos\left(d x + c\right)^{2} + 7 \, a \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/4*(7*(a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*a*cos(d*x + c)^2 + 7*a*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
352,1,123,0,0.798890," ","integrate((a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{33 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(8 \, a \cos\left(d x + c\right)^{3} + 22 \, a \cos\left(d x + c\right)^{2} + 33 \, a \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/24*(33*(a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*a*cos(d*x + c)^3 + 22*a*cos(d*x + c)^2 + 33*a*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
353,1,107,0,0.830233," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(584 \, a^{2} \cos\left(d x + c\right)^{4} + 292 \, a^{2} \cos\left(d x + c\right)^{3} + 219 \, a^{2} \cos\left(d x + c\right)^{2} + 130 \, a^{2} \cos\left(d x + c\right) + 35 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(584*a^2*cos(d*x + c)^4 + 292*a^2*cos(d*x + c)^3 + 219*a^2*cos(d*x + c)^2 + 130*a^2*cos(d*x + c) + 35*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^5 + d*cos(d*x + c)^4)*sqrt(cos(d*x + c)))","A",0
354,1,94,0,1.054400," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(46 \, a^{2} \cos\left(d x + c\right)^{3} + 23 \, a^{2} \cos\left(d x + c\right)^{2} + 12 \, a^{2} \cos\left(d x + c\right) + 3 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{21 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/21*(46*a^2*cos(d*x + c)^3 + 23*a^2*cos(d*x + c)^2 + 12*a^2*cos(d*x + c) + 3*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^4 + d*cos(d*x + c)^3)*sqrt(cos(d*x + c)))","A",0
355,1,81,0,1.025103," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(43 \, a^{2} \cos\left(d x + c\right)^{2} + 14 \, a^{2} \cos\left(d x + c\right) + 3 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/15*(43*a^2*cos(d*x + c)^2 + 14*a^2*cos(d*x + c) + 3*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/((d*cos(d*x + c)^3 + d*cos(d*x + c)^2)*sqrt(cos(d*x + c)))","A",0
356,1,128,0,1.052553," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(8 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}\right)}}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"-2/3*(3*(a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*a^2*cos(d*x + c) + a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
357,1,111,0,0.790415," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{5 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{d \cos\left(d x + c\right) + d}"," ",0,"-(5*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (a^2*cos(d*x + c) + 2*a^2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
358,1,120,0,1.000996," ","integrate((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{19 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(2 \, a^{2} \cos\left(d x + c\right)^{2} + 11 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/4*(19*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (2*a^2*cos(d*x + c)^2 + 11*a^2*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
359,1,133,0,0.819481," ","integrate((a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{75 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(8 \, a^{2} \cos\left(d x + c\right)^{3} + 34 \, a^{2} \cos\left(d x + c\right)^{2} + 75 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/24*(75*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (8*a^2*cos(d*x + c)^3 + 34*a^2*cos(d*x + c)^2 + 75*a^2*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
360,1,146,0,0.780305," ","integrate((a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{489 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{{\left(48 \, a^{2} \cos\left(d x + c\right)^{4} + 184 \, a^{2} \cos\left(d x + c\right)^{3} + 326 \, a^{2} \cos\left(d x + c\right)^{2} + 489 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"-1/192*(489*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - (48*a^2*cos(d*x + c)^4 + 184*a^2*cos(d*x + c)^3 + 326*a^2*cos(d*x + c)^2 + 489*a^2*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
361,1,130,0,1.250419," ","integrate(sec(d*x+c)^(7/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{15 \, {\left(\sqrt{2} \cos\left(d x + c\right)^{3} + \sqrt{2} \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + \frac{2 \, {\left(13 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 3\right)} \sqrt{\cos\left(d x + c\right) + 1} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{15 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/15*(15*(sqrt(2)*cos(d*x + c)^3 + sqrt(2)*cos(d*x + c)^2)*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*(13*cos(d*x + c)^2 - cos(d*x + c) + 3)*sqrt(cos(d*x + c) + 1)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
362,1,114,0,1.096643," ","integrate(sec(d*x+c)^(5/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{3 \, {\left(\sqrt{2} \cos\left(d x + c\right)^{2} + \sqrt{2} \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + \frac{2 \, \sqrt{\cos\left(d x + c\right) + 1} {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*(sqrt(2)*cos(d*x + c)^2 + sqrt(2)*cos(d*x + c))*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*sqrt(cos(d*x + c) + 1)*(cos(d*x + c) - 1)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
363,1,86,0,1.691829," ","integrate(sec(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + \frac{2 \, \sqrt{\cos\left(d x + c\right) + 1} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{d \cos\left(d x + c\right) + d}"," ",0,"((sqrt(2)*cos(d*x + c) + sqrt(2))*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*sqrt(cos(d*x + c) + 1)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
364,1,39,0,1.043935," ","integrate(sec(d*x+c)^(1/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right)}{d}"," ",0,"-sqrt(2)*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c))/d","A",0
365,1,70,0,1.094393," ","integrate(1/sec(d*x+c)^(1/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - 2 \, \arctan\left(\frac{\sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right)}{d}"," ",0,"(sqrt(2)*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*arctan(sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)))/d","A",0
366,1,125,0,0.933102," ","integrate(1/sec(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - \sqrt{\cos\left(d x + c\right) + 1} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"-((sqrt(2)*cos(d*x + c) + sqrt(2))*arctan(sqrt(2)*sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) - (cos(d*x + c) + 1)*arctan(sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))/sin(d*x + c)) - sqrt(cos(d*x + c) + 1)*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)","A",0
367,1,141,0,1.234077," ","integrate(sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{15 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(13 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{15 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/15*(15*sqrt(2)*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*sqrt(a*cos(d*x + c) + a)*(13*cos(d*x + c)^2 - cos(d*x + c) + 3)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)","A",0
368,1,125,0,0.719666," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\frac{3 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*sqrt(2)*(a*cos(d*x + c)^2 + a*cos(d*x + c))*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*sqrt(a*cos(d*x + c) + a)*(cos(d*x + c) - 1)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))","A",0
369,1,98,0,1.878999," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{a d \cos\left(d x + c\right) + a d}"," ",0,"(sqrt(2)*(a*cos(d*x + c) + a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)","A",0
370,1,144,0,1.176830," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{2 \, d}, -\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a} d}\right]"," ",0,"[1/2*sqrt(2)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(-1/a)*sqrt(cos(d*x + c))*sin(d*x + c) - 3*cos(d*x + c)^2 - 2*cos(d*x + c) + 1)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/d, -sqrt(2)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/(sqrt(a)*d)]","A",0
371,1,89,0,1.155255," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{a d}"," ",0,"(sqrt(2)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))))/(a*d)","A",0
372,1,143,0,0.936640," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"(sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - sqrt(2)*(a*cos(d*x + c) + a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c)))/sqrt(a) + sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)","A",0
373,1,161,0,1.071607," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{33 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(19 \, \cos\left(d x + c\right)^{2} + 12 \, \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/12*(33*sqrt(2)*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(19*cos(d*x + c)^2 + 12*cos(d*x + c) - 4)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c))","A",0
374,1,136,0,1.116684," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{7 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(5 \, \cos\left(d x + c\right) + 4\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(7*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(5*cos(d*x + c) + 4)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
375,1,126,0,1.002008," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/4*(3*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
376,1,125,0,1.341951," ","integrate(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/4*(sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
377,1,182,0,1.417942," ","integrate(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{5 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 8 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(5*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 8*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))*sin(d*x + c))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
378,1,201,0,1.214347," ","integrate(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{9 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 12 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/4*(9*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 12*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(2*cos(d*x + c)^2 + 3*cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^2*d*cos(d*x + c)^2 + 2*a^2*d*cos(d*x + c) + a^2*d)","A",0
379,1,195,0,0.982250," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{489 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(299 \, \cos\left(d x + c\right)^{3} + 503 \, \cos\left(d x + c\right)^{2} + 160 \, \cos\left(d x + c\right) - 32\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/96*(489*sqrt(2)*(cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(299*cos(d*x + c)^3 + 503*cos(d*x + c)^2 + 160*cos(d*x + c) - 32)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c))","A",0
380,1,170,0,0.885605," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{75 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(49 \, \cos\left(d x + c\right)^{2} + 85 \, \cos\left(d x + c\right) + 32\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(75*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(49*cos(d*x + c)^2 + 85*cos(d*x + c) + 32)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
381,1,169,0,1.096405," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{19 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(9 \, \cos\left(d x + c\right)^{2} + 13 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(19*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*sqrt(a*cos(d*x + c) + a)*(9*cos(d*x + c)^2 + 13*cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
382,1,167,0,1.197181," ","integrate(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(\cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(5*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(cos(d*x + c)^2 + 5*cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
383,1,169,0,1.041992," ","integrate(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(7 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(3*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(7*cos(d*x + c)^2 + 3*cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
384,1,235,0,1.535141," ","integrate(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{43 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 64 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} {\left(15 \, \cos\left(d x + c\right)^{2} + 11 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/32*(43*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 64*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a*cos(d*x + c) + a)*(15*cos(d*x + c)^2 + 11*cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
385,1,245,0,1.797848," ","integrate(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{115 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 160 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(16 \, \cos\left(d x + c\right)^{3} + 55 \, \cos\left(d x + c\right)^{2} + 35 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{32 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/32*(115*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 160*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(16*cos(d*x + c)^3 + 55*cos(d*x + c)^2 + 35*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","A",0
386,1,229,0,1.246917," ","integrate(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{3045 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} + 4 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(1887 \, \cos\left(d x + c\right)^{4} + 5082 \, \cos\left(d x + c\right)^{3} + 4251 \, \cos\left(d x + c\right)^{2} + 896 \, \cos\left(d x + c\right) - 128\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} + 4 \, a^{4} d \cos\left(d x + c\right)^{4} + 6 \, a^{4} d \cos\left(d x + c\right)^{3} + 4 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/384*(3045*sqrt(2)*(cos(d*x + c)^5 + 4*cos(d*x + c)^4 + 6*cos(d*x + c)^3 + 4*cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(1887*cos(d*x + c)^4 + 5082*cos(d*x + c)^3 + 4251*cos(d*x + c)^2 + 896*cos(d*x + c) - 128)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^5 + 4*a^4*d*cos(d*x + c)^4 + 6*a^4*d*cos(d*x + c)^3 + 4*a^4*d*cos(d*x + c)^2 + a^4*d*cos(d*x + c))","A",0
387,1,204,0,1.065789," ","integrate(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{1089 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(691 \, \cos\left(d x + c\right)^{3} + 1874 \, \cos\left(d x + c\right)^{2} + 1599 \, \cos\left(d x + c\right) + 384\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(1089*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(691*cos(d*x + c)^3 + 1874*cos(d*x + c)^2 + 1599*cos(d*x + c) + 384)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
388,1,203,0,1.077085," ","integrate(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{189 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(103 \, \cos\left(d x + c\right)^{3} + 266 \, \cos\left(d x + c\right)^{2} + 195 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(189*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(103*cos(d*x + c)^3 + 266*cos(d*x + c)^2 + 195*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
389,1,203,0,1.258983," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{39 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} - 39 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(39*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) + 2*(5*cos(d*x + c)^3 - 2*cos(d*x + c)^2 - 39*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
390,1,203,0,1.898844," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{21 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(17 \, \cos\left(d x + c\right)^{3} + 70 \, \cos\left(d x + c\right)^{2} + 21 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(21*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(17*cos(d*x + c)^3 + 70*cos(d*x + c)^2 + 21*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
391,1,203,0,1.226250," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(67 \, \cos\left(d x + c\right)^{3} + 50 \, \cos\left(d x + c\right)^{2} + 15 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(15*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(67*cos(d*x + c)^3 + 50*cos(d*x + c)^2 + 15*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
392,1,279,0,2.291930," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{531 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 768 \, {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(247 \, \cos\left(d x + c\right)^{3} + 362 \, \cos\left(d x + c\right)^{2} + 147 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"1/384*(531*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 768*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(247*cos(d*x + c)^3 + 362*cos(d*x + c)^2 + 147*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
393,1,289,0,2.378877," ","integrate(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{1911 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2688 \, {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(192 \, \cos\left(d x + c\right)^{4} + 1099 \, \cos\left(d x + c\right)^{3} + 1442 \, \cos\left(d x + c\right)^{2} + 567 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} + 4 \, a^{4} d \cos\left(d x + c\right)^{3} + 6 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d \cos\left(d x + c\right) + a^{4} d\right)}}"," ",0,"-1/384*(1911*sqrt(2)*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2688*(cos(d*x + c)^4 + 4*cos(d*x + c)^3 + 6*cos(d*x + c)^2 + 4*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(192*cos(d*x + c)^4 + 1099*cos(d*x + c)^3 + 1442*cos(d*x + c)^2 + 567*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^4*d*cos(d*x + c)^4 + 4*a^4*d*cos(d*x + c)^3 + 6*a^4*d*cos(d*x + c)^2 + 4*a^4*d*cos(d*x + c) + a^4*d)","A",0
394,1,237,0,1.030550," ","integrate(1/(a+a*cos(d*x+c))^(9/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{45 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} + 5 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(73 \, \cos\left(d x + c\right)^{4} + 351 \, \cos\left(d x + c\right)^{3} + 195 \, \cos\left(d x + c\right)^{2} + 45 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{2048 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"-1/2048*(45*sqrt(2)*(cos(d*x + c)^5 + 5*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 10*cos(d*x + c)^2 + 5*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(73*cos(d*x + c)^4 + 351*cos(d*x + c)^3 + 195*cos(d*x + c)^2 + 45*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
395,1,237,0,1.156440," ","integrate(1/(a+a*cos(d*x+c))^(9/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{105 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{5} + 5 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{\sqrt{a} \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(853 \, \cos\left(d x + c\right)^{4} + 819 \, \cos\left(d x + c\right)^{3} + 455 \, \cos\left(d x + c\right)^{2} + 105 \, \cos\left(d x + c\right)\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{6144 \, {\left(a^{5} d \cos\left(d x + c\right)^{5} + 5 \, a^{5} d \cos\left(d x + c\right)^{4} + 10 \, a^{5} d \cos\left(d x + c\right)^{3} + 10 \, a^{5} d \cos\left(d x + c\right)^{2} + 5 \, a^{5} d \cos\left(d x + c\right) + a^{5} d\right)}}"," ",0,"-1/6144*(105*sqrt(2)*(cos(d*x + c)^5 + 5*cos(d*x + c)^4 + 10*cos(d*x + c)^3 + 10*cos(d*x + c)^2 + 5*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(sqrt(a)*sin(d*x + c))) - 2*(853*cos(d*x + c)^4 + 819*cos(d*x + c)^3 + 455*cos(d*x + c)^2 + 105*cos(d*x + c))*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(cos(d*x + c)))/(a^5*d*cos(d*x + c)^5 + 5*a^5*d*cos(d*x + c)^4 + 10*a^5*d*cos(d*x + c)^3 + 10*a^5*d*cos(d*x + c)^2 + 5*a^5*d*cos(d*x + c) + a^5*d)","A",0
396,1,41,0,1.089317," ","integrate((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/4),x, algorithm=""fricas"")","\frac{4 \, \sqrt{a \cos\left(d x + c\right) + a} a \sin\left(d x + c\right)}{{\left(d \cos\left(d x + c\right) + d\right)} \cos\left(d x + c\right)^{\frac{1}{4}}}"," ",0,"4*sqrt(a*cos(d*x + c) + a)*a*sin(d*x + c)/((d*cos(d*x + c) + d)*cos(d*x + c)^(1/4))","A",0
397,0,0,0,1.132992," ","integrate(cos(d*x+c)^m*(a+a*cos(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \cos\left(d x + c\right)^{4} + 4 \, a^{4} \cos\left(d x + c\right)^{3} + 6 \, a^{4} \cos\left(d x + c\right)^{2} + 4 \, a^{4} \cos\left(d x + c\right) + a^{4}\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((a^4*cos(d*x + c)^4 + 4*a^4*cos(d*x + c)^3 + 6*a^4*cos(d*x + c)^2 + 4*a^4*cos(d*x + c) + a^4)*cos(d*x + c)^m, x)","F",0
398,0,0,0,1.085624," ","integrate(cos(d*x+c)^m*(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) + a^{3}\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3 + 3*a^3*cos(d*x + c)^2 + 3*a^3*cos(d*x + c) + a^3)*cos(d*x + c)^m, x)","F",0
399,0,0,0,0.756618," ","integrate(cos(d*x+c)^m*(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2)*cos(d*x + c)^m, x)","F",0
400,0,0,0,1.408674," ","integrate(cos(d*x+c)^m*(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((a*cos(d*x + c) + a)*cos(d*x + c)^m, x)","F",0
401,0,0,0,1.056412," ","integrate(cos(d*x+c)^m/(a+a*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{m}}{a \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^m/(a*cos(d*x + c) + a), x)","F",0
402,0,0,0,1.053433," ","integrate(cos(d*x+c)^m/(a+a*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{m}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(cos(d*x + c)^m/(a^2*cos(d*x + c)^2 + 2*a^2*cos(d*x + c) + a^2), x)","F",0
403,1,97,0,1.124574," ","integrate(cos(d*x+c)^7*(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3675 \, b d x + {\left(1680 \, b \cos\left(d x + c\right)^{7} + 1920 \, a \cos\left(d x + c\right)^{6} + 1960 \, b \cos\left(d x + c\right)^{5} + 2304 \, a \cos\left(d x + c\right)^{4} + 2450 \, b \cos\left(d x + c\right)^{3} + 3072 \, a \cos\left(d x + c\right)^{2} + 3675 \, b \cos\left(d x + c\right) + 6144 \, a\right)} \sin\left(d x + c\right)}{13440 \, d}"," ",0,"1/13440*(3675*b*d*x + (1680*b*cos(d*x + c)^7 + 1920*a*cos(d*x + c)^6 + 1960*b*cos(d*x + c)^5 + 2304*a*cos(d*x + c)^4 + 2450*b*cos(d*x + c)^3 + 3072*a*cos(d*x + c)^2 + 3675*b*cos(d*x + c) + 6144*a)*sin(d*x + c))/d","A",0
404,1,86,0,0.913384," ","integrate(cos(d*x+c)^6*(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{525 \, a d x + {\left(240 \, b \cos\left(d x + c\right)^{6} + 280 \, a \cos\left(d x + c\right)^{5} + 288 \, b \cos\left(d x + c\right)^{4} + 350 \, a \cos\left(d x + c\right)^{3} + 384 \, b \cos\left(d x + c\right)^{2} + 525 \, a \cos\left(d x + c\right) + 768 \, b\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(525*a*d*x + (240*b*cos(d*x + c)^6 + 280*a*cos(d*x + c)^5 + 288*b*cos(d*x + c)^4 + 350*a*cos(d*x + c)^3 + 384*b*cos(d*x + c)^2 + 525*a*cos(d*x + c) + 768*b)*sin(d*x + c))/d","A",0
405,1,75,0,0.991418," ","integrate(cos(d*x+c)^5*(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{75 \, b d x + {\left(40 \, b \cos\left(d x + c\right)^{5} + 48 \, a \cos\left(d x + c\right)^{4} + 50 \, b \cos\left(d x + c\right)^{3} + 64 \, a \cos\left(d x + c\right)^{2} + 75 \, b \cos\left(d x + c\right) + 128 \, a\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(75*b*d*x + (40*b*cos(d*x + c)^5 + 48*a*cos(d*x + c)^4 + 50*b*cos(d*x + c)^3 + 64*a*cos(d*x + c)^2 + 75*b*cos(d*x + c) + 128*a)*sin(d*x + c))/d","A",0
406,1,64,0,0.763869," ","integrate(cos(d*x+c)^4*(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{45 \, a d x + {\left(24 \, b \cos\left(d x + c\right)^{4} + 30 \, a \cos\left(d x + c\right)^{3} + 32 \, b \cos\left(d x + c\right)^{2} + 45 \, a \cos\left(d x + c\right) + 64 \, b\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*a*d*x + (24*b*cos(d*x + c)^4 + 30*a*cos(d*x + c)^3 + 32*b*cos(d*x + c)^2 + 45*a*cos(d*x + c) + 64*b)*sin(d*x + c))/d","A",0
407,1,53,0,1.027768," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, b d x + {\left(6 \, b \cos\left(d x + c\right)^{3} + 8 \, a \cos\left(d x + c\right)^{2} + 9 \, b \cos\left(d x + c\right) + 16 \, a\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(9*b*d*x + (6*b*cos(d*x + c)^3 + 8*a*cos(d*x + c)^2 + 9*b*cos(d*x + c) + 16*a)*sin(d*x + c))/d","A",0
408,1,42,0,1.194448," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a d x + {\left(2 \, b \cos\left(d x + c\right)^{2} + 3 \, a \cos\left(d x + c\right) + 4 \, b\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*a*d*x + (2*b*cos(d*x + c)^2 + 3*a*cos(d*x + c) + 4*b)*sin(d*x + c))/d","A",0
409,1,29,0,0.900557," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\frac{b d x + {\left(b \cos\left(d x + c\right) + 2 \, a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b*d*x + (b*cos(d*x + c) + 2*a)*sin(d*x + c))/d","A",0
410,1,17,0,0.760558," ","integrate(a+b*cos(d*x+c),x, algorithm=""fricas"")","\frac{a d x + b \sin\left(d x + c\right)}{d}"," ",0,"(a*d*x + b*sin(d*x + c))/d","A",0
411,1,36,0,0.889432," ","integrate((a+b*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","\frac{2 \, b d x + a \log\left(\sin\left(d x + c\right) + 1\right) - a \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"1/2*(2*b*d*x + a*log(sin(d*x + c) + 1) - a*log(-sin(d*x + c) + 1))/d","B",0
412,1,60,0,1.005145," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, a \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(b*cos(d*x + c)*log(sin(d*x + c) + 1) - b*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*a*sin(d*x + c))/(d*cos(d*x + c))","B",0
413,1,74,0,0.938960," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)^3,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 \, {\left(2 \, b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}{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*(2*b*cos(d*x + c) + a)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
414,1,88,0,0.786616," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, b \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, b \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, a \cos\left(d x + c\right)^{2} + 3 \, b \cos\left(d x + c\right) + 2 \, a\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*b*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*b*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(4*a*cos(d*x + c)^2 + 3*b*cos(d*x + c) + 2*a)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
415,1,99,0,1.035088," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{9 \, a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, b \cos\left(d x + c\right)^{3} + 9 \, a \cos\left(d x + c\right)^{2} + 8 \, b \cos\left(d x + c\right) + 6 \, a\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(9*a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 9*a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*b*cos(d*x + c)^3 + 9*a*cos(d*x + c)^2 + 8*b*cos(d*x + c) + 6*a)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
416,1,110,0,1.001251," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{45 \, b \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 45 \, b \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(64 \, a \cos\left(d x + c\right)^{4} + 45 \, b \cos\left(d x + c\right)^{3} + 32 \, a \cos\left(d x + c\right)^{2} + 30 \, b \cos\left(d x + c\right) + 24 \, a\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(45*b*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 45*b*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(64*a*cos(d*x + c)^4 + 45*b*cos(d*x + c)^3 + 32*a*cos(d*x + c)^2 + 30*b*cos(d*x + c) + 24*a)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
417,1,110,0,0.976152," ","integrate(cos(d*x+c)^4*(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, a^{2} + 5 \, b^{2}\right)} d x + {\left(40 \, b^{2} \cos\left(d x + c\right)^{5} + 96 \, a b \cos\left(d x + c\right)^{4} + 128 \, a b \cos\left(d x + c\right)^{2} + 10 \, {\left(6 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 256 \, a b + 15 \, {\left(6 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(6*a^2 + 5*b^2)*d*x + (40*b^2*cos(d*x + c)^5 + 96*a*b*cos(d*x + c)^4 + 128*a*b*cos(d*x + c)^2 + 10*(6*a^2 + 5*b^2)*cos(d*x + c)^3 + 256*a*b + 15*(6*a^2 + 5*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
418,1,86,0,0.955000," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{45 \, a b d x + {\left(12 \, b^{2} \cos\left(d x + c\right)^{4} + 30 \, a b \cos\left(d x + c\right)^{3} + 45 \, a b \cos\left(d x + c\right) + 4 \, {\left(5 \, a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 40 \, a^{2} + 32 \, b^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(45*a*b*d*x + (12*b^2*cos(d*x + c)^4 + 30*a*b*cos(d*x + c)^3 + 45*a*b*cos(d*x + c) + 4*(5*a^2 + 4*b^2)*cos(d*x + c)^2 + 40*a^2 + 32*b^2)*sin(d*x + c))/d","A",0
419,1,77,0,0.817064," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} d x + {\left(6 \, b^{2} \cos\left(d x + c\right)^{3} + 16 \, a b \cos\left(d x + c\right)^{2} + 32 \, a b + 3 \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(4*a^2 + 3*b^2)*d*x + (6*b^2*cos(d*x + c)^3 + 16*a*b*cos(d*x + c)^2 + 32*a*b + 3*(4*a^2 + 3*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
420,1,52,0,0.721307," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a b d x + {\left(b^{2} \cos\left(d x + c\right)^{2} + 3 \, a b \cos\left(d x + c\right) + 3 \, a^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(3*a*b*d*x + (b^2*cos(d*x + c)^2 + 3*a*b*cos(d*x + c) + 3*a^2 + 2*b^2)*sin(d*x + c))/d","A",0
421,1,40,0,0.909812," ","integrate((a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} d x + {\left(b^{2} \cos\left(d x + c\right) + 4 \, a b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*a^2 + b^2)*d*x + (b^2*cos(d*x + c) + 4*a*b)*sin(d*x + c))/d","A",0
422,1,52,0,1.138548," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c),x, algorithm=""fricas"")","\frac{4 \, a b d x + a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, b^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(4*a*b*d*x + a^2*log(sin(d*x + c) + 1) - a^2*log(-sin(d*x + c) + 1) + 2*b^2*sin(d*x + c))/d","A",0
423,1,74,0,0.911586," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{b^{2} d x \cos\left(d x + c\right) + a b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - a b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + a^{2} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"(b^2*d*x*cos(d*x + c) + a*b*cos(d*x + c)*log(sin(d*x + c) + 1) - a*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + a^2*sin(d*x + c))/(d*cos(d*x + c))","B",0
424,1,93,0,0.888612," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((a^2 + 2*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (a^2 + 2*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(4*a*b*cos(d*x + c) + a^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
425,1,100,0,1.096402," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, a b \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a b \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/6*(3*a*b*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*a*b*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(3*a*b*cos(d*x + c) + (2*a^2 + 3*b^2)*cos(d*x + c)^2 + a^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
426,1,133,0,0.667106," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(32 \, a b \cos\left(d x + c\right)^{3} + 16 \, a b \cos\left(d x + c\right) + 3 \, {\left(3 \, a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 6 \, a^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(3*a^2 + 4*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*a^2 + 4*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(32*a*b*cos(d*x + c)^3 + 16*a*b*cos(d*x + c) + 3*(3*a^2 + 4*b^2)*cos(d*x + c)^2 + 6*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
427,1,136,0,1.427775," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{45 \, a b \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 45 \, a b \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(45 \, a b \cos\left(d x + c\right)^{3} + 8 \, {\left(4 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 30 \, a b \cos\left(d x + c\right) + 4 \, {\left(4 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 12 \, a^{2}\right)} \sin\left(d x + c\right)}{120 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/120*(45*a*b*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 45*a*b*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(45*a*b*cos(d*x + c)^3 + 8*(4*a^2 + 5*b^2)*cos(d*x + c)^4 + 30*a*b*cos(d*x + c) + 4*(4*a^2 + 5*b^2)*cos(d*x + c)^2 + 12*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
428,1,132,0,1.034710," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(18 \, a^{2} b + 5 \, b^{3}\right)} d x + {\left(40 \, b^{3} \cos\left(d x + c\right)^{5} + 144 \, a b^{2} \cos\left(d x + c\right)^{4} + 10 \, {\left(18 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{3} + 160 \, a^{3} + 384 \, a b^{2} + 16 \, {\left(5 \, a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(18 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(18*a^2*b + 5*b^3)*d*x + (40*b^3*cos(d*x + c)^5 + 144*a*b^2*cos(d*x + c)^4 + 10*(18*a^2*b + 5*b^3)*cos(d*x + c)^3 + 160*a^3 + 384*a*b^2 + 16*(5*a^3 + 12*a*b^2)*cos(d*x + c)^2 + 15*(18*a^2*b + 5*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
429,1,110,0,1.450132," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} d x + {\left(24 \, b^{3} \cos\left(d x + c\right)^{4} + 90 \, a b^{2} \cos\left(d x + c\right)^{3} + 240 \, a^{2} b + 64 \, b^{3} + 8 \, {\left(15 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(4*a^3 + 9*a*b^2)*d*x + (24*b^3*cos(d*x + c)^4 + 90*a*b^2*cos(d*x + c)^3 + 240*a^2*b + 64*b^3 + 8*(15*a^2*b + 4*b^3)*cos(d*x + c)^2 + 15*(4*a^3 + 9*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
430,1,84,0,1.377878," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, a^{2} b + b^{3}\right)} d x + {\left(2 \, b^{3} \cos\left(d x + c\right)^{3} + 8 \, a b^{2} \cos\left(d x + c\right)^{2} + 8 \, a^{3} + 16 \, a b^{2} + 3 \, {\left(4 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(3*(4*a^2*b + b^3)*d*x + (2*b^3*cos(d*x + c)^3 + 8*a*b^2*cos(d*x + c)^2 + 8*a^3 + 16*a*b^2 + 3*(4*a^2*b + b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
431,1,66,0,0.694834," ","integrate((a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} d x + {\left(2 \, b^{3} \cos\left(d x + c\right)^{2} + 9 \, a b^{2} \cos\left(d x + c\right) + 18 \, a^{2} b + 4 \, b^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(2*a^3 + 3*a*b^2)*d*x + (2*b^3*cos(d*x + c)^2 + 9*a*b^2*cos(d*x + c) + 18*a^2*b + 4*b^3)*sin(d*x + c))/d","A",0
432,1,72,0,0.853720," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c),x, algorithm=""fricas"")","\frac{a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, a^{2} b + b^{3}\right)} d x + {\left(b^{3} \cos\left(d x + c\right) + 6 \, a b^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a^3*log(sin(d*x + c) + 1) - a^3*log(-sin(d*x + c) + 1) + (6*a^2*b + b^3)*d*x + (b^3*cos(d*x + c) + 6*a*b^2)*sin(d*x + c))/d","A",0
433,1,94,0,1.078301," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{6 \, a b^{2} d x \cos\left(d x + c\right) + 3 \, a^{2} b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a^{2} b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(b^{3} \cos\left(d x + c\right) + a^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(6*a*b^2*d*x*cos(d*x + c) + 3*a^2*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*a^2*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(b^3*cos(d*x + c) + a^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
434,1,112,0,1.124969," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, b^{3} d x \cos\left(d x + c\right)^{2} + {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*b^3*d*x*cos(d*x + c)^2 + (a^3 + 6*a*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (a^3 + 6*a*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(6*a^2*b*cos(d*x + c) + a^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
435,1,126,0,1.080213," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(9 \, a^{2} b \cos\left(d x + c\right) + 2 \, a^{3} + 2 \, {\left(2 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(3*(3*a^2*b + 2*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(3*a^2*b + 2*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(9*a^2*b*cos(d*x + c) + 2*a^3 + 2*(2*a^3 + 9*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
436,1,140,0,1.044179," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{3} + 4 \, 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} + 4 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, a^{2} b \cos\left(d x + c\right) + 8 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{3} + 2 \, a^{3} + 3 \, {\left(a^{3} + 4 \, 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 + 4*a*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(a^3 + 4*a*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*a^2*b*cos(d*x + c) + 8*(2*a^2*b + b^3)*cos(d*x + c)^3 + 2*a^3 + 3*(a^3 + 4*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
437,1,170,0,0.893386," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(9 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(9 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(4 \, a^{3} + 15 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + 90 \, a^{2} b \cos\left(d x + c\right) + 15 \, {\left(9 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{3} + 24 \, a^{3} + 8 \, {\left(4 \, a^{3} + 15 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(9*a^2*b + 4*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(9*a^2*b + 4*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(4*a^3 + 15*a*b^2)*cos(d*x + c)^4 + 90*a^2*b*cos(d*x + c) + 15*(9*a^2*b + 4*b^3)*cos(d*x + c)^3 + 24*a^3 + 8*(4*a^3 + 15*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
438,1,171,0,0.890638," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(6 \, a^{3} b + 5 \, a b^{3}\right)} d x + {\left(60 \, b^{4} \cos\left(d x + c\right)^{6} + 280 \, a b^{3} \cos\left(d x + c\right)^{5} + 72 \, {\left(7 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + 280 \, a^{4} + 1344 \, a^{2} b^{2} + 192 \, b^{4} + 70 \, {\left(6 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(35 \, a^{4} + 168 \, a^{2} b^{2} + 24 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 105 \, {\left(6 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(105*(6*a^3*b + 5*a*b^3)*d*x + (60*b^4*cos(d*x + c)^6 + 280*a*b^3*cos(d*x + c)^5 + 72*(7*a^2*b^2 + b^4)*cos(d*x + c)^4 + 280*a^4 + 1344*a^2*b^2 + 192*b^4 + 70*(6*a^3*b + 5*a*b^3)*cos(d*x + c)^3 + 4*(35*a^4 + 168*a^2*b^2 + 24*b^4)*cos(d*x + c)^2 + 105*(6*a^3*b + 5*a*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
439,1,150,0,0.810383," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, a^{4} + 36 \, a^{2} b^{2} + 5 \, b^{4}\right)} d x + {\left(40 \, b^{4} \cos\left(d x + c\right)^{5} + 192 \, a b^{3} \cos\left(d x + c\right)^{4} + 640 \, a^{3} b + 512 \, a b^{3} + 10 \, {\left(36 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)^{3} + 64 \, {\left(5 \, a^{3} b + 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(8 \, a^{4} + 36 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(8*a^4 + 36*a^2*b^2 + 5*b^4)*d*x + (40*b^4*cos(d*x + c)^5 + 192*a*b^3*cos(d*x + c)^4 + 640*a^3*b + 512*a*b^3 + 10*(36*a^2*b^2 + 5*b^4)*cos(d*x + c)^3 + 64*(5*a^3*b + 4*a*b^3)*cos(d*x + c)^2 + 15*(8*a^4 + 36*a^2*b^2 + 5*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
440,1,121,0,1.044220," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d x + {\left(6 \, b^{4} \cos\left(d x + c\right)^{4} + 30 \, a b^{3} \cos\left(d x + c\right)^{3} + 30 \, a^{4} + 120 \, a^{2} b^{2} + 16 \, b^{4} + 4 \, {\left(15 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(15*(4*a^3*b + 3*a*b^3)*d*x + (6*b^4*cos(d*x + c)^4 + 30*a*b^3*cos(d*x + c)^3 + 30*a^4 + 120*a^2*b^2 + 16*b^4 + 4*(15*a^2*b^2 + 2*b^4)*cos(d*x + c)^2 + 15*(4*a^3*b + 3*a*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
441,1,96,0,0.774781," ","integrate((a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, a^{4} + 24 \, a^{2} b^{2} + 3 \, b^{4}\right)} d x + {\left(6 \, b^{4} \cos\left(d x + c\right)^{3} + 32 \, a b^{3} \cos\left(d x + c\right)^{2} + 96 \, a^{3} b + 64 \, a b^{3} + 9 \, {\left(8 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(8*a^4 + 24*a^2*b^2 + 3*b^4)*d*x + (6*b^4*cos(d*x + c)^3 + 32*a*b^3*cos(d*x + c)^2 + 96*a^3*b + 64*a*b^3 + 9*(8*a^2*b^2 + b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
442,1,98,0,1.149005," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c),x, algorithm=""fricas"")","\frac{3 \, a^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 12 \, {\left(2 \, a^{3} b + a b^{3}\right)} d x + 2 \, {\left(b^{4} \cos\left(d x + c\right)^{2} + 6 \, a b^{3} \cos\left(d x + c\right) + 18 \, a^{2} b^{2} + 2 \, b^{4}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*a^4*log(sin(d*x + c) + 1) - 3*a^4*log(-sin(d*x + c) + 1) + 12*(2*a^3*b + a*b^3)*d*x + 2*(b^4*cos(d*x + c)^2 + 6*a*b^3*cos(d*x + c) + 18*a^2*b^2 + 2*b^4)*sin(d*x + c))/d","A",0
443,1,116,0,1.219027," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^2,x, algorithm=""fricas"")","\frac{4 \, a^{3} b \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, a^{3} b \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(12 \, a^{2} b^{2} + b^{4}\right)} d x \cos\left(d x + c\right) + {\left(b^{4} \cos\left(d x + c\right)^{2} + 8 \, a b^{3} \cos\left(d x + c\right) + 2 \, a^{4}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(4*a^3*b*cos(d*x + c)*log(sin(d*x + c) + 1) - 4*a^3*b*cos(d*x + c)*log(-sin(d*x + c) + 1) + (12*a^2*b^2 + b^4)*d*x*cos(d*x + c) + (b^4*cos(d*x + c)^2 + 8*a*b^3*cos(d*x + c) + 2*a^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
444,1,130,0,0.751169," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^3,x, algorithm=""fricas"")","\frac{16 \, a b^{3} d x \cos\left(d x + c\right)^{2} + {\left(a^{4} + 12 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{4} + 12 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, b^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{3} b \cos\left(d x + c\right) + a^{4}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(16*a*b^3*d*x*cos(d*x + c)^2 + (a^4 + 12*a^2*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (a^4 + 12*a^2*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*b^4*cos(d*x + c)^2 + 8*a^3*b*cos(d*x + c) + a^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
445,1,138,0,1.227226," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, a^{3} b \cos\left(d x + c\right) + a^{4} + 2 \, {\left(a^{4} + 9 \, a^{2} 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^4*d*x*cos(d*x + c)^3 + 3*(a^3*b + 2*a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(a^3*b + 2*a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + (6*a^3*b*cos(d*x + c) + a^4 + 2*(a^4 + 9*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
446,1,163,0,0.914550," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^5,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{4} + 24 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, a^{4} + 24 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(32 \, a^{3} b \cos\left(d x + c\right) + 6 \, a^{4} + 32 \, {\left(2 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(a^{4} + 8 \, a^{2} b^{2}\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*(3*(3*a^4 + 24*a^2*b^2 + 8*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*a^4 + 24*a^2*b^2 + 8*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(32*a^3*b*cos(d*x + c) + 6*a^4 + 32*(2*a^3*b + 3*a*b^3)*cos(d*x + c)^3 + 9*(a^4 + 8*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
447,1,182,0,1.097290," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^6,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, a^{3} b + 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(3 \, a^{3} b + 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(30 \, a^{3} b \cos\left(d x + c\right) + 2 \, {\left(8 \, a^{4} + 60 \, a^{2} b^{2} + 15 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 6 \, a^{4} + 15 \, {\left(3 \, a^{3} b + 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{4} + 15 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/60*(15*(3*a^3*b + 4*a*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(3*a^3*b + 4*a*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(30*a^3*b*cos(d*x + c) + 2*(8*a^4 + 60*a^2*b^2 + 15*b^4)*cos(d*x + c)^4 + 6*a^4 + 15*(3*a^3*b + 4*a*b^3)*cos(d*x + c)^3 + 4*(2*a^4 + 15*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
448,1,217,0,1.099313," ","integrate((a+b*cos(d*x+c))^4*sec(d*x+c)^7,x, algorithm=""fricas"")","\frac{15 \, {\left(5 \, a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(5 \, a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(128 \, {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} + 192 \, a^{3} b \cos\left(d x + c\right) + 15 \, {\left(5 \, a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 40 \, a^{4} + 64 \, {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(5 \, a^{4} + 36 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(5*a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(5*a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(128*(4*a^3*b + 5*a*b^3)*cos(d*x + c)^5 + 192*a^3*b*cos(d*x + c) + 15*(5*a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c)^4 + 40*a^4 + 64*(4*a^3*b + 5*a*b^3)*cos(d*x + c)^3 + 10*(5*a^4 + 36*a^2*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
449,1,479,0,1.716990," ","integrate(cos(d*x+c)^5/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{12 \, \sqrt{-a^{2} + b^{2}} a^{5} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 3 \, {\left(8 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} - 3 \, b^{6}\right)} d x + {\left(24 \, a^{5} b - 8 \, a^{3} b^{3} - 16 \, a b^{5} - 6 \, {\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(4 \, a^{4} b^{2} - a^{2} b^{4} - 3 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} b^{5} - b^{7}\right)} d}, -\frac{24 \, \sqrt{a^{2} - b^{2}} a^{5} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - 3 \, {\left(8 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} - 3 \, b^{6}\right)} d x + {\left(24 \, a^{5} b - 8 \, a^{3} b^{3} - 16 \, a b^{5} - 6 \, {\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(4 \, a^{4} b^{2} - a^{2} b^{4} - 3 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{2} b^{5} - b^{7}\right)} d}\right]"," ",0,"[-1/24*(12*sqrt(-a^2 + b^2)*a^5*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 3*(8*a^6 - 4*a^4*b^2 - a^2*b^4 - 3*b^6)*d*x + (24*a^5*b - 8*a^3*b^3 - 16*a*b^5 - 6*(a^2*b^4 - b^6)*cos(d*x + c)^3 + 8*(a^3*b^3 - a*b^5)*cos(d*x + c)^2 - 3*(4*a^4*b^2 - a^2*b^4 - 3*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d), -1/24*(24*sqrt(a^2 - b^2)*a^5*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*(8*a^6 - 4*a^4*b^2 - a^2*b^4 - 3*b^6)*d*x + (24*a^5*b - 8*a^3*b^3 - 16*a*b^5 - 6*(a^2*b^4 - b^6)*cos(d*x + c)^3 + 8*(a^3*b^3 - a*b^5)*cos(d*x + c)^2 - 3*(4*a^4*b^2 - a^2*b^4 - 3*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d)]","A",0
450,1,400,0,1.174740," ","integrate(cos(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} + b^{2}} a^{4} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 3 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} d x - {\left(6 \, a^{4} b - 2 \, a^{2} b^{3} - 4 \, b^{5} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}, \frac{6 \, \sqrt{a^{2} - b^{2}} a^{4} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - 3 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} d x + {\left(6 \, a^{4} b - 2 \, a^{2} b^{3} - 4 \, b^{5} + 2 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{4} - b^{6}\right)} d}\right]"," ",0,"[-1/6*(3*sqrt(-a^2 + b^2)*a^4*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 3*(2*a^5 - a^3*b^2 - a*b^4)*d*x - (6*a^4*b - 2*a^2*b^3 - 4*b^5 + 2*(a^2*b^3 - b^5)*cos(d*x + c)^2 - 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d), 1/6*(6*sqrt(a^2 - b^2)*a^4*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*(2*a^5 - a^3*b^2 - a*b^4)*d*x + (6*a^4*b - 2*a^2*b^3 - 4*b^5 + 2*(a^2*b^3 - b^5)*cos(d*x + c)^2 - 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d)]","A",0
451,1,334,0,0.968144," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} a^{3} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d x + {\left(2 \, a^{3} b - 2 \, a b^{3} - {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} - b^{5}\right)} d}, -\frac{2 \, \sqrt{a^{2} - b^{2}} a^{3} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d x + {\left(2 \, a^{3} b - 2 \, a b^{3} - {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} - b^{5}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*a^3*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (2*a^4 - a^2*b^2 - b^4)*d*x + (2*a^3*b - 2*a*b^3 - (a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d), -1/2*(2*sqrt(a^2 - b^2)*a^3*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*a^4 - a^2*b^2 - b^4)*d*x + (2*a^3*b - 2*a*b^3 - (a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d)]","A",0
452,1,269,0,1.096835," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} a^{2} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left(a^{3} - a b^{2}\right)} d x - 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d}, \frac{\sqrt{a^{2} - b^{2}} a^{2} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(a^{3} - a b^{2}\right)} d x + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*a^2*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*(a^3 - a*b^2)*d*x - 2*(a^2*b - b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d), (sqrt(a^2 - b^2)*a^2*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (a^3 - a*b^2)*d*x + (a^2*b - b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d)]","A",0
453,1,223,0,1.226534," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} - b^{2}\right)} d x - \sqrt{-a^{2} + b^{2}} a \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right)}{2 \, {\left(a^{2} b - b^{3}\right)} d}, \frac{{\left(a^{2} - b^{2}\right)} d x - \sqrt{a^{2} - b^{2}} a \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right)}{{\left(a^{2} b - b^{3}\right)} d}\right]"," ",0,"[1/2*(2*(a^2 - b^2)*d*x - sqrt(-a^2 + b^2)*a*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)))/((a^2*b - b^3)*d), ((a^2 - b^2)*d*x - sqrt(a^2 - b^2)*a*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))))/((a^2*b - b^3)*d)]","A",0
454,1,175,0,1.134457," ","integrate(1/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}, \frac{\arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right)}{\sqrt{a^{2} - b^{2}} d}\right]"," ",0,"[-1/2*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2))/((a^2 - b^2)*d), arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))/(sqrt(a^2 - b^2)*d)]","A",0
455,1,278,0,1.077323," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} b \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} - b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}, -\frac{2 \, \sqrt{a^{2} - b^{2}} b \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} - b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*b*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (a^2 - b^2)*log(sin(d*x + c) + 1) + (a^2 - b^2)*log(-sin(d*x + c) + 1))/((a^3 - a*b^2)*d), -1/2*(2*sqrt(a^2 - b^2)*b*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (a^2 - b^2)*log(sin(d*x + c) + 1) + (a^2 - b^2)*log(-sin(d*x + c) + 1))/((a^3 - a*b^2)*d)]","A",0
456,1,382,0,1.298864," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} b^{2} \cos\left(d x + c\right) \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cos\left(d x + c\right)}, \frac{2 \, \sqrt{a^{2} - b^{2}} b^{2} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right) - {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\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*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + (a^2*b - b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) - (a^2*b - b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d*cos(d*x + c)), 1/2*(2*sqrt(a^2 - b^2)*b^2*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c) - (a^2*b - b^3)*cos(d*x + c)*log(sin(d*x + c) + 1) + (a^2*b - b^3)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d*cos(d*x + c))]","B",0
457,1,459,0,1.683753," ","integrate(sec(d*x+c)^3/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-a^{2} + b^{2}} b^{3} \cos\left(d x + c\right)^{2} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} - a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2}}, -\frac{4 \, \sqrt{a^{2} - b^{2}} b^{3} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} - a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[-1/4*(2*sqrt(-a^2 + b^2)*b^3*cos(d*x + c)^2*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (a^4 + a^2*b^2 - 2*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (a^4 + a^2*b^2 - 2*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(a^4 - a^2*b^2 - 2*(a^3*b - a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d*cos(d*x + c)^2), -1/4*(4*sqrt(a^2 - b^2)*b^3*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^2 - (a^4 + a^2*b^2 - 2*b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (a^4 + a^2*b^2 - 2*b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(a^4 - a^2*b^2 - 2*(a^3*b - a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d*cos(d*x + c)^2)]","A",0
458,1,535,0,1.349115," ","integrate(sec(d*x+c)^4/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{-a^{2} + b^{2}} b^{4} \cos\left(d x + c\right)^{3} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 3 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a^{5} - 2 \, a^{3} b^{2} + 2 \, {\left(2 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(d x + c\right)^{3}}, \frac{12 \, \sqrt{a^{2} - b^{2}} b^{4} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{5} - 2 \, a^{3} b^{2} + 2 \, {\left(2 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{6} - a^{4} b^{2}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/12*(6*sqrt(-a^2 + b^2)*b^4*cos(d*x + c)^3*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 3*(a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) - 2*(2*a^5 - 2*a^3*b^2 + 2*(2*a^5 + a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 - 3*(a^4*b - a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d*cos(d*x + c)^3), 1/12*(12*sqrt(a^2 - b^2)*b^4*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^3 - 3*(a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*a^5 - 2*a^3*b^2 + 2*(2*a^5 + a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 - 3*(a^4*b - a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6 - a^4*b^2)*d*cos(d*x + c)^3)]","A",0
459,1,747,0,1.298480," ","integrate(cos(d*x+c)^5/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(4 \, a^{7} b - 7 \, a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(4 \, a^{8} - 7 \, a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} d x + 3 \, {\left(4 \, a^{7} - 5 \, a^{5} b^{2} + {\left(4 \, a^{6} b - 5 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(12 \, a^{7} b - 19 \, a^{5} b^{3} + 5 \, a^{3} b^{5} + 2 \, a b^{7} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d\right)}}, -\frac{3 \, {\left(4 \, a^{7} b - 7 \, a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(4 \, a^{8} - 7 \, a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} d x - 3 \, {\left(4 \, a^{7} - 5 \, a^{5} b^{2} + {\left(4 \, a^{6} b - 5 \, a^{4} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(12 \, a^{7} b - 19 \, a^{5} b^{3} + 5 \, a^{3} b^{5} + 2 \, a b^{7} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d\right)}}\right]"," ",0,"[-1/6*(6*(4*a^7*b - 7*a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*x*cos(d*x + c) + 6*(4*a^8 - 7*a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*d*x + 3*(4*a^7 - 5*a^5*b^2 + (4*a^6*b - 5*a^4*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(12*a^7*b - 19*a^5*b^3 + 5*a^3*b^5 + 2*a*b^7 + (a^4*b^4 - 2*a^2*b^6 + b^8)*cos(d*x + c)^3 - 2*(a^5*b^3 - 2*a^3*b^5 + a*b^7)*cos(d*x + c)^2 + 2*(3*a^6*b^2 - 5*a^4*b^4 + a^2*b^6 + b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c) + (a^5*b^5 - 2*a^3*b^7 + a*b^9)*d), -1/3*(3*(4*a^7*b - 7*a^5*b^3 + 2*a^3*b^5 + a*b^7)*d*x*cos(d*x + c) + 3*(4*a^8 - 7*a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*d*x - 3*(4*a^7 - 5*a^5*b^2 + (4*a^6*b - 5*a^4*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (12*a^7*b - 19*a^5*b^3 + 5*a^3*b^5 + 2*a*b^7 + (a^4*b^4 - 2*a^2*b^6 + b^8)*cos(d*x + c)^3 - 2*(a^5*b^3 - 2*a^3*b^5 + a*b^7)*cos(d*x + c)^2 + 2*(3*a^6*b^2 - 5*a^4*b^4 + a^2*b^6 + b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c) + (a^5*b^5 - 2*a^3*b^7 + a*b^9)*d)]","A",0
460,1,651,0,1.053720," ","integrate(cos(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(6 \, a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, a^{7} - 11 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + a b^{6}\right)} d x - {\left(3 \, a^{6} - 4 \, a^{4} b^{2} + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(6 \, a^{6} b - 10 \, a^{4} b^{3} + 4 \, a^{2} b^{5} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d\right)}}, \frac{{\left(6 \, a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + b^{7}\right)} d x \cos\left(d x + c\right) + {\left(6 \, a^{7} - 11 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + a b^{6}\right)} d x - 2 \, {\left(3 \, a^{6} - 4 \, a^{4} b^{2} + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, a^{6} b - 10 \, a^{4} b^{3} + 4 \, a^{2} b^{5} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d\right)}}\right]"," ",0,"[1/2*((6*a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + b^7)*d*x*cos(d*x + c) + (6*a^7 - 11*a^5*b^2 + 4*a^3*b^4 + a*b^6)*d*x - (3*a^6 - 4*a^4*b^2 + (3*a^5*b - 4*a^3*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (6*a^6*b - 10*a^4*b^3 + 4*a^2*b^5 - (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2 + 3*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c) + (a^5*b^4 - 2*a^3*b^6 + a*b^8)*d), 1/2*((6*a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + b^7)*d*x*cos(d*x + c) + (6*a^7 - 11*a^5*b^2 + 4*a^3*b^4 + a*b^6)*d*x - 2*(3*a^6 - 4*a^4*b^2 + (3*a^5*b - 4*a^3*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*a^6*b - 10*a^4*b^3 + 4*a^2*b^5 - (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2 + 3*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c) + (a^5*b^4 - 2*a^3*b^6 + a*b^8)*d)]","A",0
461,1,554,0,1.739100," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x + {\left(2 \, a^{5} - 3 \, a^{3} b^{2} + {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} d\right)}}, -\frac{2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x - {\left(2 \, a^{5} - 3 \, a^{3} b^{2} + {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5} + {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} d}\right]"," ",0,"[-1/2*(4*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x*cos(d*x + c) + 4*(a^6 - 2*a^4*b^2 + a^2*b^4)*d*x + (2*a^5 - 3*a^3*b^2 + (2*a^4*b - 3*a^2*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(2*a^5*b - 3*a^3*b^3 + a*b^5 + (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*d*cos(d*x + c) + (a^5*b^3 - 2*a^3*b^5 + a*b^7)*d), -(2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x*cos(d*x + c) + 2*(a^6 - 2*a^4*b^2 + a^2*b^4)*d*x - (2*a^5 - 3*a^3*b^2 + (2*a^4*b - 3*a^2*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*a^5*b - 3*a^3*b^3 + a*b^5 + (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^4 - 2*a^2*b^6 + b^8)*d*cos(d*x + c) + (a^5*b^3 - 2*a^3*b^5 + a*b^7)*d)]","A",0
462,1,470,0,1.410249," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x - {\left(a^{4} - 2 \, a^{2} b^{2} + {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d\right)}}, \frac{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x - {\left(a^{4} - 2 \, a^{2} b^{2} + {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d}\right]"," ",0,"[1/2*(2*(a^4*b - 2*a^2*b^3 + b^5)*d*x*cos(d*x + c) + 2*(a^5 - 2*a^3*b^2 + a*b^4)*d*x - (a^4 - 2*a^2*b^2 + (a^3*b - 2*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(a^4*b - a^2*b^3)*sin(d*x + c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d*cos(d*x + c) + (a^5*b^2 - 2*a^3*b^4 + a*b^6)*d), ((a^4*b - 2*a^2*b^3 + b^5)*d*x*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d*x - (a^4 - 2*a^2*b^2 + (a^3*b - 2*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (a^4*b - a^2*b^3)*sin(d*x + c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d*cos(d*x + c) + (a^5*b^2 - 2*a^3*b^4 + a*b^6)*d)]","B",0
463,1,321,0,1.003338," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} \cos\left(d x + c\right) + a b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}, -\frac{{\left(b^{2} \cos\left(d x + c\right) + a b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d}\right]"," ",0,"[1/2*((b^2*cos(d*x + c) + a*b)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d), -((b^2*cos(d*x + c) + a*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (a^3 - a*b^2)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d)]","A",0
464,1,320,0,1.351682," ","integrate(1/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}, \frac{{\left(a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d}\right]"," ",0,"[1/2*((a*b*cos(d*x + c) + a^2)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(a^2*b - b^3)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d), ((a*b*cos(d*x + c) + a^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (a^2*b - b^3)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d)]","A",0
465,1,592,0,1.856820," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a^{3} b - a b^{3} + {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)}}, -\frac{2 \, {\left(2 \, a^{3} b - a b^{3} + {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cos\left(d x + c\right) + {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)}}\right]"," ",0,"[-1/2*((2*a^3*b - a*b^3 + (2*a^2*b^2 - b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - (a^5 - 2*a^3*b^2 + a*b^4 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + (a^5 - 2*a^3*b^2 + a*b^4 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(a^3*b^2 - a*b^4)*sin(d*x + c))/((a^6*b - 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c) + (a^7 - 2*a^5*b^2 + a^3*b^4)*d), -1/2*(2*(2*a^3*b - a*b^3 + (2*a^2*b^2 - b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (a^5 - 2*a^3*b^2 + a*b^4 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + (a^5 - 2*a^3*b^2 + a*b^4 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(a^3*b^2 - a*b^4)*sin(d*x + c))/((a^6*b - 2*a^4*b^3 + a^2*b^5)*d*cos(d*x + c) + (a^7 - 2*a^5*b^2 + a^3*b^4)*d)]","B",0
466,1,750,0,2.113138," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(d x + c\right)\right)}}, \frac{{\left({\left(3 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(((3*a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + (3*a^3*b^2 - 2*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*((a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + (a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) - 2*((a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + (a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(a^6 - 2*a^4*b^2 + a^2*b^4 + (a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b - 2*a^5*b^3 + a^3*b^5)*d*cos(d*x + c)^2 + (a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(d*x + c)), (((3*a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + (3*a^3*b^2 - 2*a*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - ((a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + (a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*log(sin(d*x + c) + 1) + ((a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + (a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (a^6 - 2*a^4*b^2 + a^2*b^4 + (a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b - 2*a^5*b^3 + a^3*b^5)*d*cos(d*x + c)^2 + (a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(d*x + c))]","B",0
467,1,899,0,3.271082," ","integrate(sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left({\left(4 \, a^{2} b^{4} - 3 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left({\left(a^{6} b + 4 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 6 \, b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{6} b + 4 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 6 \, b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} - 2 \, {\left(2 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)}}, -\frac{4 \, {\left({\left(4 \, a^{2} b^{4} - 3 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left({\left(a^{6} b + 4 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 6 \, b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{6} b + 4 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 6 \, b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4} - 2 \, {\left(2 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/4*(2*((4*a^2*b^4 - 3*b^6)*cos(d*x + c)^3 + (4*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - ((a^6*b + 4*a^4*b^3 - 11*a^2*b^5 + 6*b^7)*cos(d*x + c)^3 + (a^7 + 4*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^6*b + 4*a^4*b^3 - 11*a^2*b^5 + 6*b^7)*cos(d*x + c)^3 + (a^7 + 4*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^7 - 2*a^5*b^2 + a^3*b^4 - 2*(2*a^5*b^2 - 5*a^3*b^4 + 3*a*b^6)*cos(d*x + c)^2 - 3*(a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b - 2*a^6*b^3 + a^4*b^5)*d*cos(d*x + c)^3 + (a^9 - 2*a^7*b^2 + a^5*b^4)*d*cos(d*x + c)^2), -1/4*(4*((4*a^2*b^4 - 3*b^6)*cos(d*x + c)^3 + (4*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - ((a^6*b + 4*a^4*b^3 - 11*a^2*b^5 + 6*b^7)*cos(d*x + c)^3 + (a^7 + 4*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^6*b + 4*a^4*b^3 - 11*a^2*b^5 + 6*b^7)*cos(d*x + c)^3 + (a^7 + 4*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^7 - 2*a^5*b^2 + a^3*b^4 - 2*(2*a^5*b^2 - 5*a^3*b^4 + 3*a*b^6)*cos(d*x + c)^2 - 3*(a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b - 2*a^6*b^3 + a^4*b^5)*d*cos(d*x + c)^3 + (a^9 - 2*a^7*b^2 + a^5*b^4)*d*cos(d*x + c)^2)]","B",0
468,1,1001,0,2.773736," ","integrate(sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{3} b^{4} - 4 \, a b^{6}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 3 \, {\left({\left(a^{6} b^{2} + 2 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + 4 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{7} b + 2 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 4 \, a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(a^{6} b^{2} + 2 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + 4 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{7} b + 2 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 4 \, a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4} + {\left(2 \, a^{7} b + 5 \, a^{5} b^{3} - 19 \, a^{3} b^{5} + 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{8} + a^{6} b^{2} - 5 \, a^{4} b^{4} + 3 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)}}, \frac{6 \, {\left({\left(5 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{3} b^{4} - 4 \, a b^{6}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - 3 \, {\left({\left(a^{6} b^{2} + 2 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + 4 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{7} b + 2 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 4 \, a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(a^{6} b^{2} + 2 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + 4 \, b^{8}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{7} b + 2 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 4 \, a b^{7}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4} + {\left(2 \, a^{7} b + 5 \, a^{5} b^{3} - 19 \, a^{3} b^{5} + 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{8} + a^{6} b^{2} - 5 \, a^{4} b^{4} + 3 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{4} + {\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[-1/6*(3*((5*a^2*b^5 - 4*b^7)*cos(d*x + c)^4 + (5*a^3*b^4 - 4*a*b^6)*cos(d*x + c)^3)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 3*((a^6*b^2 + 2*a^4*b^4 - 7*a^2*b^6 + 4*b^8)*cos(d*x + c)^4 + (a^7*b + 2*a^5*b^3 - 7*a^3*b^5 + 4*a*b^7)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) - 3*((a^6*b^2 + 2*a^4*b^4 - 7*a^2*b^6 + 4*b^8)*cos(d*x + c)^4 + (a^7*b + 2*a^5*b^3 - 7*a^3*b^5 + 4*a*b^7)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 2*(a^8 - 2*a^6*b^2 + a^4*b^4 + (2*a^7*b + 5*a^5*b^3 - 19*a^3*b^5 + 12*a*b^7)*cos(d*x + c)^3 + 2*(a^8 + a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6)*cos(d*x + c)^2 - 2*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^4 + (a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c)^3), 1/6*(6*((5*a^2*b^5 - 4*b^7)*cos(d*x + c)^4 + (5*a^3*b^4 - 4*a*b^6)*cos(d*x + c)^3)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*((a^6*b^2 + 2*a^4*b^4 - 7*a^2*b^6 + 4*b^8)*cos(d*x + c)^4 + (a^7*b + 2*a^5*b^3 - 7*a^3*b^5 + 4*a*b^7)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 3*((a^6*b^2 + 2*a^4*b^4 - 7*a^2*b^6 + 4*b^8)*cos(d*x + c)^4 + (a^7*b + 2*a^5*b^3 - 7*a^3*b^5 + 4*a*b^7)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) + 2*(a^8 - 2*a^6*b^2 + a^4*b^4 + (2*a^7*b + 5*a^5*b^3 - 19*a^3*b^5 + 12*a*b^7)*cos(d*x + c)^3 + 2*(a^8 + a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6)*cos(d*x + c)^2 - 2*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^4 + (a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c)^3)]","A",0
469,1,1161,0,1.205204," ","integrate(cos(d*x+c)^5/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(12 \, a^{8} b^{2} - 35 \, a^{6} b^{4} + 33 \, a^{4} b^{6} - 9 \, a^{2} b^{8} - b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(12 \, a^{9} b - 35 \, a^{7} b^{3} + 33 \, a^{5} b^{5} - 9 \, a^{3} b^{7} - a b^{9}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(12 \, a^{10} - 35 \, a^{8} b^{2} + 33 \, a^{6} b^{4} - 9 \, a^{4} b^{6} - a^{2} b^{8}\right)} d x - {\left(12 \, a^{9} - 29 \, a^{7} b^{2} + 20 \, a^{5} b^{4} + {\left(12 \, a^{7} b^{2} - 29 \, a^{5} b^{4} + 20 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{8} b - 29 \, a^{6} b^{3} + 20 \, a^{4} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(12 \, a^{9} b - 33 \, a^{7} b^{3} + 27 \, a^{5} b^{5} - 6 \, a^{3} b^{7} - {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, a^{8} b^{2} - 50 \, a^{6} b^{4} + 43 \, a^{4} b^{6} - 11 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{7} - 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{6} - 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} - a b^{12}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{5} - 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} - a^{2} b^{11}\right)} d\right)}}, \frac{{\left(12 \, a^{8} b^{2} - 35 \, a^{6} b^{4} + 33 \, a^{4} b^{6} - 9 \, a^{2} b^{8} - b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{9} b - 35 \, a^{7} b^{3} + 33 \, a^{5} b^{5} - 9 \, a^{3} b^{7} - a b^{9}\right)} d x \cos\left(d x + c\right) + {\left(12 \, a^{10} - 35 \, a^{8} b^{2} + 33 \, a^{6} b^{4} - 9 \, a^{4} b^{6} - a^{2} b^{8}\right)} d x - {\left(12 \, a^{9} - 29 \, a^{7} b^{2} + 20 \, a^{5} b^{4} + {\left(12 \, a^{7} b^{2} - 29 \, a^{5} b^{4} + 20 \, a^{3} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{8} b - 29 \, a^{6} b^{3} + 20 \, a^{4} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(12 \, a^{9} b - 33 \, a^{7} b^{3} + 27 \, a^{5} b^{5} - 6 \, a^{3} b^{7} - {\left(a^{6} b^{4} - 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} - b^{10}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{7} b^{3} - 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} - a b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, a^{8} b^{2} - 50 \, a^{6} b^{4} + 43 \, a^{4} b^{6} - 11 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{7} - 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} - b^{13}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{6} - 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} - a b^{12}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{5} - 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} - a^{2} b^{11}\right)} d\right)}}\right]"," ",0,"[1/4*(2*(12*a^8*b^2 - 35*a^6*b^4 + 33*a^4*b^6 - 9*a^2*b^8 - b^10)*d*x*cos(d*x + c)^2 + 4*(12*a^9*b - 35*a^7*b^3 + 33*a^5*b^5 - 9*a^3*b^7 - a*b^9)*d*x*cos(d*x + c) + 2*(12*a^10 - 35*a^8*b^2 + 33*a^6*b^4 - 9*a^4*b^6 - a^2*b^8)*d*x - (12*a^9 - 29*a^7*b^2 + 20*a^5*b^4 + (12*a^7*b^2 - 29*a^5*b^4 + 20*a^3*b^6)*cos(d*x + c)^2 + 2*(12*a^8*b - 29*a^6*b^3 + 20*a^4*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(12*a^9*b - 33*a^7*b^3 + 27*a^5*b^5 - 6*a^3*b^7 - (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*cos(d*x + c)^3 + 4*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9)*cos(d*x + c)^2 + (18*a^8*b^2 - 50*a^6*b^4 + 43*a^4*b^6 - 11*a^2*b^8)*cos(d*x + c))*sin(d*x + c))/((a^6*b^7 - 3*a^4*b^9 + 3*a^2*b^11 - b^13)*d*cos(d*x + c)^2 + 2*(a^7*b^6 - 3*a^5*b^8 + 3*a^3*b^10 - a*b^12)*d*cos(d*x + c) + (a^8*b^5 - 3*a^6*b^7 + 3*a^4*b^9 - a^2*b^11)*d), 1/2*((12*a^8*b^2 - 35*a^6*b^4 + 33*a^4*b^6 - 9*a^2*b^8 - b^10)*d*x*cos(d*x + c)^2 + 2*(12*a^9*b - 35*a^7*b^3 + 33*a^5*b^5 - 9*a^3*b^7 - a*b^9)*d*x*cos(d*x + c) + (12*a^10 - 35*a^8*b^2 + 33*a^6*b^4 - 9*a^4*b^6 - a^2*b^8)*d*x - (12*a^9 - 29*a^7*b^2 + 20*a^5*b^4 + (12*a^7*b^2 - 29*a^5*b^4 + 20*a^3*b^6)*cos(d*x + c)^2 + 2*(12*a^8*b - 29*a^6*b^3 + 20*a^4*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (12*a^9*b - 33*a^7*b^3 + 27*a^5*b^5 - 6*a^3*b^7 - (a^6*b^4 - 3*a^4*b^6 + 3*a^2*b^8 - b^10)*cos(d*x + c)^3 + 4*(a^7*b^3 - 3*a^5*b^5 + 3*a^3*b^7 - a*b^9)*cos(d*x + c)^2 + (18*a^8*b^2 - 50*a^6*b^4 + 43*a^4*b^6 - 11*a^2*b^8)*cos(d*x + c))*sin(d*x + c))/((a^6*b^7 - 3*a^4*b^9 + 3*a^2*b^11 - b^13)*d*cos(d*x + c)^2 + 2*(a^7*b^6 - 3*a^5*b^8 + 3*a^3*b^10 - a*b^12)*d*cos(d*x + c) + (a^8*b^5 - 3*a^6*b^7 + 3*a^4*b^9 - a^2*b^11)*d)]","A",0
470,1,1029,0,1.320639," ","integrate(cos(d*x+c)^4/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 24 \, {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d x + 3 \, {\left(2 \, a^{8} - 5 \, a^{6} b^{2} + 4 \, a^{4} b^{4} + {\left(2 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + 4 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{7} b - 5 \, a^{5} b^{3} + 4 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(6 \, a^{8} b - 17 \, a^{6} b^{3} + 13 \, a^{4} b^{5} - 2 \, a^{2} b^{7} + 2 \, {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{7} b^{2} - 25 \, a^{5} b^{4} + 20 \, a^{3} b^{6} - 4 \, a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{5} - 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{4} - 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d\right)}}, -\frac{6 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 12 \, {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d x - 3 \, {\left(2 \, a^{8} - 5 \, a^{6} b^{2} + 4 \, a^{4} b^{4} + {\left(2 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + 4 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{7} b - 5 \, a^{5} b^{3} + 4 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, a^{8} b - 17 \, a^{6} b^{3} + 13 \, a^{4} b^{5} - 2 \, a^{2} b^{7} + 2 \, {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{7} b^{2} - 25 \, a^{5} b^{4} + 20 \, a^{3} b^{6} - 4 \, a b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{5} - 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} - a b^{11}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{4} - 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d\right)}}\right]"," ",0,"[-1/4*(12*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d*x*cos(d*x + c)^2 + 24*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*d*x*cos(d*x + c) + 12*(a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*x + 3*(2*a^8 - 5*a^6*b^2 + 4*a^4*b^4 + (2*a^6*b^2 - 5*a^4*b^4 + 4*a^2*b^6)*cos(d*x + c)^2 + 2*(2*a^7*b - 5*a^5*b^3 + 4*a^3*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(6*a^8*b - 17*a^6*b^3 + 13*a^4*b^5 - 2*a^2*b^7 + 2*(a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*cos(d*x + c)^2 + (9*a^7*b^2 - 25*a^5*b^4 + 20*a^3*b^6 - 4*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*d*cos(d*x + c)^2 + 2*(a^7*b^5 - 3*a^5*b^7 + 3*a^3*b^9 - a*b^11)*d*cos(d*x + c) + (a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10)*d), -1/2*(6*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d*x*cos(d*x + c)^2 + 12*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*d*x*cos(d*x + c) + 6*(a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*x - 3*(2*a^8 - 5*a^6*b^2 + 4*a^4*b^4 + (2*a^6*b^2 - 5*a^4*b^4 + 4*a^2*b^6)*cos(d*x + c)^2 + 2*(2*a^7*b - 5*a^5*b^3 + 4*a^3*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*a^8*b - 17*a^6*b^3 + 13*a^4*b^5 - 2*a^2*b^7 + 2*(a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*cos(d*x + c)^2 + (9*a^7*b^2 - 25*a^5*b^4 + 20*a^3*b^6 - 4*a*b^8)*cos(d*x + c))*sin(d*x + c))/((a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*d*cos(d*x + c)^2 + 2*(a^7*b^5 - 3*a^5*b^7 + 3*a^3*b^9 - a*b^11)*d*cos(d*x + c) + (a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10)*d)]","B",0
471,1,913,0,1.091833," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x \cos\left(d x + c\right) + 4 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x - {\left(2 \, a^{7} - 5 \, a^{5} b^{2} + 6 \, a^{3} b^{4} + {\left(2 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(2 \, a^{7} b - 7 \, a^{5} b^{3} + 5 \, a^{3} b^{5} + 3 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{4} - 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} - a^{2} b^{9}\right)} d\right)}}, \frac{2 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d x - {\left(2 \, a^{7} - 5 \, a^{5} b^{2} + 6 \, a^{3} b^{4} + {\left(2 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{7} b - 7 \, a^{5} b^{3} + 5 \, a^{3} b^{5} + 3 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b^{4} - 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b^{3} - 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} - a^{2} b^{9}\right)} d\right)}}\right]"," ",0,"[1/4*(4*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*x*cos(d*x + c)^2 + 8*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x*cos(d*x + c) + 4*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x - (2*a^7 - 5*a^5*b^2 + 6*a^3*b^4 + (2*a^5*b^2 - 5*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + 2*(2*a^6*b - 5*a^4*b^3 + 6*a^2*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(2*a^7*b - 7*a^5*b^3 + 5*a^3*b^5 + 3*(a^6*b^2 - 3*a^4*b^4 + 2*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*d*cos(d*x + c)^2 + 2*(a^7*b^4 - 3*a^5*b^6 + 3*a^3*b^8 - a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 3*a^6*b^5 + 3*a^4*b^7 - a^2*b^9)*d), 1/2*(2*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*x*cos(d*x + c)^2 + 4*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*d*x*cos(d*x + c) + 2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*x - (2*a^7 - 5*a^5*b^2 + 6*a^3*b^4 + (2*a^5*b^2 - 5*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + 2*(2*a^6*b - 5*a^4*b^3 + 6*a^2*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*a^7*b - 7*a^5*b^3 + 5*a^3*b^5 + 3*(a^6*b^2 - 3*a^4*b^4 + 2*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*d*cos(d*x + c)^2 + 2*(a^7*b^4 - 3*a^5*b^6 + 3*a^3*b^8 - a*b^10)*d*cos(d*x + c) + (a^8*b^3 - 3*a^6*b^5 + 3*a^4*b^7 - a^2*b^9)*d)]","B",0
472,1,587,0,0.818795," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left(3 \, a^{4} b - 3 \, a^{2} b^{3} - {\left(a^{5} - 5 \, a^{3} b^{2} + 4 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\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 \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}, \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(3 \, a^{4} b - 3 \, a^{2} b^{3} - {\left(a^{5} - 5 \, a^{3} b^{2} + 4 \, a b^{4}\right)} \cos\left(d x + c\right)\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 \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*((a^4 + 2*a^2*b^2 + (a^2*b^2 + 2*b^4)*cos(d*x + c)^2 + 2*(a^3*b + 2*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*(3*a^4*b - 3*a^2*b^3 - (a^5 - 5*a^3*b^2 + 4*a*b^4)*cos(d*x + c))*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*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d), 1/2*((a^4 + 2*a^2*b^2 + (a^2*b^2 + 2*b^4)*cos(d*x + c)^2 + 2*(a^3*b + 2*a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (3*a^4*b - 3*a^2*b^3 - (a^5 - 5*a^3*b^2 + 4*a*b^4)*cos(d*x + c))*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*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d)]","A",0
473,1,555,0,0.862000," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{2} b^{2} \cos\left(d x + c\right) + a^{3} b\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4} + {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\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 \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}, -\frac{3 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{2} b^{2} \cos\left(d x + c\right) + a^{3} b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4} + {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)\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 \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*(3*(a*b^3*cos(d*x + c)^2 + 2*a^2*b^2*cos(d*x + c) + a^3*b)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(2*a^5 - a^3*b^2 - a*b^4 + (a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c))*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*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d), -1/2*(3*(a*b^3*cos(d*x + c)^2 + 2*a^2*b^2*cos(d*x + c) + a^3*b)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (2*a^5 - a^3*b^2 - a*b^4 + (a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c))*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*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d)]","B",0
474,1,585,0,0.789673," ","integrate(1/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a^{4} + a^{2} b^{2} + {\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)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5} + 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^{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 \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}, \frac{{\left(2 \, a^{4} + a^{2} b^{2} + {\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)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5} + 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^{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 \cos\left(d x + c\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*((2*a^4 + a^2*b^2 + (2*a^2*b^2 + b^4)*cos(d*x + c)^2 + 2*(2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*(4*a^4*b - 5*a^2*b^3 + b^5 + 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*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*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d), 1/2*((2*a^4 + a^2*b^2 + (2*a^2*b^2 + b^4)*cos(d*x + c)^2 + 2*(2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (4*a^4*b - 5*a^2*b^3 + b^5 + 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*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*cos(d*x + c) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d)]","B",0
475,1,1142,0,2.757001," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5} + {\left(6 \, a^{4} b^{3} - 5 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \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)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \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)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(6 \, a^{6} b^{2} - 9 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + {\left(5 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 2 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{9} b^{2} - 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} - a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d\right)}}, -\frac{{\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5} + {\left(6 \, a^{4} b^{3} - 5 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \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)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} + {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \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)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(6 \, a^{6} b^{2} - 9 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + {\left(5 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 2 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{9} b^{2} - 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} - a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*((6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5 + (6*a^4*b^3 - 5*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + 2*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + 2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(6*a^6*b^2 - 9*a^4*b^4 + 3*a^2*b^6 + (5*a^5*b^3 - 7*a^3*b^5 + 2*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - 3*a^7*b^4 + 3*a^5*b^6 - a^3*b^8)*d*cos(d*x + c)^2 + 2*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c) + (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d), -1/2*((6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5 + (6*a^4*b^3 - 5*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + 2*(6*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 + (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^2 + 2*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (6*a^6*b^2 - 9*a^4*b^4 + 3*a^2*b^6 + (5*a^5*b^3 - 7*a^3*b^5 + 2*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - 3*a^7*b^4 + 3*a^5*b^6 - a^3*b^8)*d*cos(d*x + c)^2 + 2*(a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c) + (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d)]","B",0
476,1,1346,0,2.502934," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, a^{4} b^{4} - 5 \, a^{2} b^{6} + 2 \, b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 2 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 6 \, {\left({\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left({\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a^{9} - 6 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 2 \, a^{3} b^{6} + {\left(2 \, a^{7} b^{2} - 13 \, a^{5} b^{4} + 17 \, a^{3} b^{6} - 6 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, a^{8} b - 20 \, a^{6} b^{3} + 25 \, a^{4} b^{5} - 9 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{10} b^{2} - 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} - a^{4} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{11} b - 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} - a^{5} b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} d \cos\left(d x + c\right)\right)}}, \frac{3 \, {\left({\left(4 \, a^{4} b^{4} - 5 \, a^{2} b^{6} + 2 \, b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 2 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - 3 \, {\left({\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, a^{9} - 6 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 2 \, a^{3} b^{6} + {\left(2 \, a^{7} b^{2} - 13 \, a^{5} b^{4} + 17 \, a^{3} b^{6} - 6 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, a^{8} b - 20 \, a^{6} b^{3} + 25 \, a^{4} b^{5} - 9 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{10} b^{2} - 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} - a^{4} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{11} b - 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} - a^{5} b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(3*((4*a^4*b^4 - 5*a^2*b^6 + 2*b^8)*cos(d*x + c)^3 + 2*(4*a^5*b^3 - 5*a^3*b^5 + 2*a*b^7)*cos(d*x + c)^2 + (4*a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 6*((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*cos(d*x + c)^3 + 2*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*cos(d*x + c)^2 + (a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) - 6*((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*cos(d*x + c)^3 + 2*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*cos(d*x + c)^2 + (a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(2*a^9 - 6*a^7*b^2 + 6*a^5*b^4 - 2*a^3*b^6 + (2*a^7*b^2 - 13*a^5*b^4 + 17*a^3*b^6 - 6*a*b^8)*cos(d*x + c)^2 + (4*a^8*b - 20*a^6*b^3 + 25*a^4*b^5 - 9*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8)*d*cos(d*x + c)^3 + 2*(a^11*b - 3*a^9*b^3 + 3*a^7*b^5 - a^5*b^7)*d*cos(d*x + c)^2 + (a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*d*cos(d*x + c)), 1/2*(3*((4*a^4*b^4 - 5*a^2*b^6 + 2*b^8)*cos(d*x + c)^3 + 2*(4*a^5*b^3 - 5*a^3*b^5 + 2*a*b^7)*cos(d*x + c)^2 + (4*a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*cos(d*x + c)^3 + 2*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*cos(d*x + c)^2 + (a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*cos(d*x + c)^3 + 2*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*cos(d*x + c)^2 + (a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (2*a^9 - 6*a^7*b^2 + 6*a^5*b^4 - 2*a^3*b^6 + (2*a^7*b^2 - 13*a^5*b^4 + 17*a^3*b^6 - 6*a*b^8)*cos(d*x + c)^2 + (4*a^8*b - 20*a^6*b^3 + 25*a^4*b^5 - 9*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/((a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8)*d*cos(d*x + c)^3 + 2*(a^11*b - 3*a^9*b^3 + 3*a^7*b^5 - a^5*b^7)*d*cos(d*x + c)^2 + (a^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*d*cos(d*x + c))]","B",0
477,1,1524,0,6.035649," ","integrate(sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(20 \, a^{4} b^{5} - 29 \, a^{2} b^{7} + 12 \, b^{9}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(20 \, a^{5} b^{4} - 29 \, a^{3} b^{6} + 12 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(20 \, a^{6} b^{3} - 29 \, a^{4} b^{5} + 12 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - {\left({\left(a^{8} b^{2} + 9 \, a^{6} b^{4} - 33 \, a^{4} b^{6} + 35 \, a^{2} b^{8} - 12 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b + 9 \, a^{7} b^{3} - 33 \, a^{5} b^{5} + 35 \, a^{3} b^{7} - 12 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{10} + 9 \, a^{8} b^{2} - 33 \, a^{6} b^{4} + 35 \, a^{4} b^{6} - 12 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{8} b^{2} + 9 \, a^{6} b^{4} - 33 \, a^{4} b^{6} + 35 \, a^{2} b^{8} - 12 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b + 9 \, a^{7} b^{3} - 33 \, a^{5} b^{5} + 35 \, a^{3} b^{7} - 12 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{10} + 9 \, a^{8} b^{2} - 33 \, a^{6} b^{4} + 35 \, a^{4} b^{6} - 12 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6} - 3 \, {\left(2 \, a^{7} b^{3} - 9 \, a^{5} b^{5} + 11 \, a^{3} b^{7} - 4 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left(11 \, a^{8} b^{2} - 43 \, a^{6} b^{4} + 50 \, a^{4} b^{6} - 18 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} b^{2} - 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} - a^{5} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{12} b - 3 \, a^{10} b^{3} + 3 \, a^{8} b^{5} - a^{6} b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{13} - 3 \, a^{11} b^{2} + 3 \, a^{9} b^{4} - a^{7} b^{6}\right)} d \cos\left(d x + c\right)^{2}\right)}}, -\frac{2 \, {\left({\left(20 \, a^{4} b^{5} - 29 \, a^{2} b^{7} + 12 \, b^{9}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(20 \, a^{5} b^{4} - 29 \, a^{3} b^{6} + 12 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + {\left(20 \, a^{6} b^{3} - 29 \, a^{4} b^{5} + 12 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left({\left(a^{8} b^{2} + 9 \, a^{6} b^{4} - 33 \, a^{4} b^{6} + 35 \, a^{2} b^{8} - 12 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b + 9 \, a^{7} b^{3} - 33 \, a^{5} b^{5} + 35 \, a^{3} b^{7} - 12 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{10} + 9 \, a^{8} b^{2} - 33 \, a^{6} b^{4} + 35 \, a^{4} b^{6} - 12 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{8} b^{2} + 9 \, a^{6} b^{4} - 33 \, a^{4} b^{6} + 35 \, a^{2} b^{8} - 12 \, b^{10}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{9} b + 9 \, a^{7} b^{3} - 33 \, a^{5} b^{5} + 35 \, a^{3} b^{7} - 12 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{10} + 9 \, a^{8} b^{2} - 33 \, a^{6} b^{4} + 35 \, a^{4} b^{6} - 12 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6} - 3 \, {\left(2 \, a^{7} b^{3} - 9 \, a^{5} b^{5} + 11 \, a^{3} b^{7} - 4 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left(11 \, a^{8} b^{2} - 43 \, a^{6} b^{4} + 50 \, a^{4} b^{6} - 18 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} b^{2} - 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} - a^{5} b^{8}\right)} d \cos\left(d x + c\right)^{4} + 2 \, {\left(a^{12} b - 3 \, a^{10} b^{3} + 3 \, a^{8} b^{5} - a^{6} b^{7}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{13} - 3 \, a^{11} b^{2} + 3 \, a^{9} b^{4} - a^{7} b^{6}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/4*(((20*a^4*b^5 - 29*a^2*b^7 + 12*b^9)*cos(d*x + c)^4 + 2*(20*a^5*b^4 - 29*a^3*b^6 + 12*a*b^8)*cos(d*x + c)^3 + (20*a^6*b^3 - 29*a^4*b^5 + 12*a^2*b^7)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - ((a^8*b^2 + 9*a^6*b^4 - 33*a^4*b^6 + 35*a^2*b^8 - 12*b^10)*cos(d*x + c)^4 + 2*(a^9*b + 9*a^7*b^3 - 33*a^5*b^5 + 35*a^3*b^7 - 12*a*b^9)*cos(d*x + c)^3 + (a^10 + 9*a^8*b^2 - 33*a^6*b^4 + 35*a^4*b^6 - 12*a^2*b^8)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^8*b^2 + 9*a^6*b^4 - 33*a^4*b^6 + 35*a^2*b^8 - 12*b^10)*cos(d*x + c)^4 + 2*(a^9*b + 9*a^7*b^3 - 33*a^5*b^5 + 35*a^3*b^7 - 12*a*b^9)*cos(d*x + c)^3 + (a^10 + 9*a^8*b^2 - 33*a^6*b^4 + 35*a^4*b^6 - 12*a^2*b^8)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6 - 3*(2*a^7*b^3 - 9*a^5*b^5 + 11*a^3*b^7 - 4*a*b^9)*cos(d*x + c)^3 - (11*a^8*b^2 - 43*a^6*b^4 + 50*a^4*b^6 - 18*a^2*b^8)*cos(d*x + c)^2 - 4*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*cos(d*x + c))*sin(d*x + c))/((a^11*b^2 - 3*a^9*b^4 + 3*a^7*b^6 - a^5*b^8)*d*cos(d*x + c)^4 + 2*(a^12*b - 3*a^10*b^3 + 3*a^8*b^5 - a^6*b^7)*d*cos(d*x + c)^3 + (a^13 - 3*a^11*b^2 + 3*a^9*b^4 - a^7*b^6)*d*cos(d*x + c)^2), -1/4*(2*((20*a^4*b^5 - 29*a^2*b^7 + 12*b^9)*cos(d*x + c)^4 + 2*(20*a^5*b^4 - 29*a^3*b^6 + 12*a*b^8)*cos(d*x + c)^3 + (20*a^6*b^3 - 29*a^4*b^5 + 12*a^2*b^7)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - ((a^8*b^2 + 9*a^6*b^4 - 33*a^4*b^6 + 35*a^2*b^8 - 12*b^10)*cos(d*x + c)^4 + 2*(a^9*b + 9*a^7*b^3 - 33*a^5*b^5 + 35*a^3*b^7 - 12*a*b^9)*cos(d*x + c)^3 + (a^10 + 9*a^8*b^2 - 33*a^6*b^4 + 35*a^4*b^6 - 12*a^2*b^8)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((a^8*b^2 + 9*a^6*b^4 - 33*a^4*b^6 + 35*a^2*b^8 - 12*b^10)*cos(d*x + c)^4 + 2*(a^9*b + 9*a^7*b^3 - 33*a^5*b^5 + 35*a^3*b^7 - 12*a*b^9)*cos(d*x + c)^3 + (a^10 + 9*a^8*b^2 - 33*a^6*b^4 + 35*a^4*b^6 - 12*a^2*b^8)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6 - 3*(2*a^7*b^3 - 9*a^5*b^5 + 11*a^3*b^7 - 4*a*b^9)*cos(d*x + c)^3 - (11*a^8*b^2 - 43*a^6*b^4 + 50*a^4*b^6 - 18*a^2*b^8)*cos(d*x + c)^2 - 4*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*cos(d*x + c))*sin(d*x + c))/((a^11*b^2 - 3*a^9*b^4 + 3*a^7*b^6 - a^5*b^8)*d*cos(d*x + c)^4 + 2*(a^12*b - 3*a^10*b^3 + 3*a^8*b^5 - a^6*b^7)*d*cos(d*x + c)^3 + (a^13 - 3*a^11*b^2 + 3*a^9*b^4 - a^7*b^6)*d*cos(d*x + c)^2)]","B",0
478,1,1593,0,1.268417," ","integrate(cos(d*x+c)^5/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{48 \, {\left(a^{9} b^{3} - 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 144 \, {\left(a^{10} b^{2} - 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} - 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 144 \, {\left(a^{11} b - 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} d x \cos\left(d x + c\right) + 48 \, {\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d x + 3 \, {\left(8 \, a^{11} - 28 \, a^{9} b^{2} + 35 \, a^{7} b^{4} - 20 \, a^{5} b^{6} + {\left(8 \, a^{8} b^{3} - 28 \, a^{6} b^{5} + 35 \, a^{4} b^{7} - 20 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{9} b^{2} - 28 \, a^{7} b^{4} + 35 \, a^{5} b^{6} - 20 \, a^{3} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, a^{10} b - 28 \, a^{8} b^{3} + 35 \, a^{6} b^{5} - 20 \, a^{4} b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(24 \, a^{11} b - 92 \, a^{9} b^{3} + 133 \, a^{7} b^{5} - 71 \, a^{5} b^{7} + 6 \, a^{3} b^{9} + 6 \, {\left(a^{8} b^{4} - 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(44 \, a^{9} b^{3} - 169 \, a^{7} b^{5} + 239 \, a^{5} b^{7} - 132 \, a^{3} b^{9} + 18 \, a b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, a^{10} b^{2} - 77 \, a^{8} b^{4} + 110 \, a^{6} b^{6} - 59 \, a^{4} b^{8} + 6 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{8} - 4 \, a^{6} b^{10} + 6 \, a^{4} b^{12} - 4 \, a^{2} b^{14} + b^{16}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{7} - 4 \, a^{7} b^{9} + 6 \, a^{5} b^{11} - 4 \, a^{3} b^{13} + a b^{15}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{6} - 4 \, a^{8} b^{8} + 6 \, a^{6} b^{10} - 4 \, a^{4} b^{12} + a^{2} b^{14}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{5} - 4 \, a^{9} b^{7} + 6 \, a^{7} b^{9} - 4 \, a^{5} b^{11} + a^{3} b^{13}\right)} d\right)}}, -\frac{24 \, {\left(a^{9} b^{3} - 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 72 \, {\left(a^{10} b^{2} - 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} - 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 72 \, {\left(a^{11} b - 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} d x \cos\left(d x + c\right) + 24 \, {\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} d x - 3 \, {\left(8 \, a^{11} - 28 \, a^{9} b^{2} + 35 \, a^{7} b^{4} - 20 \, a^{5} b^{6} + {\left(8 \, a^{8} b^{3} - 28 \, a^{6} b^{5} + 35 \, a^{4} b^{7} - 20 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{9} b^{2} - 28 \, a^{7} b^{4} + 35 \, a^{5} b^{6} - 20 \, a^{3} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, a^{10} b - 28 \, a^{8} b^{3} + 35 \, a^{6} b^{5} - 20 \, a^{4} b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(24 \, a^{11} b - 92 \, a^{9} b^{3} + 133 \, a^{7} b^{5} - 71 \, a^{5} b^{7} + 6 \, a^{3} b^{9} + 6 \, {\left(a^{8} b^{4} - 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(44 \, a^{9} b^{3} - 169 \, a^{7} b^{5} + 239 \, a^{5} b^{7} - 132 \, a^{3} b^{9} + 18 \, a b^{11}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(20 \, a^{10} b^{2} - 77 \, a^{8} b^{4} + 110 \, a^{6} b^{6} - 59 \, a^{4} b^{8} + 6 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{8} - 4 \, a^{6} b^{10} + 6 \, a^{4} b^{12} - 4 \, a^{2} b^{14} + b^{16}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{7} - 4 \, a^{7} b^{9} + 6 \, a^{5} b^{11} - 4 \, a^{3} b^{13} + a b^{15}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{6} - 4 \, a^{8} b^{8} + 6 \, a^{6} b^{10} - 4 \, a^{4} b^{12} + a^{2} b^{14}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{5} - 4 \, a^{9} b^{7} + 6 \, a^{7} b^{9} - 4 \, a^{5} b^{11} + a^{3} b^{13}\right)} d\right)}}\right]"," ",0,"[-1/12*(48*(a^9*b^3 - 4*a^7*b^5 + 6*a^5*b^7 - 4*a^3*b^9 + a*b^11)*d*x*cos(d*x + c)^3 + 144*(a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10)*d*x*cos(d*x + c)^2 + 144*(a^11*b - 4*a^9*b^3 + 6*a^7*b^5 - 4*a^5*b^7 + a^3*b^9)*d*x*cos(d*x + c) + 48*(a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*d*x + 3*(8*a^11 - 28*a^9*b^2 + 35*a^7*b^4 - 20*a^5*b^6 + (8*a^8*b^3 - 28*a^6*b^5 + 35*a^4*b^7 - 20*a^2*b^9)*cos(d*x + c)^3 + 3*(8*a^9*b^2 - 28*a^7*b^4 + 35*a^5*b^6 - 20*a^3*b^8)*cos(d*x + c)^2 + 3*(8*a^10*b - 28*a^8*b^3 + 35*a^6*b^5 - 20*a^4*b^7)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(24*a^11*b - 92*a^9*b^3 + 133*a^7*b^5 - 71*a^5*b^7 + 6*a^3*b^9 + 6*(a^8*b^4 - 4*a^6*b^6 + 6*a^4*b^8 - 4*a^2*b^10 + b^12)*cos(d*x + c)^3 + (44*a^9*b^3 - 169*a^7*b^5 + 239*a^5*b^7 - 132*a^3*b^9 + 18*a*b^11)*cos(d*x + c)^2 + 3*(20*a^10*b^2 - 77*a^8*b^4 + 110*a^6*b^6 - 59*a^4*b^8 + 6*a^2*b^10)*cos(d*x + c))*sin(d*x + c))/((a^8*b^8 - 4*a^6*b^10 + 6*a^4*b^12 - 4*a^2*b^14 + b^16)*d*cos(d*x + c)^3 + 3*(a^9*b^7 - 4*a^7*b^9 + 6*a^5*b^11 - 4*a^3*b^13 + a*b^15)*d*cos(d*x + c)^2 + 3*(a^10*b^6 - 4*a^8*b^8 + 6*a^6*b^10 - 4*a^4*b^12 + a^2*b^14)*d*cos(d*x + c) + (a^11*b^5 - 4*a^9*b^7 + 6*a^7*b^9 - 4*a^5*b^11 + a^3*b^13)*d), -1/6*(24*(a^9*b^3 - 4*a^7*b^5 + 6*a^5*b^7 - 4*a^3*b^9 + a*b^11)*d*x*cos(d*x + c)^3 + 72*(a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10)*d*x*cos(d*x + c)^2 + 72*(a^11*b - 4*a^9*b^3 + 6*a^7*b^5 - 4*a^5*b^7 + a^3*b^9)*d*x*cos(d*x + c) + 24*(a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*d*x - 3*(8*a^11 - 28*a^9*b^2 + 35*a^7*b^4 - 20*a^5*b^6 + (8*a^8*b^3 - 28*a^6*b^5 + 35*a^4*b^7 - 20*a^2*b^9)*cos(d*x + c)^3 + 3*(8*a^9*b^2 - 28*a^7*b^4 + 35*a^5*b^6 - 20*a^3*b^8)*cos(d*x + c)^2 + 3*(8*a^10*b - 28*a^8*b^3 + 35*a^6*b^5 - 20*a^4*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (24*a^11*b - 92*a^9*b^3 + 133*a^7*b^5 - 71*a^5*b^7 + 6*a^3*b^9 + 6*(a^8*b^4 - 4*a^6*b^6 + 6*a^4*b^8 - 4*a^2*b^10 + b^12)*cos(d*x + c)^3 + (44*a^9*b^3 - 169*a^7*b^5 + 239*a^5*b^7 - 132*a^3*b^9 + 18*a*b^11)*cos(d*x + c)^2 + 3*(20*a^10*b^2 - 77*a^8*b^4 + 110*a^6*b^6 - 59*a^4*b^8 + 6*a^2*b^10)*cos(d*x + c))*sin(d*x + c))/((a^8*b^8 - 4*a^6*b^10 + 6*a^4*b^12 - 4*a^2*b^14 + b^16)*d*cos(d*x + c)^3 + 3*(a^9*b^7 - 4*a^7*b^9 + 6*a^5*b^11 - 4*a^3*b^13 + a*b^15)*d*cos(d*x + c)^2 + 3*(a^10*b^6 - 4*a^8*b^8 + 6*a^6*b^10 - 4*a^4*b^12 + a^2*b^14)*d*cos(d*x + c) + (a^11*b^5 - 4*a^9*b^7 + 6*a^7*b^9 - 4*a^5*b^11 + a^3*b^13)*d)]","B",0
479,1,1445,0,1.294188," ","integrate(cos(d*x+c)^4/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 36 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 36 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d x \cos\left(d x + c\right) + 12 \, {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d x - 3 \, {\left(2 \, a^{10} - 7 \, a^{8} b^{2} + 8 \, a^{6} b^{4} - 8 \, a^{4} b^{6} + {\left(2 \, a^{7} b^{3} - 7 \, a^{5} b^{5} + 8 \, a^{3} b^{7} - 8 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{8} b^{2} - 7 \, a^{6} b^{4} + 8 \, a^{4} b^{6} - 8 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{9} b - 7 \, a^{7} b^{3} + 8 \, a^{5} b^{5} - 8 \, a^{3} b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(6 \, a^{10} b - 23 \, a^{8} b^{3} + 43 \, a^{6} b^{5} - 26 \, a^{4} b^{7} + {\left(11 \, a^{8} b^{3} - 43 \, a^{6} b^{5} + 68 \, a^{4} b^{7} - 36 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 7 \, a^{5} b^{6} - 4 \, a^{3} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\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 \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{5} - 4 \, a^{8} b^{7} + 6 \, a^{6} b^{9} - 4 \, a^{4} b^{11} + a^{2} b^{13}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{4} - 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} - 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d\right)}}, \frac{6 \, {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d x - 3 \, {\left(2 \, a^{10} - 7 \, a^{8} b^{2} + 8 \, a^{6} b^{4} - 8 \, a^{4} b^{6} + {\left(2 \, a^{7} b^{3} - 7 \, a^{5} b^{5} + 8 \, a^{3} b^{7} - 8 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{8} b^{2} - 7 \, a^{6} b^{4} + 8 \, a^{4} b^{6} - 8 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{9} b - 7 \, a^{7} b^{3} + 8 \, a^{5} b^{5} - 8 \, a^{3} b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, a^{10} b - 23 \, a^{8} b^{3} + 43 \, a^{6} b^{5} - 26 \, a^{4} b^{7} + {\left(11 \, a^{8} b^{3} - 43 \, a^{6} b^{5} + 68 \, a^{4} b^{7} - 36 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 7 \, a^{5} b^{6} - 4 \, a^{3} b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\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 \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b^{5} - 4 \, a^{8} b^{7} + 6 \, a^{6} b^{9} - 4 \, a^{4} b^{11} + a^{2} b^{13}\right)} d \cos\left(d x + c\right) + {\left(a^{11} b^{4} - 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} - 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d\right)}}\right]"," ",0,"[1/12*(12*(a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*x*cos(d*x + c)^3 + 36*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*x*cos(d*x + c)^2 + 36*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*x*cos(d*x + c) + 12*(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*x - 3*(2*a^10 - 7*a^8*b^2 + 8*a^6*b^4 - 8*a^4*b^6 + (2*a^7*b^3 - 7*a^5*b^5 + 8*a^3*b^7 - 8*a*b^9)*cos(d*x + c)^3 + 3*(2*a^8*b^2 - 7*a^6*b^4 + 8*a^4*b^6 - 8*a^2*b^8)*cos(d*x + c)^2 + 3*(2*a^9*b - 7*a^7*b^3 + 8*a^5*b^5 - 8*a^3*b^7)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(6*a^10*b - 23*a^8*b^3 + 43*a^6*b^5 - 26*a^4*b^7 + (11*a^8*b^3 - 43*a^6*b^5 + 68*a^4*b^7 - 36*a^2*b^9)*cos(d*x + c)^2 + 15*(a^9*b^2 - 4*a^7*b^4 + 7*a^5*b^6 - 4*a^3*b^8)*cos(d*x + c))*sin(d*x + c))/((a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d*cos(d*x + c)^3 + 3*(a^9*b^6 - 4*a^7*b^8 + 6*a^5*b^10 - 4*a^3*b^12 + a*b^14)*d*cos(d*x + c)^2 + 3*(a^10*b^5 - 4*a^8*b^7 + 6*a^6*b^9 - 4*a^4*b^11 + a^2*b^13)*d*cos(d*x + c) + (a^11*b^4 - 4*a^9*b^6 + 6*a^7*b^8 - 4*a^5*b^10 + a^3*b^12)*d), 1/6*(6*(a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*x*cos(d*x + c)^3 + 18*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*x*cos(d*x + c)^2 + 18*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*x*cos(d*x + c) + 6*(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*x - 3*(2*a^10 - 7*a^8*b^2 + 8*a^6*b^4 - 8*a^4*b^6 + (2*a^7*b^3 - 7*a^5*b^5 + 8*a^3*b^7 - 8*a*b^9)*cos(d*x + c)^3 + 3*(2*a^8*b^2 - 7*a^6*b^4 + 8*a^4*b^6 - 8*a^2*b^8)*cos(d*x + c)^2 + 3*(2*a^9*b - 7*a^7*b^3 + 8*a^5*b^5 - 8*a^3*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*a^10*b - 23*a^8*b^3 + 43*a^6*b^5 - 26*a^4*b^7 + (11*a^8*b^3 - 43*a^6*b^5 + 68*a^4*b^7 - 36*a^2*b^9)*cos(d*x + c)^2 + 15*(a^9*b^2 - 4*a^7*b^4 + 7*a^5*b^6 - 4*a^3*b^8)*cos(d*x + c))*sin(d*x + c))/((a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d*cos(d*x + c)^3 + 3*(a^9*b^6 - 4*a^7*b^8 + 6*a^5*b^10 - 4*a^3*b^12 + a*b^14)*d*cos(d*x + c)^2 + 3*(a^10*b^5 - 4*a^8*b^7 + 6*a^6*b^9 - 4*a^4*b^11 + a^2*b^13)*d*cos(d*x + c) + (a^11*b^4 - 4*a^9*b^6 + 6*a^7*b^8 - 4*a^5*b^10 + a^3*b^12)*d)]","B",0
480,1,893,0,1.004254," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, a^{5} b + 2 \, a^{3} b^{3} + {\left(3 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left(4 \, a^{7} + 7 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + {\left(2 \, a^{7} - 7 \, a^{5} b^{2} + 23 \, a^{3} b^{4} - 18 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{6} b + 8 \, a^{4} b^{3} - 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}, -\frac{3 \, {\left(3 \, a^{5} b + 2 \, a^{3} b^{3} + {\left(3 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(4 \, a^{7} + 7 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + {\left(2 \, a^{7} - 7 \, a^{5} b^{2} + 23 \, a^{3} b^{4} - 18 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{6} b + 8 \, a^{4} b^{3} - 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(3*a^5*b + 2*a^3*b^3 + (3*a^2*b^4 + 2*b^6)*cos(d*x + c)^3 + 3*(3*a^3*b^3 + 2*a*b^5)*cos(d*x + c)^2 + 3*(3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*(4*a^7 + 7*a^5*b^2 - 11*a^3*b^4 + (2*a^7 - 7*a^5*b^2 + 23*a^3*b^4 - 18*a*b^6)*cos(d*x + c)^2 + 3*(a^6*b + 8*a^4*b^3 - 9*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d), -1/6*(3*(3*a^5*b + 2*a^3*b^3 + (3*a^2*b^4 + 2*b^6)*cos(d*x + c)^3 + 3*(3*a^3*b^3 + 2*a*b^5)*cos(d*x + c)^2 + 3*(3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (4*a^7 + 7*a^5*b^2 - 11*a^3*b^4 + (2*a^7 - 7*a^5*b^2 + 23*a^3*b^4 - 18*a*b^6)*cos(d*x + c)^2 + 3*(a^6*b + 8*a^4*b^3 - 9*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d)]","A",0
481,1,893,0,0.918486," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{6} + 4 \, a^{4} b^{2} + {\left(a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{5} b + 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(13 \, a^{6} b - 11 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - {\left(a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + 6 \, b^{7}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{7} - 10 \, a^{5} b^{2} + 7 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}, \frac{3 \, {\left(a^{6} + 4 \, a^{4} b^{2} + {\left(a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{5} b + 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(13 \, a^{6} b - 11 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - {\left(a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + 6 \, b^{7}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{7} - 10 \, a^{5} b^{2} + 7 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(a^6 + 4*a^4*b^2 + (a^3*b^3 + 4*a*b^5)*cos(d*x + c)^3 + 3*(a^4*b^2 + 4*a^2*b^4)*cos(d*x + c)^2 + 3*(a^5*b + 4*a^3*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(13*a^6*b - 11*a^4*b^3 - 2*a^2*b^5 - (a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + 6*b^7)*cos(d*x + c)^2 - 3*(a^7 - 10*a^5*b^2 + 7*a^3*b^4 + 2*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d), 1/6*(3*(a^6 + 4*a^4*b^2 + (a^3*b^3 + 4*a*b^5)*cos(d*x + c)^3 + 3*(a^4*b^2 + 4*a^2*b^4)*cos(d*x + c)^2 + 3*(a^5*b + 4*a^3*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (13*a^6*b - 11*a^4*b^3 - 2*a^2*b^5 - (a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + 6*b^7)*cos(d*x + c)^2 - 3*(a^7 - 10*a^5*b^2 + 7*a^3*b^4 + 2*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d)]","B",0
482,1,891,0,0.703409," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, a^{5} b + a^{3} b^{3} + {\left(4 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 2 \, {\left(6 \, a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 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} + 3 \, {\left(2 \, a^{6} b + 7 \, a^{4} b^{3} - 10 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}, -\frac{3 \, {\left(4 \, a^{5} b + a^{3} b^{3} + {\left(4 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(6 \, a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 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} + 3 \, {\left(2 \, a^{6} b + 7 \, a^{4} b^{3} - 10 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(4*a^5*b + a^3*b^3 + (4*a^2*b^4 + b^6)*cos(d*x + c)^3 + 3*(4*a^3*b^3 + a*b^5)*cos(d*x + c)^2 + 3*(4*a^4*b^2 + a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 2*(6*a^7 + 4*a^5*b^2 - 11*a^3*b^4 + a*b^6 + (2*a^5*b^2 + 11*a^3*b^4 - 13*a*b^6)*cos(d*x + c)^2 + 3*(2*a^6*b + 7*a^4*b^3 - 10*a^2*b^5 + b^7)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d), -1/6*(3*(4*a^5*b + a^3*b^3 + (4*a^2*b^4 + b^6)*cos(d*x + c)^3 + 3*(4*a^3*b^3 + a*b^5)*cos(d*x + c)^2 + 3*(4*a^4*b^2 + a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (6*a^7 + 4*a^5*b^2 - 11*a^3*b^4 + a*b^6 + (2*a^5*b^2 + 11*a^3*b^4 - 13*a*b^6)*cos(d*x + c)^2 + 3*(2*a^6*b + 7*a^4*b^3 - 10*a^2*b^5 + b^7)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d)]","B",0
483,1,895,0,1.021764," ","integrate(1/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + {\left(2 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 2 \, {\left(18 \, a^{6} b - 23 \, a^{4} b^{3} + 7 \, a^{2} b^{5} - 2 \, b^{7} + {\left(11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(9 \, a^{5} b^{2} - 8 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}, \frac{3 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + {\left(2 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - {\left(18 \, a^{6} b - 23 \, a^{4} b^{3} + 7 \, a^{2} b^{5} - 2 \, b^{7} + {\left(11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(9 \, a^{5} b^{2} - 8 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(2*a^6 + 3*a^4*b^2 + (2*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3 + 3*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^2 + 3*(2*a^5*b + 3*a^3*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 2*(18*a^6*b - 23*a^4*b^3 + 7*a^2*b^5 - 2*b^7 + (11*a^4*b^3 - 7*a^2*b^5 - 4*b^7)*cos(d*x + c)^2 + 3*(9*a^5*b^2 - 8*a^3*b^4 - a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d), 1/6*(3*(2*a^6 + 3*a^4*b^2 + (2*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3 + 3*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^2 + 3*(2*a^5*b + 3*a^3*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - (18*a^6*b - 23*a^4*b^3 + 7*a^2*b^5 - 2*b^7 + (11*a^4*b^3 - 7*a^2*b^5 - 4*b^7)*cos(d*x + c)^2 + 3*(9*a^5*b^2 - 8*a^3*b^4 - a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*d*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*d*cos(d*x + c) + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d)]","B",0
484,1,1815,0,5.128511," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, a^{9} b - 8 \, a^{7} b^{3} + 7 \, a^{5} b^{5} - 2 \, a^{3} b^{7} + {\left(8 \, a^{6} b^{4} - 8 \, a^{4} b^{6} + 7 \, a^{2} b^{8} - 2 \, b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{7} b^{3} - 8 \, a^{5} b^{5} + 7 \, a^{3} b^{7} - 2 \, a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, a^{8} b^{2} - 8 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - 2 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) - 6 \, {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8} + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8} + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(36 \, a^{9} b^{2} - 68 \, a^{7} b^{4} + 43 \, a^{5} b^{6} - 11 \, a^{3} b^{8} + {\left(26 \, a^{7} b^{4} - 43 \, a^{5} b^{6} + 23 \, a^{3} b^{8} - 6 \, a b^{10}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, a^{8} b^{3} - 7 \, a^{6} b^{5} + 4 \, a^{4} b^{7} - a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{12} b^{3} - 4 \, a^{10} b^{5} + 6 \, a^{8} b^{7} - 4 \, a^{6} b^{9} + a^{4} b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{13} b^{2} - 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} - 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d\right)}}, -\frac{3 \, {\left(8 \, a^{9} b - 8 \, a^{7} b^{3} + 7 \, a^{5} b^{5} - 2 \, a^{3} b^{7} + {\left(8 \, a^{6} b^{4} - 8 \, a^{4} b^{6} + 7 \, a^{2} b^{8} - 2 \, b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{7} b^{3} - 8 \, a^{5} b^{5} + 7 \, a^{3} b^{7} - 2 \, a b^{9}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(8 \, a^{8} b^{2} - 8 \, a^{6} b^{4} + 7 \, a^{4} b^{6} - 2 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - 3 \, {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8} + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8} + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{10} b - 4 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 4 \, a^{4} b^{7} + a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - {\left(36 \, a^{9} b^{2} - 68 \, a^{7} b^{4} + 43 \, a^{5} b^{6} - 11 \, a^{3} b^{8} + {\left(26 \, a^{7} b^{4} - 43 \, a^{5} b^{6} + 23 \, a^{3} b^{8} - 6 \, a b^{10}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(4 \, a^{8} b^{3} - 7 \, a^{6} b^{5} + 4 \, a^{4} b^{7} - a^{2} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{12} b^{3} - 4 \, a^{10} b^{5} + 6 \, a^{8} b^{7} - 4 \, a^{6} b^{9} + a^{4} b^{11}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{13} b^{2} - 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} - 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right) + {\left(a^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(8*a^9*b - 8*a^7*b^3 + 7*a^5*b^5 - 2*a^3*b^7 + (8*a^6*b^4 - 8*a^4*b^6 + 7*a^2*b^8 - 2*b^10)*cos(d*x + c)^3 + 3*(8*a^7*b^3 - 8*a^5*b^5 + 7*a^3*b^7 - 2*a*b^9)*cos(d*x + c)^2 + 3*(8*a^8*b^2 - 8*a^6*b^4 + 7*a^4*b^6 - 2*a^2*b^8)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 - 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) - 6*(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8 + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) + 6*(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8 + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(36*a^9*b^2 - 68*a^7*b^4 + 43*a^5*b^6 - 11*a^3*b^8 + (26*a^7*b^4 - 43*a^5*b^6 + 23*a^3*b^8 - 6*a*b^10)*cos(d*x + c)^2 + 15*(4*a^8*b^3 - 7*a^6*b^5 + 4*a^4*b^7 - a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^12*b^3 - 4*a^10*b^5 + 6*a^8*b^7 - 4*a^6*b^9 + a^4*b^11)*d*cos(d*x + c)^3 + 3*(a^13*b^2 - 4*a^11*b^4 + 6*a^9*b^6 - 4*a^7*b^8 + a^5*b^10)*d*cos(d*x + c)^2 + 3*(a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c) + (a^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*d), -1/6*(3*(8*a^9*b - 8*a^7*b^3 + 7*a^5*b^5 - 2*a^3*b^7 + (8*a^6*b^4 - 8*a^4*b^6 + 7*a^2*b^8 - 2*b^10)*cos(d*x + c)^3 + 3*(8*a^7*b^3 - 8*a^5*b^5 + 7*a^3*b^7 - 2*a*b^9)*cos(d*x + c)^2 + 3*(8*a^8*b^2 - 8*a^6*b^4 + 7*a^4*b^6 - 2*a^2*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 3*(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8 + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8 + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*cos(d*x + c)^3 + 3*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c)^2 + 3*(a^10*b - 4*a^8*b^3 + 6*a^6*b^5 - 4*a^4*b^7 + a^2*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) - (36*a^9*b^2 - 68*a^7*b^4 + 43*a^5*b^6 - 11*a^3*b^8 + (26*a^7*b^4 - 43*a^5*b^6 + 23*a^3*b^8 - 6*a*b^10)*cos(d*x + c)^2 + 15*(4*a^8*b^3 - 7*a^6*b^5 + 4*a^4*b^7 - a^2*b^9)*cos(d*x + c))*sin(d*x + c))/((a^12*b^3 - 4*a^10*b^5 + 6*a^8*b^7 - 4*a^6*b^9 + a^4*b^11)*d*cos(d*x + c)^3 + 3*(a^13*b^2 - 4*a^11*b^4 + 6*a^9*b^6 - 4*a^7*b^8 + a^5*b^10)*d*cos(d*x + c)^2 + 3*(a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c) + (a^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*d)]","B",0
485,1,2048,0,6.321308," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(20 \, a^{6} b^{5} - 35 \, a^{4} b^{7} + 28 \, a^{2} b^{9} - 8 \, b^{11}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(20 \, a^{7} b^{4} - 35 \, a^{5} b^{6} + 28 \, a^{3} b^{8} - 8 \, a b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, a^{8} b^{3} - 35 \, a^{6} b^{5} + 28 \, a^{4} b^{7} - 8 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(20 \, a^{9} b^{2} - 35 \, a^{7} b^{4} + 28 \, a^{5} b^{6} - 8 \, a^{3} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right) + 24 \, {\left({\left(a^{8} b^{4} - 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{9} b^{3} - 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{2} - 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} - 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{11} b - 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 24 \, {\left({\left(a^{8} b^{4} - 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{9} b^{3} - 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{2} - 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} - 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{11} b - 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(6 \, a^{12} - 24 \, a^{10} b^{2} + 36 \, a^{8} b^{4} - 24 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + {\left(6 \, a^{9} b^{3} - 71 \, a^{7} b^{5} + 133 \, a^{5} b^{7} - 92 \, a^{3} b^{9} + 24 \, a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{10} b^{2} - 59 \, a^{8} b^{4} + 110 \, a^{6} b^{6} - 77 \, a^{4} b^{8} + 20 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, a^{11} b - 132 \, a^{9} b^{3} + 239 \, a^{7} b^{5} - 169 \, a^{5} b^{7} + 44 \, a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{13} b^{3} - 4 \, a^{11} b^{5} + 6 \, a^{9} b^{7} - 4 \, a^{7} b^{9} + a^{5} b^{11}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{14} b^{2} - 4 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 4 \, a^{8} b^{8} + a^{6} b^{10}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{15} b - 4 \, a^{13} b^{3} + 6 \, a^{11} b^{5} - 4 \, a^{9} b^{7} + a^{7} b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{16} - 4 \, a^{14} b^{2} + 6 \, a^{12} b^{4} - 4 \, a^{10} b^{6} + a^{8} b^{8}\right)} d \cos\left(d x + c\right)\right)}}, \frac{3 \, {\left({\left(20 \, a^{6} b^{5} - 35 \, a^{4} b^{7} + 28 \, a^{2} b^{9} - 8 \, b^{11}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(20 \, a^{7} b^{4} - 35 \, a^{5} b^{6} + 28 \, a^{3} b^{8} - 8 \, a b^{10}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, a^{8} b^{3} - 35 \, a^{6} b^{5} + 28 \, a^{4} b^{7} - 8 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2} + {\left(20 \, a^{9} b^{2} - 35 \, a^{7} b^{4} + 28 \, a^{5} b^{6} - 8 \, a^{3} b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right) - 12 \, {\left({\left(a^{8} b^{4} - 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{9} b^{3} - 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{2} - 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} - 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{11} b - 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 12 \, {\left({\left(a^{8} b^{4} - 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{9} b^{3} - 4 \, a^{7} b^{5} + 6 \, a^{5} b^{7} - 4 \, a^{3} b^{9} + a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{2} - 4 \, a^{8} b^{4} + 6 \, a^{6} b^{6} - 4 \, a^{4} b^{8} + a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{11} b - 4 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 4 \, a^{5} b^{7} + a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, a^{12} - 24 \, a^{10} b^{2} + 36 \, a^{8} b^{4} - 24 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + {\left(6 \, a^{9} b^{3} - 71 \, a^{7} b^{5} + 133 \, a^{5} b^{7} - 92 \, a^{3} b^{9} + 24 \, a b^{11}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{10} b^{2} - 59 \, a^{8} b^{4} + 110 \, a^{6} b^{6} - 77 \, a^{4} b^{8} + 20 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + {\left(18 \, a^{11} b - 132 \, a^{9} b^{3} + 239 \, a^{7} b^{5} - 169 \, a^{5} b^{7} + 44 \, a^{3} b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{13} b^{3} - 4 \, a^{11} b^{5} + 6 \, a^{9} b^{7} - 4 \, a^{7} b^{9} + a^{5} b^{11}\right)} d \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{14} b^{2} - 4 \, a^{12} b^{4} + 6 \, a^{10} b^{6} - 4 \, a^{8} b^{8} + a^{6} b^{10}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{15} b - 4 \, a^{13} b^{3} + 6 \, a^{11} b^{5} - 4 \, a^{9} b^{7} + a^{7} b^{9}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{16} - 4 \, a^{14} b^{2} + 6 \, a^{12} b^{4} - 4 \, a^{10} b^{6} + a^{8} b^{8}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/12*(3*((20*a^6*b^5 - 35*a^4*b^7 + 28*a^2*b^9 - 8*b^11)*cos(d*x + c)^4 + 3*(20*a^7*b^4 - 35*a^5*b^6 + 28*a^3*b^8 - 8*a*b^10)*cos(d*x + c)^3 + 3*(20*a^8*b^3 - 35*a^6*b^5 + 28*a^4*b^7 - 8*a^2*b^9)*cos(d*x + c)^2 + (20*a^9*b^2 - 35*a^7*b^4 + 28*a^5*b^6 - 8*a^3*b^8)*cos(d*x + c))*sqrt(-a^2 + b^2)*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)) + 24*((a^8*b^4 - 4*a^6*b^6 + 6*a^4*b^8 - 4*a^2*b^10 + b^12)*cos(d*x + c)^4 + 3*(a^9*b^3 - 4*a^7*b^5 + 6*a^5*b^7 - 4*a^3*b^9 + a*b^11)*cos(d*x + c)^3 + 3*(a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10)*cos(d*x + c)^2 + (a^11*b - 4*a^9*b^3 + 6*a^7*b^5 - 4*a^5*b^7 + a^3*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) - 24*((a^8*b^4 - 4*a^6*b^6 + 6*a^4*b^8 - 4*a^2*b^10 + b^12)*cos(d*x + c)^4 + 3*(a^9*b^3 - 4*a^7*b^5 + 6*a^5*b^7 - 4*a^3*b^9 + a*b^11)*cos(d*x + c)^3 + 3*(a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10)*cos(d*x + c)^2 + (a^11*b - 4*a^9*b^3 + 6*a^7*b^5 - 4*a^5*b^7 + a^3*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(6*a^12 - 24*a^10*b^2 + 36*a^8*b^4 - 24*a^6*b^6 + 6*a^4*b^8 + (6*a^9*b^3 - 71*a^7*b^5 + 133*a^5*b^7 - 92*a^3*b^9 + 24*a*b^11)*cos(d*x + c)^3 + 3*(6*a^10*b^2 - 59*a^8*b^4 + 110*a^6*b^6 - 77*a^4*b^8 + 20*a^2*b^10)*cos(d*x + c)^2 + (18*a^11*b - 132*a^9*b^3 + 239*a^7*b^5 - 169*a^5*b^7 + 44*a^3*b^9)*cos(d*x + c))*sin(d*x + c))/((a^13*b^3 - 4*a^11*b^5 + 6*a^9*b^7 - 4*a^7*b^9 + a^5*b^11)*d*cos(d*x + c)^4 + 3*(a^14*b^2 - 4*a^12*b^4 + 6*a^10*b^6 - 4*a^8*b^8 + a^6*b^10)*d*cos(d*x + c)^3 + 3*(a^15*b - 4*a^13*b^3 + 6*a^11*b^5 - 4*a^9*b^7 + a^7*b^9)*d*cos(d*x + c)^2 + (a^16 - 4*a^14*b^2 + 6*a^12*b^4 - 4*a^10*b^6 + a^8*b^8)*d*cos(d*x + c)), 1/6*(3*((20*a^6*b^5 - 35*a^4*b^7 + 28*a^2*b^9 - 8*b^11)*cos(d*x + c)^4 + 3*(20*a^7*b^4 - 35*a^5*b^6 + 28*a^3*b^8 - 8*a*b^10)*cos(d*x + c)^3 + 3*(20*a^8*b^3 - 35*a^6*b^5 + 28*a^4*b^7 - 8*a^2*b^9)*cos(d*x + c)^2 + (20*a^9*b^2 - 35*a^7*b^4 + 28*a^5*b^6 - 8*a^3*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))) - 12*((a^8*b^4 - 4*a^6*b^6 + 6*a^4*b^8 - 4*a^2*b^10 + b^12)*cos(d*x + c)^4 + 3*(a^9*b^3 - 4*a^7*b^5 + 6*a^5*b^7 - 4*a^3*b^9 + a*b^11)*cos(d*x + c)^3 + 3*(a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10)*cos(d*x + c)^2 + (a^11*b - 4*a^9*b^3 + 6*a^7*b^5 - 4*a^5*b^7 + a^3*b^9)*cos(d*x + c))*log(sin(d*x + c) + 1) + 12*((a^8*b^4 - 4*a^6*b^6 + 6*a^4*b^8 - 4*a^2*b^10 + b^12)*cos(d*x + c)^4 + 3*(a^9*b^3 - 4*a^7*b^5 + 6*a^5*b^7 - 4*a^3*b^9 + a*b^11)*cos(d*x + c)^3 + 3*(a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 - 4*a^4*b^8 + a^2*b^10)*cos(d*x + c)^2 + (a^11*b - 4*a^9*b^3 + 6*a^7*b^5 - 4*a^5*b^7 + a^3*b^9)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (6*a^12 - 24*a^10*b^2 + 36*a^8*b^4 - 24*a^6*b^6 + 6*a^4*b^8 + (6*a^9*b^3 - 71*a^7*b^5 + 133*a^5*b^7 - 92*a^3*b^9 + 24*a*b^11)*cos(d*x + c)^3 + 3*(6*a^10*b^2 - 59*a^8*b^4 + 110*a^6*b^6 - 77*a^4*b^8 + 20*a^2*b^10)*cos(d*x + c)^2 + (18*a^11*b - 132*a^9*b^3 + 239*a^7*b^5 - 169*a^5*b^7 + 44*a^3*b^9)*cos(d*x + c))*sin(d*x + c))/((a^13*b^3 - 4*a^11*b^5 + 6*a^9*b^7 - 4*a^7*b^9 + a^5*b^11)*d*cos(d*x + c)^4 + 3*(a^14*b^2 - 4*a^12*b^4 + 6*a^10*b^6 - 4*a^8*b^8 + a^6*b^10)*d*cos(d*x + c)^3 + 3*(a^15*b - 4*a^13*b^3 + 6*a^11*b^5 - 4*a^9*b^7 + a^7*b^9)*d*cos(d*x + c)^2 + (a^16 - 4*a^14*b^2 + 6*a^12*b^4 - 4*a^10*b^6 + a^8*b^8)*d*cos(d*x + c))]","B",0
486,0,0,0,1.463804," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
487,0,0,0,0.838243," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
488,0,0,0,0.870616," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right), x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c), x)","F",0
489,0,0,0,0.749704," ","integrate((a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a), x)","F",0
490,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,0,0,0,1.251237," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*cos(d*x + c)^4 + a*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
494,0,0,0,1.331995," ","integrate(cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*cos(d*x + c)^3 + a*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
495,0,0,0,0.868369," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
496,0,0,0,0.782831," ","integrate((a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2), x)","F",0
497,0,0,0,3.557774," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right), x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
498,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,0,0,0,1.383712," ","integrate(cos(d*x+c)^3*(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{5} + 2 \, a b \cos\left(d x + c\right)^{4} + a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^5 + 2*a*b*cos(d*x + c)^4 + a^2*cos(d*x + c)^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
501,0,0,0,1.291824," ","integrate(cos(d*x+c)^2*(a+b*cos(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)^{3} + a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^4 + 2*a*b*cos(d*x + c)^3 + a^2*cos(d*x + c)^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
502,0,0,0,1.186804," ","integrate(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{3} + 2 \, a b \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^3 + 2*a*b*cos(d*x + c)^2 + a^2*cos(d*x + c))*sqrt(b*cos(d*x + c) + a), x)","F",0
503,0,0,0,1.425103," ","integrate((a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a), x)","F",0
504,0,0,0,2.711493," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c), x)","F",0
505,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,0,0,0,1.421372," ","integrate((a+b*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sqrt{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sqrt(b*cos(d*x + c) + a), x)","F",0
509,0,0,0,0.807915," ","integrate(cos(d*x+c)^3*(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{3}, x\right)"," ",0,"integral(sqrt(4*cos(d*x + c) + 3)*cos(d*x + c)^3, x)","F",0
510,0,0,0,1.296835," ","integrate(cos(d*x+c)^2*(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(4*cos(d*x + c) + 3)*cos(d*x + c)^2, x)","F",0
511,0,0,0,1.236410," ","integrate(cos(d*x+c)*(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right), x\right)"," ",0,"integral(sqrt(4*cos(d*x + c) + 3)*cos(d*x + c), x)","F",0
512,0,0,0,1.158436," ","integrate((3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, \cos\left(d x + c\right) + 3}, x\right)"," ",0,"integral(sqrt(4*cos(d*x + c) + 3), x)","F",0
513,0,0,0,2.654568," ","integrate(sec(d*x+c)*(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right), x\right)"," ",0,"integral(sqrt(4*cos(d*x + c) + 3)*sec(d*x + c), x)","F",0
514,0,0,0,1.586097," ","integrate(sec(d*x+c)^2*(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(4*cos(d*x + c) + 3)*sec(d*x + c)^2, x)","F",0
515,0,0,0,1.837837," ","integrate(sec(d*x+c)^3*(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral(sqrt(4*cos(d*x + c) + 3)*sec(d*x + c)^3, x)","F",0
516,0,0,0,1.842849," ","integrate(cos(d*x+c)^3*(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{3}, x\right)"," ",0,"integral(sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c)^3, x)","F",0
517,0,0,0,0.978127," ","integrate(cos(d*x+c)^2*(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c)^2, x)","F",0
518,0,0,0,1.093120," ","integrate(cos(d*x+c)*(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right), x\right)"," ",0,"integral(sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c), x)","F",0
519,0,0,0,1.767126," ","integrate((3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-4 \, \cos\left(d x + c\right) + 3}, x\right)"," ",0,"integral(sqrt(-4*cos(d*x + c) + 3), x)","F",0
520,0,0,0,2.530886," ","integrate(sec(d*x+c)*(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right), x\right)"," ",0,"integral(sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c), x)","F",0
521,0,0,0,1.770541," ","integrate(sec(d*x+c)^2*(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c)^2, x)","F",0
522,0,0,0,1.763845," ","integrate(sec(d*x+c)^3*(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral(sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c)^3, x)","F",0
523,0,0,0,1.537824," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{3}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^3/sqrt(b*cos(d*x + c) + a), x)","F",0
524,0,0,0,0.944076," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{2}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^2/sqrt(b*cos(d*x + c) + a), x)","F",0
525,0,0,0,0.718461," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)/sqrt(b*cos(d*x + c) + a), x)","F",0
526,0,0,0,1.077283," ","integrate(1/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(1/sqrt(b*cos(d*x + c) + a), x)","F",0
527,-1,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
528,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
530,0,0,0,0.980200," ","integrate(cos(d*x+c)^4/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\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 \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^4/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
531,0,0,0,1.416788," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^3/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
532,0,0,0,1.599834," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\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 \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^2/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
533,0,0,0,1.292228," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
534,0,0,0,1.192756," ","integrate(1/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
535,-1,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,0,0,0,2.459852," ","integrate(cos(d*x+c)^5/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{5}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^5/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
539,0,0,0,1.638638," ","integrate(cos(d*x+c)^4/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^4/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
540,0,0,0,1.605259," ","integrate(cos(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^3/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
541,0,0,0,1.773244," ","integrate(cos(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^2/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
542,0,0,0,1.359189," ","integrate(cos(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
543,0,0,0,1.527552," ","integrate(1/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
544,-1,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,0,0,0,2.823377," ","integrate(1/(a+b*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{b^{4} \cos\left(d x + c\right)^{4} + 4 \, a b^{3} \cos\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} + 4 \, a^{3} b \cos\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/(b^4*cos(d*x + c)^4 + 4*a*b^3*cos(d*x + c)^3 + 6*a^2*b^2*cos(d*x + c)^2 + 4*a^3*b*cos(d*x + c) + a^4), x)","F",0
547,0,0,0,1.913189," ","integrate(cos(d*x+c)^3/(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{3}}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(cos(d*x + c)^3/sqrt(4*cos(d*x + c) + 3), x)","F",0
548,0,0,0,1.505625," ","integrate(cos(d*x+c)^2/(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{2}}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(cos(d*x + c)^2/sqrt(4*cos(d*x + c) + 3), x)","F",0
549,0,0,0,1.461387," ","integrate(cos(d*x+c)/(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(cos(d*x + c)/sqrt(4*cos(d*x + c) + 3), x)","F",0
550,0,0,0,1.100644," ","integrate(1/(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(1/sqrt(4*cos(d*x + c) + 3), x)","F",0
551,0,0,0,2.124279," ","integrate(sec(d*x+c)/(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(sec(d*x + c)/sqrt(4*cos(d*x + c) + 3), x)","F",0
552,0,0,0,2.266455," ","integrate(sec(d*x+c)^2/(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{2}}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(sec(d*x + c)^2/sqrt(4*cos(d*x + c) + 3), x)","F",0
553,0,0,0,2.275994," ","integrate(sec(d*x+c)^3/(3+4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{3}}{\sqrt{4 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(sec(d*x + c)^3/sqrt(4*cos(d*x + c) + 3), x)","F",0
554,0,0,0,1.161551," ","integrate(cos(d*x+c)^3/(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{3}}{4 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c)^3/(4*cos(d*x + c) - 3), x)","F",0
555,0,0,0,1.300428," ","integrate(cos(d*x+c)^2/(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)^{2}}{4 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c)^2/(4*cos(d*x + c) - 3), x)","F",0
556,0,0,0,0.742425," ","integrate(cos(d*x+c)/(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-4 \, \cos\left(d x + c\right) + 3} \cos\left(d x + c\right)}{4 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-4*cos(d*x + c) + 3)*cos(d*x + c)/(4*cos(d*x + c) - 3), x)","F",0
557,0,0,0,1.204666," ","integrate(1/(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-4 \, \cos\left(d x + c\right) + 3}}{4 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-4*cos(d*x + c) + 3)/(4*cos(d*x + c) - 3), x)","F",0
558,0,0,0,2.840105," ","integrate(sec(d*x+c)/(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)}{4 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c)/(4*cos(d*x + c) - 3), x)","F",0
559,0,0,0,1.643382," ","integrate(sec(d*x+c)^2/(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{2}}{4 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c)^2/(4*cos(d*x + c) - 3), x)","F",0
560,0,0,0,1.628097," ","integrate(sec(d*x+c)^3/(3-4*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-4 \, \cos\left(d x + c\right) + 3} \sec\left(d x + c\right)^{3}}{4 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-4*cos(d*x + c) + 3)*sec(d*x + c)^3/(4*cos(d*x + c) - 3), x)","F",0
561,0,0,0,2.929317," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
562,0,0,0,1.563947," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
563,0,0,0,2.042186," ","integrate((A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(cos(d*x + c)), x)","F",0
564,0,0,0,1.893376," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/sqrt(cos(d*x + c)), x)","F",0
565,0,0,0,0.978558," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/cos(d*x + c)^(3/2), x)","F",0
566,0,0,0,1.305139," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/cos(d*x + c)^(5/2), x)","F",0
567,0,0,0,1.256242," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/cos(d*x + c)^(7/2), x)","F",0
568,0,0,0,2.058368," ","integrate(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^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)^{3} + a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^4 + 2*a*b*cos(d*x + c)^3 + a^2*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
569,0,0,0,1.538400," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{3} + 2 \, a b \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^3 + 2*a*b*cos(d*x + c)^2 + a^2*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
570,0,0,0,0.854129," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(cos(d*x + c)), x)","F",0
571,0,0,0,1.156826," ","integrate((a+b*cos(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)/sqrt(cos(d*x + c)), x)","F",0
572,0,0,0,0.746773," ","integrate((a+b*cos(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)/cos(d*x + c)^(3/2), x)","F",0
573,0,0,0,1.035855," ","integrate((a+b*cos(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)/cos(d*x + c)^(5/2), x)","F",0
574,0,0,0,1.090827," ","integrate((a+b*cos(d*x+c))^2/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)/cos(d*x + c)^(7/2), x)","F",0
575,0,0,0,1.581808," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{4} + 3 \, a b^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} b \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^4 + 3*a*b^2*cos(d*x + c)^3 + 3*a^2*b*cos(d*x + c)^2 + a^3*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
576,0,0,0,1.150929," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sqrt(cos(d*x + c)), x)","F",0
577,0,0,0,1.827353," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)/sqrt(cos(d*x + c)), x)","F",0
578,0,0,0,1.300390," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)/cos(d*x + c)^(3/2), x)","F",0
579,0,0,0,1.175111," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)/cos(d*x + c)^(5/2), x)","F",0
580,0,0,0,0.851434," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)/cos(d*x + c)^(7/2), x)","F",0
581,0,0,0,0.871926," ","integrate((a+b*cos(d*x+c))^3/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)/cos(d*x + c)^(9/2), x)","F",0
582,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,0,0,0,152.495646," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/(b*cos(d*x + c) + a), x)","F",0
584,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(9/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,0,0,0,160.504466," ","integrate(cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{7}{2}}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(cos(d*x + c)^(7/2)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
597,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,0,0,0,88.705580," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
604,0,0,0,3.067352," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
605,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,0,0,0,1.408880," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
607,0,0,0,1.902820," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
608,0,0,0,2.514941," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
609,0,0,0,1.586202," ","integrate((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
610,0,0,0,3.291713," ","integrate(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
611,0,0,0,3.992195," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
612,0,0,0,1.293955," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)/sqrt(cos(d*x + c)), x)","F",0
613,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,0,0,0,1.407707," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(5/2), x)","F",0
615,0,0,0,1.032318," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(7/2), x)","F",0
616,0,0,0,0.682694," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(9/2), x)","F",0
617,0,0,0,0.762409," ","integrate((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)/cos(d*x + c)^(11/2), x)","F",0
618,0,0,0,2.227004," ","integrate(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
619,0,0,0,3.670745," ","integrate((a+b*cos(d*x+c))^(5/2)/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 \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
620,0,0,0,56.373390," ","integrate((a+b*cos(d*x+c))^(5/2)/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 \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
621,0,0,0,61.289178," ","integrate((a+b*cos(d*x+c))^(5/2)/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 \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
622,0,0,0,1.111394," ","integrate((a+b*cos(d*x+c))^(5/2)/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 \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
623,0,0,0,0.845455," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(9/2), x)","F",0
624,0,0,0,0.937467," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(11/2), x)","F",0
625,0,0,0,0.738371," ","integrate((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\cos\left(d x + c\right)^{\frac{13}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/cos(d*x + c)^(13/2), x)","F",0
626,0,0,0,1.371329," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
627,0,0,0,65.069253," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
628,0,0,0,0.964472," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
629,0,0,0,2.339192," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^3 + a*cos(d*x + c)^2), x)","F",0
630,0,0,0,1.839635," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)^4 + a*cos(d*x + c)^3), x)","F",0
631,0,0,0,3.017469," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
632,0,0,0,81.384910," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
633,0,0,0,1.994998," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
634,0,0,0,1.217846," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{3} + 2 \, a b \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^3 + 2*a*b*cos(d*x + c)^2 + a^2*cos(d*x + c)), x)","F",0
635,0,0,0,0.983873," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{4} + 2 \, a b \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^4 + 2*a*b*cos(d*x + c)^3 + a^2*cos(d*x + c)^2), x)","F",0
636,0,0,0,0.840151," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{5} + 2 \, a b \cos\left(d x + c\right)^{4} + a^{2} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^5 + 2*a*b*cos(d*x + c)^4 + a^2*cos(d*x + c)^3), x)","F",0
637,0,0,0,1.348636," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{6} + 2 \, a b \cos\left(d x + c\right)^{5} + a^{2} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^6 + 2*a*b*cos(d*x + c)^5 + a^2*cos(d*x + c)^4), x)","F",0
638,0,0,0,62.140679," ","integrate(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(5/2)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
639,0,0,0,1.047026," ","integrate(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(3/2)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
640,0,0,0,2.170312," ","integrate(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
641,0,0,0,1.125751," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{4} + 3 \, a b^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} b \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^4 + 3*a*b^2*cos(d*x + c)^3 + 3*a^2*b*cos(d*x + c)^2 + a^3*cos(d*x + c)), x)","F",0
642,0,0,0,2.246848," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{5} + 3 \, a b^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^5 + 3*a*b^2*cos(d*x + c)^4 + 3*a^2*b*cos(d*x + c)^3 + a^3*cos(d*x + c)^2), x)","F",0
643,0,0,0,1.302898," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{6} + 3 \, a b^{2} \cos\left(d x + c\right)^{5} + 3 \, a^{2} b \cos\left(d x + c\right)^{4} + a^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^6 + 3*a*b^2*cos(d*x + c)^5 + 3*a^2*b*cos(d*x + c)^4 + a^3*cos(d*x + c)^3), x)","F",0
644,0,0,0,0.719136," ","integrate(1/cos(d*x+c)^(1/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, \cos\left(d x + c\right) + 2} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))/(3*cos(d*x + c)^2 + 2*cos(d*x + c)), x)","F",0
645,0,0,0,1.878177," ","integrate(1/cos(d*x+c)^(1/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, \cos\left(d x + c\right) - 2} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(3*cos(d*x + c) - 2)*sqrt(cos(d*x + c))/(3*cos(d*x + c)^2 - 2*cos(d*x + c)), x)","F",0
646,0,0,0,1.421735," ","integrate(1/(2-3*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, \cos\left(d x + c\right) + 2} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))/(3*cos(d*x + c)^2 - 2*cos(d*x + c)), x)","F",0
647,0,0,0,1.946503," ","integrate(1/(-2-3*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, \cos\left(d x + c\right) - 2} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-3*cos(d*x + c) - 2)*sqrt(cos(d*x + c))/(3*cos(d*x + c)^2 + 2*cos(d*x + c)), x)","F",0
648,0,0,0,1.611865," ","integrate(1/cos(d*x+c)^(1/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, \cos\left(d x + c\right) + 3} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(2*cos(d*x + c) + 3)*sqrt(cos(d*x + c))/(2*cos(d*x + c)^2 + 3*cos(d*x + c)), x)","F",0
649,0,0,0,0.885009," ","integrate(1/(3-2*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, \cos\left(d x + c\right) + 3} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-2*cos(d*x + c) + 3)*sqrt(cos(d*x + c))/(2*cos(d*x + c)^2 - 3*cos(d*x + c)), x)","F",0
650,0,0,0,1.636423," ","integrate(1/cos(d*x+c)^(1/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, \cos\left(d x + c\right) - 3} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(2*cos(d*x + c) - 3)*sqrt(cos(d*x + c))/(2*cos(d*x + c)^2 - 3*cos(d*x + c)), x)","F",0
651,0,0,0,1.307547," ","integrate(1/(-3-2*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, \cos\left(d x + c\right) - 3} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-2*cos(d*x + c) - 3)*sqrt(cos(d*x + c))/(2*cos(d*x + c)^2 + 3*cos(d*x + c)), x)","F",0
652,0,0,0,0.765035," ","integrate(1/(-cos(d*x+c))^(1/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{3 \, \cos\left(d x + c\right) + 2}}{3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-cos(d*x + c))*sqrt(3*cos(d*x + c) + 2)/(3*cos(d*x + c)^2 + 2*cos(d*x + c)), x)","F",0
653,0,0,0,0.999238," ","integrate(1/(-cos(d*x+c))^(1/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{3 \, \cos\left(d x + c\right) - 2}}{3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-cos(d*x + c))*sqrt(3*cos(d*x + c) - 2)/(3*cos(d*x + c)^2 - 2*cos(d*x + c)), x)","F",0
654,0,0,0,0.807819," ","integrate(1/(2-3*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{-3 \, \cos\left(d x + c\right) + 2}}{3 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(-cos(d*x + c))*sqrt(-3*cos(d*x + c) + 2)/(3*cos(d*x + c)^2 - 2*cos(d*x + c)), x)","F",0
655,0,0,0,0.734623," ","integrate(1/(-2-3*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{-3 \, \cos\left(d x + c\right) - 2}}{3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(-cos(d*x + c))*sqrt(-3*cos(d*x + c) - 2)/(3*cos(d*x + c)^2 + 2*cos(d*x + c)), x)","F",0
656,0,0,0,0.656786," ","integrate(1/(-cos(d*x+c))^(1/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{2 \, \cos\left(d x + c\right) + 3}}{2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-cos(d*x + c))*sqrt(2*cos(d*x + c) + 3)/(2*cos(d*x + c)^2 + 3*cos(d*x + c)), x)","F",0
657,0,0,0,0.864070," ","integrate(1/(3-2*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{-2 \, \cos\left(d x + c\right) + 3}}{2 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(-cos(d*x + c))*sqrt(-2*cos(d*x + c) + 3)/(2*cos(d*x + c)^2 - 3*cos(d*x + c)), x)","F",0
658,0,0,0,1.509832," ","integrate(1/(-cos(d*x+c))^(1/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{2 \, \cos\left(d x + c\right) - 3}}{2 \, \cos\left(d x + c\right)^{2} - 3 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-cos(d*x + c))*sqrt(2*cos(d*x + c) - 3)/(2*cos(d*x + c)^2 - 3*cos(d*x + c)), x)","F",0
659,0,0,0,1.423263," ","integrate(1/(-3-2*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{-2 \, \cos\left(d x + c\right) - 3}}{2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(-cos(d*x + c))*sqrt(-2*cos(d*x + c) - 3)/(2*cos(d*x + c)^2 + 3*cos(d*x + c)), x)","F",0
660,0,0,0,1.949937," ","integrate(cos(d*x+c)^(1/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{3 \, \cos\left(d x + c\right) + 2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/sqrt(3*cos(d*x + c) + 2), x)","F",0
661,0,0,0,2.193272," ","integrate(cos(d*x+c)^(1/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{3 \, \cos\left(d x + c\right) - 2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/sqrt(3*cos(d*x + c) - 2), x)","F",0
662,0,0,0,1.205306," ","integrate(cos(d*x+c)^(1/2)/(2-3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, \cos\left(d x + c\right) + 2} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right) - 2}, x\right)"," ",0,"integral(-sqrt(-3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))/(3*cos(d*x + c) - 2), x)","F",0
663,0,0,0,1.562693," ","integrate(cos(d*x+c)^(1/2)/(-2-3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, \cos\left(d x + c\right) - 2} \sqrt{\cos\left(d x + c\right)}}{3 \, \cos\left(d x + c\right) + 2}, x\right)"," ",0,"integral(-sqrt(-3*cos(d*x + c) - 2)*sqrt(cos(d*x + c))/(3*cos(d*x + c) + 2), x)","F",0
664,0,0,0,1.474048," ","integrate(cos(d*x+c)^(1/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{2 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/sqrt(2*cos(d*x + c) + 3), x)","F",0
665,0,0,0,0.856623," ","integrate(cos(d*x+c)^(1/2)/(3-2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, \cos\left(d x + c\right) + 3} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-2*cos(d*x + c) + 3)*sqrt(cos(d*x + c))/(2*cos(d*x + c) - 3), x)","F",0
666,0,0,0,1.061922," ","integrate(cos(d*x+c)^(1/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{2 \, \cos\left(d x + c\right) - 3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/sqrt(2*cos(d*x + c) - 3), x)","F",0
667,0,0,0,1.325536," ","integrate(cos(d*x+c)^(1/2)/(-3-2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, \cos\left(d x + c\right) - 3} \sqrt{\cos\left(d x + c\right)}}{2 \, \cos\left(d x + c\right) + 3}, x\right)"," ",0,"integral(-sqrt(-2*cos(d*x + c) - 3)*sqrt(cos(d*x + c))/(2*cos(d*x + c) + 3), x)","F",0
668,0,0,0,1.695459," ","integrate((-cos(d*x+c))^(1/2)/(2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{3 \, \cos\left(d x + c\right) + 2}}, x\right)"," ",0,"integral(sqrt(-cos(d*x + c))/sqrt(3*cos(d*x + c) + 2), x)","F",0
669,0,0,0,1.382272," ","integrate((-cos(d*x+c))^(1/2)/(-2+3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{3 \, \cos\left(d x + c\right) - 2}}, x\right)"," ",0,"integral(sqrt(-cos(d*x + c))/sqrt(3*cos(d*x + c) - 2), x)","F",0
670,0,0,0,1.294954," ","integrate((-cos(d*x+c))^(1/2)/(2-3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{-3 \, \cos\left(d x + c\right) + 2}}{3 \, \cos\left(d x + c\right) - 2}, x\right)"," ",0,"integral(-sqrt(-cos(d*x + c))*sqrt(-3*cos(d*x + c) + 2)/(3*cos(d*x + c) - 2), x)","F",0
671,0,0,0,1.402644," ","integrate((-cos(d*x+c))^(1/2)/(-2-3*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{-3 \, \cos\left(d x + c\right) - 2}}{3 \, \cos\left(d x + c\right) + 2}, x\right)"," ",0,"integral(-sqrt(-cos(d*x + c))*sqrt(-3*cos(d*x + c) - 2)/(3*cos(d*x + c) + 2), x)","F",0
672,0,0,0,1.070371," ","integrate((-cos(d*x+c))^(1/2)/(3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{2 \, \cos\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(sqrt(-cos(d*x + c))/sqrt(2*cos(d*x + c) + 3), x)","F",0
673,0,0,0,1.545005," ","integrate((-cos(d*x+c))^(1/2)/(3-2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{-2 \, \cos\left(d x + c\right) + 3}}{2 \, \cos\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-cos(d*x + c))*sqrt(-2*cos(d*x + c) + 3)/(2*cos(d*x + c) - 3), x)","F",0
674,0,0,0,2.047853," ","integrate((-cos(d*x+c))^(1/2)/(-3+2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\cos\left(d x + c\right)}}{\sqrt{2 \, \cos\left(d x + c\right) - 3}}, x\right)"," ",0,"integral(sqrt(-cos(d*x + c))/sqrt(2*cos(d*x + c) - 3), x)","F",0
675,0,0,0,3.855667," ","integrate((-cos(d*x+c))^(1/2)/(-3-2*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\cos\left(d x + c\right)} \sqrt{-2 \, \cos\left(d x + c\right) - 3}}{2 \, \cos\left(d x + c\right) + 3}, x\right)"," ",0,"integral(-sqrt(-cos(d*x + c))*sqrt(-2*cos(d*x + c) - 3)/(2*cos(d*x + c) + 3), x)","F",0
676,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(2/3)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/3)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
678,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(1/3)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
679,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(2/3)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
680,0,0,0,5.659399," ","integrate(cos(d*x+c)^(7/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{7}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^(7/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
681,0,0,0,5.215732," ","integrate(cos(d*x+c)^(5/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^(5/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
682,0,0,0,3.566891," ","integrate(cos(d*x+c)^(4/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{4}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^(4/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
683,0,0,0,3.795509," ","integrate(cos(d*x+c)^(2/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{2}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^(2/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
684,0,0,0,1.965858," ","integrate(cos(d*x+c)^(1/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{1}{3}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^(1/3)/sqrt(b*cos(d*x + c) + a), x)","F",0
685,0,0,0,3.120926," ","integrate(1/cos(d*x+c)^(1/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{2}{3}}}{b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(2/3)/(b*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
686,0,0,0,1.106935," ","integrate(1/cos(d*x+c)^(2/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{1}{3}}}{b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(1/3)/(b*cos(d*x + c)^2 + a*cos(d*x + c)), x)","F",0
687,0,0,0,0.963468," ","integrate(1/cos(d*x+c)^(4/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{2}{3}}}{b \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(2/3)/(b*cos(d*x + c)^3 + a*cos(d*x + c)^2), x)","F",0
688,0,0,0,1.501911," ","integrate(1/cos(d*x+c)^(5/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{1}{3}}}{b \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(1/3)/(b*cos(d*x + c)^3 + a*cos(d*x + c)^2), x)","F",0
689,0,0,0,1.760876," ","integrate(1/cos(d*x+c)^(7/3)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{2}{3}}}{b \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*cos(d*x + c)^(2/3)/(b*cos(d*x + c)^4 + a*cos(d*x + c)^3), x)","F",0
690,0,0,0,1.408212," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(7/2), x)","F",0
691,0,0,0,1.483396," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(5/2), x)","F",0
692,0,0,0,1.360349," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sec(d*x + c)^(3/2), x)","F",0
693,0,0,0,1.050699," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(sec(d*x + c)), x)","F",0
694,0,0,0,1.009036," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/sqrt(sec(d*x + c)), x)","F",0
695,0,0,0,1.011693," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/sec(d*x + c)^(3/2), x)","F",0
696,0,0,0,1.715718," ","integrate((A+B*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/sec(d*x + c)^(5/2), x)","F",0
697,0,0,0,1.228955," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sec(d*x + c)^(9/2), x)","F",0
698,0,0,0,0.842220," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sec(d*x + c)^(7/2), x)","F",0
699,0,0,0,0.624425," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sec(d*x + c)^(5/2), x)","F",0
700,0,0,0,1.646958," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sec(d*x + c)^(3/2), x)","F",0
701,0,0,0,1.318416," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(sec(d*x + c)), x)","F",0
702,0,0,0,2.375489," ","integrate((a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)/sqrt(sec(d*x + c)), x)","F",0
703,0,0,0,2.517759," ","integrate((a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)/sec(d*x + c)^(3/2), x)","F",0
704,0,0,0,2.338722," ","integrate((a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)/sec(d*x + c)^(5/2), x)","F",0
705,0,0,0,0.959415," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^(9/2), x)","F",0
706,0,0,0,2.335609," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^(7/2), x)","F",0
707,0,0,0,1.147416," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^(5/2), x)","F",0
708,0,0,0,0.624710," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^(3/2), x)","F",0
709,0,0,0,1.147883," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sqrt(sec(d*x + c)), x)","F",0
710,0,0,0,1.152519," ","integrate((a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)/sqrt(sec(d*x + c)), x)","F",0
711,0,0,0,1.083425," ","integrate((a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)/sec(d*x + c)^(3/2), x)","F",0
712,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
714,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
715,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
716,0,0,0,80.169898," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(1/((b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
717,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
721,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
723,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
724,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,0,0,0,1.344895," ","integrate(sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
731,0,0,0,1.156018," ","integrate(sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2), x)","F",0
732,0,0,0,1.261262," ","integrate(sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
733,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
734,0,0,0,2.105141," ","integrate((a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
735,0,0,0,59.853698," ","integrate((a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
736,0,0,0,0.873126," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(9/2), x)","F",0
737,0,0,0,0.831939," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(7/2), x)","F",0
738,0,0,0,0.879869," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(5/2), x)","F",0
739,0,0,0,48.677855," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)*sec(d*x + c)^(3/2), x)","F",0
740,0,0,0,53.097095," ","integrate((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)*sqrt(sec(d*x + c)), x)","F",0
741,0,0,0,2.388181," ","integrate((a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
742,0,0,0,2.603303," ","integrate((a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
743,0,0,0,1.263103," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{11}{2}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(11/2), x)","F",0
744,0,0,0,0.830498," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{9}{2}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(9/2), x)","F",0
745,0,0,0,0.862568," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{2}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(7/2), x)","F",0
746,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,0,0,0,67.251162," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2), x)","F",0
748,0,0,0,59.195879," ","integrate((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
749,0,0,0,1.785965," ","integrate((a+b*cos(d*x+c))^(5/2)/sec(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 \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
750,0,0,0,2.919371," ","integrate((a+b*cos(d*x+c))^(5/2)/sec(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 \cos\left(d x + c\right) + a^{2}\right)} \sqrt{b \cos\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(b*cos(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
751,0,0,0,1.268059," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^(5/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
752,0,0,0,0.632990," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^(3/2)/sqrt(b*cos(d*x + c) + a), x)","F",0
753,0,0,0,0.514277," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{b \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/sqrt(b*cos(d*x + c) + a), x)","F",0
754,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,0,0,0,2.129643," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(1/(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)), x)","F",0
756,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,0,0,0,1.364594," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
758,0,0,0,1.334310," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
759,0,0,0,2.247590," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
760,0,0,0,1.517440," ","integrate(1/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sqrt(sec(d*x + c))), x)","F",0
761,0,0,0,61.423151," ","integrate(1/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sec(d*x + c)^(3/2)), x)","F",0
762,0,0,0,40.816156," ","integrate(1/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sec(d*x + c)^(5/2)), x)","F",0
763,0,0,0,1.045245," ","integrate(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(5/2)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
764,0,0,0,0.841380," ","integrate(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sec(d*x + c)^(3/2)/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
765,0,0,0,0.823687," ","integrate(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3), x)","F",0
766,0,0,0,0.690246," ","integrate(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sqrt(sec(d*x + c))), x)","F",0
767,0,0,0,0.560047," ","integrate(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^(3/2)), x)","F",0
768,0,0,0,45.657654," ","integrate(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \cos\left(d x + c\right) + a}}{{\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)/((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^(5/2)), x)","F",0
769,0,0,0,1.004109," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{4} \cos\left(d x + c\right)^{4} + 4 \, a b^{3} \cos\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} + 4 \, a^{3} b \cos\left(d x + c\right) + a^{4}\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b^4*cos(d*x + c)^4 + 4*a*b^3*cos(d*x + c)^3 + 6*a^2*b^2*cos(d*x + c)^2 + 4*a^3*b*cos(d*x + c) + a^4)*cos(d*x + c)^m, x)","F",0
770,0,0,0,0.889931," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*cos(d*x + c)^m, x)","F",0
771,0,0,0,0.999640," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*cos(d*x + c)^m, x)","F",0
772,0,0,0,0.992278," ","integrate(cos(d*x+c)^m*(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)*cos(d*x + c)^m, x)","F",0
773,0,0,0,0.896213," ","integrate(cos(d*x+c)^m/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^m/(b*cos(d*x + c) + a), x)","F",0
774,0,0,0,0.835897," ","integrate(cos(d*x+c)^m/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{m}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(cos(d*x + c)^m/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2), x)","F",0
775,0,0,0,0.974537," ","integrate((a+b*cos(d*x+c))^3*sec(d*x+c)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) + a^{3}\right)} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2 + 3*a^2*b*cos(d*x + c) + a^3)*sec(d*x + c)^m, x)","F",0
776,0,0,0,1.893610," ","integrate((a+b*cos(d*x+c))^2*sec(d*x+c)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}\right)} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)*sec(d*x + c)^m, x)","F",0
777,0,0,0,0.750661," ","integrate((a+b*cos(d*x+c))*sec(d*x+c)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) + a\right)} \sec\left(d x + c\right)^{m}, x\right)"," ",0,"integral((b*cos(d*x + c) + a)*sec(d*x + c)^m, x)","F",0
778,1,30,0,1.848500," ","integrate((1-cos(x))^(1/2)/(a-cos(x))^(1/2),x, algorithm=""fricas"")","\arctan\left(\frac{{\left(a - 2 \, \cos\left(x\right) - 1\right)} \sqrt{-\cos\left(x\right) + 1}}{2 \, \sqrt{a - \cos\left(x\right)} \sin\left(x\right)}\right)"," ",0,"arctan(1/2*(a - 2*cos(x) - 1)*sqrt(-cos(x) + 1)/(sqrt(a - cos(x))*sin(x)))","A",0
779,1,32,0,1.467853," ","integrate(((1-cos(x))/(a-cos(x)))^(1/2),x, algorithm=""fricas"")","-\arctan\left(-\frac{{\left(a - 2 \, \cos\left(x\right) - 1\right)} \sqrt{-\frac{\cos\left(x\right) - 1}{a - \cos\left(x\right)}}}{2 \, \sin\left(x\right)}\right)"," ",0,"-arctan(-1/2*(a - 2*cos(x) - 1)*sqrt(-(cos(x) - 1)/(a - cos(x)))/sin(x))","A",0
780,1,24,0,0.744495," ","integrate((a+a*cos(d*x+c))*(-1/2*B+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(B a \cos\left(d x + c\right) + B a\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*a*cos(d*x + c) + B*a)*sin(d*x + c)/d","A",0
781,1,70,0,0.819788," ","integrate((a+a*cos(d*x+c))^4*(-4/5*B+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(B a^{4} \cos\left(d x + c\right)^{4} + 4 \, B a^{4} \cos\left(d x + c\right)^{3} + 6 \, B a^{4} \cos\left(d x + c\right)^{2} + 4 \, B a^{4} \cos\left(d x + c\right) + B a^{4}\right)} \sin\left(d x + c\right)}{5 \, d}"," ",0,"1/5*(B*a^4*cos(d*x + c)^4 + 4*B*a^4*cos(d*x + c)^3 + 6*B*a^4*cos(d*x + c)^2 + 4*B*a^4*cos(d*x + c) + B*a^4)*sin(d*x + c)/d","B",0
782,1,27,0,1.440021," ","integrate((a+a*cos(d*x+c))^n*(-B*n/(1+n)+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a \cos\left(d x + c\right) + a\right)}^{n} B \sin\left(d x + c\right)}{d n + d}"," ",0,"(a*cos(d*x + c) + a)^n*B*sin(d*x + c)/(d*n + d)","A",0
783,1,56,0,0.751692," ","integrate((-3/2*B+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x, algorithm=""fricas"")","-\frac{B \sin\left(d x + c\right)}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/2*B*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
784,1,36,0,1.032153," ","integrate((a+a*cos(d*x+c))^(3/2)*(-3/5*B+B*cos(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B a \cos\left(d x + c\right) + B a\right)} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{5 \, d}"," ",0,"2/5*(B*a*cos(d*x + c) + B*a)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/d","A",0
785,1,36,0,0.969925," ","integrate((B+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} B \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}"," ",0,"2*sqrt(a*cos(d*x + c) + a)*B*sin(d*x + c)/(a*d*cos(d*x + c) + a*d)","A",0
786,1,68,0,0.956183," ","integrate((-5/3*B+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} B \sin\left(d x + c\right)}{3 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 3 \, a^{3} d \cos\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-2/3*sqrt(a*cos(d*x + c) + a)*B*sin(d*x + c)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 + 3*a^3*d*cos(d*x + c) + a^3*d)","B",0
787,0,0,0,0.905446," ","integrate((a+a*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(2/3), x)","F",0
788,0,0,0,1.094840," ","integrate((a+a*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} {\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(a*cos(d*x + c) + a)^(1/3), x)","F",0
789,0,0,0,1.086095," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/(a*cos(d*x + c) + a)^(1/3), x)","F",0
790,0,0,0,1.048185," ","integrate((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/(a*cos(d*x + c) + a)^(2/3), x)","F",0
791,1,194,0,3.911565," ","integrate((b*B/a+B*cos(d*x+c))/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, B a d x + \sqrt{-a^{2} + b^{2}} B \log\left(\frac{2 \, a b \cos\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(d x + c\right) + b\right)} \sin\left(d x + c\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + a^{2}}\right)}{2 \, a b d}, \frac{B a d x - \sqrt{a^{2} - b^{2}} B \arctan\left(-\frac{a \cos\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(d x + c\right)}\right)}{a b d}\right]"," ",0,"[1/2*(2*B*a*d*x + sqrt(-a^2 + b^2)*B*log((2*a*b*cos(d*x + c) + (2*a^2 - b^2)*cos(d*x + c)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(d*x + c) + b)*sin(d*x + c) - a^2 + 2*b^2)/(b^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + a^2)))/(a*b*d), (B*a*d*x - sqrt(a^2 - b^2)*B*arctan(-(a*cos(d*x + c) + b)/(sqrt(a^2 - b^2)*sin(d*x + c))))/(a*b*d)]","A",0
792,1,22,0,0.824462," ","integrate((a+b*cos(d*x+c))/(b+a*cos(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + b d}"," ",0,"sin(d*x + c)/(a*d*cos(d*x + c) + b*d)","A",0
793,1,43,0,1.880102," ","integrate((3+cos(d*x+c))/(2-cos(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, d x + 5 \, \sqrt{3} \arctan\left(\frac{2 \, \sqrt{3} \cos\left(d x + c\right) - \sqrt{3}}{3 \, \sin\left(d x + c\right)}\right)}{3 \, d}"," ",0,"-1/3*(3*d*x + 5*sqrt(3)*arctan(1/3*(2*sqrt(3)*cos(d*x + c) - sqrt(3))/sin(d*x + c)))/d","A",0
794,0,0,0,0.913521," ","integrate((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \cos\left(d x + c\right) + a} B, x\right)"," ",0,"integral(sqrt(b*cos(d*x + c) + a)*B, x)","F",0
795,0,0,0,1.198985," ","integrate((a+b*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(2/3), x)","F",0
796,0,0,0,0.994531," ","integrate((a+b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} {\left(b \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c) + a)^(1/3), x)","F",0
797,0,0,0,1.068802," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(1/3), x)","F",0
798,0,0,0,0.891886," ","integrate((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \cos\left(d x + c\right) + A}{{\left(b \cos\left(d x + c\right) + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)/(b*cos(d*x + c) + a)^(2/3), x)","F",0
799,0,0,0,0.946290," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c)), x)","F",0
800,0,0,0,2.357666," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c)), x)","F",0
801,0,0,0,2.176256," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c)), x)","F",0
802,0,0,0,0.933540," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right), x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c), x)","F",0
803,0,0,0,1.341255," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^2, x)","F",0
804,0,0,0,1.042737," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^3, x)","F",0
805,0,0,0,0.730145," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^4, x)","F",0
806,0,0,0,0.761656," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{3} + A b \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^3 + A*b*cos(d*x + c)^2)*sqrt(b*cos(d*x + c)), x)","F",0
807,0,0,0,0.954061," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*sqrt(b*cos(d*x + c)), x)","F",0
808,0,0,0,1.075727," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right), x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*sqrt(b*cos(d*x + c))*sec(d*x + c), x)","F",0
809,0,0,0,2.297580," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*sqrt(b*cos(d*x + c))*sec(d*x + c)^2, x)","F",0
810,0,0,0,3.149528," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*sqrt(b*cos(d*x + c))*sec(d*x + c)^3, x)","F",0
811,0,0,0,0.924690," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*sqrt(b*cos(d*x + c))*sec(d*x + c)^4, x)","F",0
812,0,0,0,0.857526," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{5}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*sqrt(b*cos(d*x + c))*sec(d*x + c)^5, x)","F",0
813,0,0,0,2.221382," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A b^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*b^2*cos(d*x + c)^2)*sqrt(b*cos(d*x + c)), x)","F",0
814,0,0,0,1.164032," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A b^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right), x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*b^2*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))*sec(d*x + c), x)","F",0
815,0,0,0,1.173839," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A b^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*b^2*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))*sec(d*x + c)^2, x)","F",0
816,0,0,0,2.035638," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A b^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*b^2*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))*sec(d*x + c)^3, x)","F",0
817,0,0,0,1.094461," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A b^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*b^2*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))*sec(d*x + c)^4, x)","F",0
818,0,0,0,1.040291," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A b^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{5}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*b^2*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))*sec(d*x + c)^5, x)","F",0
819,0,0,0,0.811557," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^6,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} \cos\left(d x + c\right)^{3} + A b^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{6}, x\right)"," ",0,"integral((B*b^2*cos(d*x + c)^3 + A*b^2*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))*sec(d*x + c)^6, x)","F",0
820,0,0,0,1.229457," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)}}{b}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))/b, x)","F",0
821,0,0,0,1.091106," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)}}{b}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c))/b, x)","F",0
822,0,0,0,0.665915," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/b, x)","F",0
823,0,0,0,1.195244," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/(b*cos(d*x + c)), x)","F",0
824,0,0,0,0.879600," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)/(b*cos(d*x + c)), x)","F",0
825,0,0,0,0.929374," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{2}}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^2/(b*cos(d*x + c)), x)","F",0
826,0,0,0,1.147416," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{3}}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^3/(b*cos(d*x + c)), x)","F",0
827,0,0,0,1.081311," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))/b^2, x)","F",0
828,0,0,0,1.805413," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c))/b^2, x)","F",0
829,0,0,0,0.987629," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/b^2, x)","F",0
830,0,0,0,0.869062," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/(b^2*cos(d*x + c)), x)","F",0
831,0,0,0,0.989850," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/(b^2*cos(d*x + c)^2), x)","F",0
832,0,0,0,1.051395," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)}{b^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)/(b^2*cos(d*x + c)^2), x)","F",0
833,0,0,0,1.135171," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)^{2}}{b^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)^2/(b^2*cos(d*x + c)^2), x)","F",0
834,0,0,0,0.949355," ","integrate(cos(d*x+c)^5*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*sqrt(b*cos(d*x + c))/b^3, x)","F",0
835,0,0,0,0.916299," ","integrate(cos(d*x+c)^4*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*sqrt(b*cos(d*x + c))/b^3, x)","F",0
836,0,0,0,0.934280," ","integrate(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/b^3, x)","F",0
837,0,0,0,1.057904," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/(b^3*cos(d*x + c)), x)","F",0
838,0,0,0,0.915659," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/(b^3*cos(d*x + c)^2), x)","F",0
839,0,0,0,0.961600," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/(b^3*cos(d*x + c)^3), x)","F",0
840,0,0,0,0.569434," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sec\left(d x + c\right)}{b^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sec(d*x + c)/(b^3*cos(d*x + c)^3), x)","F",0
841,0,0,0,0.833224," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)}}{b^{4} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))/(b^4*cos(d*x + c)^4), x)","F",0
842,1,252,0,0.844219," ","integrate(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{9 \, B \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(6 \, B \cos\left(d x + c\right)^{3} + 8 \, A \cos\left(d x + c\right)^{2} + 9 \, B \cos\left(d x + c\right) + 16 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)}, \frac{9 \, B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(6 \, B \cos\left(d x + c\right)^{3} + 8 \, A \cos\left(d x + c\right)^{2} + 9 \, B \cos\left(d x + c\right) + 16 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/48*(9*B*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(6*B*cos(d*x + c)^3 + 8*A*cos(d*x + c)^2 + 9*B*cos(d*x + c) + 16*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/24*(9*B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (6*B*cos(d*x + c)^3 + 8*A*cos(d*x + c)^2 + 9*B*cos(d*x + c) + 16*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
843,1,230,0,1.315968," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(2 \, B \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)}, \frac{3 \, A \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(2 \, B \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/12*(3*A*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(2*B*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 4*B)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/6*(3*A*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (2*B*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 4*B)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
844,1,204,0,0.682149," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{B \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)}, \frac{B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/4*(B*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/2*(B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
845,1,181,0,0.940561," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}, \frac{A \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + \sqrt{b \cos\left(d x + c\right)} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(A*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*sqrt(b*cos(d*x + c))*B*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), (A*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + sqrt(b*cos(d*x + c))*B*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
846,1,210,0,1.859398," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, A \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) - B \sqrt{-b} \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right)}{2 \, d}, \frac{2 \, B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) + A \sqrt{b} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right)}{2 \, d}\right]"," ",0,"[-1/2*(2*A*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c)))) - B*sqrt(-b)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b))/d, 1/2*(2*B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2))) + A*sqrt(b)*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3))/d]","A",0
847,1,205,0,0.963341," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{B \sqrt{b} \cos\left(d x + c\right)^{2} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)^{2}}, -\frac{B \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{2} - \sqrt{b \cos\left(d x + c\right)} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/2*(B*sqrt(b)*cos(d*x + c)^2*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*sqrt(b*cos(d*x + c))*A*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2), -(B*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^2 - sqrt(b*cos(d*x + c))*A*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)]","A",0
848,1,225,0,1.018309," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{b} \cos\left(d x + c\right)^{3} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{3}}, -\frac{A \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{3} - {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/4*(A*sqrt(b)*cos(d*x + c)^3*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(2*B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3), -1/2*(A*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^3 - (2*B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)]","A",0
849,1,253,0,1.069227," ","integrate((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, B \sqrt{b} \cos\left(d x + c\right)^{4} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(4 \, A \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{4}}, -\frac{3 \, B \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{4} - {\left(4 \, A \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{4}}\right]"," ",0,"[1/12*(3*B*sqrt(b)*cos(d*x + c)^4*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(4*A*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4), -1/6*(3*B*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^4 - (4*A*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)]","A",0
850,1,261,0,1.134316," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{9 \, B \sqrt{-b} b \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(6 \, B b \cos\left(d x + c\right)^{3} + 8 \, A b \cos\left(d x + c\right)^{2} + 9 \, B b \cos\left(d x + c\right) + 16 \, A b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)}, \frac{9 \, B b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(6 \, B b \cos\left(d x + c\right)^{3} + 8 \, A b \cos\left(d x + c\right)^{2} + 9 \, B b \cos\left(d x + c\right) + 16 \, A b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/48*(9*B*sqrt(-b)*b*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(6*B*b*cos(d*x + c)^3 + 8*A*b*cos(d*x + c)^2 + 9*B*b*cos(d*x + c) + 16*A*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/24*(9*B*b^(3/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (6*B*b*cos(d*x + c)^3 + 8*A*b*cos(d*x + c)^2 + 9*B*b*cos(d*x + c) + 16*A*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
851,1,237,0,1.019693," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{-b} b \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(2 \, B b \cos\left(d x + c\right)^{2} + 3 \, A b \cos\left(d x + c\right) + 4 \, B b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)}, \frac{3 \, A b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(2 \, B b \cos\left(d x + c\right)^{2} + 3 \, A b \cos\left(d x + c\right) + 4 \, B b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/12*(3*A*sqrt(-b)*b*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(2*B*b*cos(d*x + c)^2 + 3*A*b*cos(d*x + c) + 4*B*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/6*(3*A*b^(3/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (2*B*b*cos(d*x + c)^2 + 3*A*b*cos(d*x + c) + 4*B*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
852,1,209,0,1.987305," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{B \sqrt{-b} b \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(B b \cos\left(d x + c\right) + 2 \, A b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)}, \frac{B b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(B b \cos\left(d x + c\right) + 2 \, A b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/4*(B*sqrt(-b)*b*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(B*b*cos(d*x + c) + 2*A*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/2*(B*b^(3/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (B*b*cos(d*x + c) + 2*A*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
853,1,184,0,0.820360," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{-b} b \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} B b \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}, \frac{A b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + \sqrt{b \cos\left(d x + c\right)} B b \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(A*sqrt(-b)*b*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*sqrt(b*cos(d*x + c))*B*b*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), (A*b^(3/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + sqrt(b*cos(d*x + c))*B*b*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
854,1,212,0,1.095984," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{2 \, A \sqrt{-b} b \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) - B \sqrt{-b} b \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right)}{2 \, d}, \frac{2 \, B b^{\frac{3}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) + A b^{\frac{3}{2}} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right)}{2 \, d}\right]"," ",0,"[-1/2*(2*A*sqrt(-b)*b*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c)))) - B*sqrt(-b)*b*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b))/d, 1/2*(2*B*b^(3/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2))) + A*b^(3/2)*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3))/d]","A",0
855,1,208,0,1.215564," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{B b^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} A b \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)^{2}}, -\frac{B \sqrt{-b} b \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{2} - \sqrt{b \cos\left(d x + c\right)} A b \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/2*(B*b^(3/2)*cos(d*x + c)^2*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*sqrt(b*cos(d*x + c))*A*b*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2), -(B*sqrt(-b)*b*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^2 - sqrt(b*cos(d*x + c))*A*b*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)]","A",0
856,1,232,0,1.094991," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\left[\frac{A b^{\frac{3}{2}} \cos\left(d x + c\right)^{3} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(2 \, B b \cos\left(d x + c\right) + A b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{3}}, -\frac{A \sqrt{-b} b \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{3} - {\left(2 \, B b \cos\left(d x + c\right) + A b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/4*(A*b^(3/2)*cos(d*x + c)^3*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(2*B*b*cos(d*x + c) + A*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3), -1/2*(A*sqrt(-b)*b*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^3 - (2*B*b*cos(d*x + c) + A*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)]","A",0
857,1,260,0,1.036320," ","integrate((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\left[\frac{3 \, B b^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(4 \, A b \cos\left(d x + c\right)^{2} + 3 \, B b \cos\left(d x + c\right) + 2 \, A b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{4}}, -\frac{3 \, B \sqrt{-b} b \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{4} - {\left(4 \, A b \cos\left(d x + c\right)^{2} + 3 \, B b \cos\left(d x + c\right) + 2 \, A b\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{4}}\right]"," ",0,"[1/12*(3*B*b^(3/2)*cos(d*x + c)^4*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(4*A*b*cos(d*x + c)^2 + 3*B*b*cos(d*x + c) + 2*A*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4), -1/6*(3*B*sqrt(-b)*b*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^4 - (4*A*b*cos(d*x + c)^2 + 3*B*b*cos(d*x + c) + 2*A*b)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)]","A",0
858,1,279,0,1.025414," ","integrate(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","\left[\frac{9 \, B \sqrt{-b} b^{2} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(6 \, B b^{2} \cos\left(d x + c\right)^{3} + 8 \, A b^{2} \cos\left(d x + c\right)^{2} + 9 \, B b^{2} \cos\left(d x + c\right) + 16 \, A b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)}, \frac{9 \, B b^{\frac{5}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(6 \, B b^{2} \cos\left(d x + c\right)^{3} + 8 \, A b^{2} \cos\left(d x + c\right)^{2} + 9 \, B b^{2} \cos\left(d x + c\right) + 16 \, A b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{24 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/48*(9*B*sqrt(-b)*b^2*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(6*B*b^2*cos(d*x + c)^3 + 8*A*b^2*cos(d*x + c)^2 + 9*B*b^2*cos(d*x + c) + 16*A*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/24*(9*B*b^(5/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (6*B*b^2*cos(d*x + c)^3 + 8*A*b^2*cos(d*x + c)^2 + 9*B*b^2*cos(d*x + c) + 16*A*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
859,1,251,0,1.009394," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{-b} b^{2} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(2 \, B b^{2} \cos\left(d x + c\right)^{2} + 3 \, A b^{2} \cos\left(d x + c\right) + 4 \, B b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)}, \frac{3 \, A b^{\frac{5}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(2 \, B b^{2} \cos\left(d x + c\right)^{2} + 3 \, A b^{2} \cos\left(d x + c\right) + 4 \, B b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/12*(3*A*sqrt(-b)*b^2*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(2*B*b^2*cos(d*x + c)^2 + 3*A*b^2*cos(d*x + c) + 4*B*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/6*(3*A*b^(5/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (2*B*b^2*cos(d*x + c)^2 + 3*A*b^2*cos(d*x + c) + 4*B*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
860,1,219,0,2.472021," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{B \sqrt{-b} b^{2} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, {\left(B b^{2} \cos\left(d x + c\right) + 2 \, A b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)}, \frac{B b^{\frac{5}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(B b^{2} \cos\left(d x + c\right) + 2 \, A b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}\right]"," ",0,"[1/4*(B*sqrt(-b)*b^2*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*(B*b^2*cos(d*x + c) + 2*A*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), 1/2*(B*b^(5/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (B*b^2*cos(d*x + c) + 2*A*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
861,1,190,0,1.969455," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{-b} b^{2} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} B b^{2} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}, \frac{A b^{\frac{5}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + \sqrt{b \cos\left(d x + c\right)} B b^{2} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(A*sqrt(-b)*b^2*cos(d*x + c)*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) + 2*sqrt(b*cos(d*x + c))*B*b^2*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)), (A*b^(5/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + sqrt(b*cos(d*x + c))*B*b^2*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c))]","A",0
862,1,216,0,1.693970," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","\left[-\frac{2 \, A \sqrt{-b} b^{2} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) - B \sqrt{-b} b^{2} \log\left(2 \, b \cos\left(d x + c\right)^{2} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right)}{2 \, d}, \frac{2 \, B b^{\frac{5}{2}} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) + A b^{\frac{5}{2}} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right)}{2 \, d}\right]"," ",0,"[-1/2*(2*A*sqrt(-b)*b^2*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c)))) - B*sqrt(-b)*b^2*log(2*b*cos(d*x + c)^2 - 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b))/d, 1/2*(2*B*b^(5/2)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2))) + A*b^(5/2)*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3))/d]","A",0
863,1,214,0,1.428174," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","\left[\frac{B b^{\frac{5}{2}} \cos\left(d x + c\right)^{2} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} A b^{2} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)^{2}}, -\frac{B \sqrt{-b} b^{2} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{2} - \sqrt{b \cos\left(d x + c\right)} A b^{2} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/2*(B*b^(5/2)*cos(d*x + c)^2*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*sqrt(b*cos(d*x + c))*A*b^2*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2), -(B*sqrt(-b)*b^2*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^2 - sqrt(b*cos(d*x + c))*A*b^2*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2)]","A",0
864,1,242,0,0.938501," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x, algorithm=""fricas"")","\left[\frac{A b^{\frac{5}{2}} \cos\left(d x + c\right)^{3} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(2 \, B b^{2} \cos\left(d x + c\right) + A b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{3}}, -\frac{A \sqrt{-b} b^{2} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{3} - {\left(2 \, B b^{2} \cos\left(d x + c\right) + A b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/4*(A*b^(5/2)*cos(d*x + c)^3*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(2*B*b^2*cos(d*x + c) + A*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3), -1/2*(A*sqrt(-b)*b^2*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^3 - (2*B*b^2*cos(d*x + c) + A*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^3)]","A",0
865,1,274,0,1.033768," ","integrate((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x, algorithm=""fricas"")","\left[\frac{3 \, B b^{\frac{5}{2}} \cos\left(d x + c\right)^{4} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(4 \, A b^{2} \cos\left(d x + c\right)^{2} + 3 \, B b^{2} \cos\left(d x + c\right) + 2 \, A b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, d \cos\left(d x + c\right)^{4}}, -\frac{3 \, B \sqrt{-b} b^{2} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{4} - {\left(4 \, A b^{2} \cos\left(d x + c\right)^{2} + 3 \, B b^{2} \cos\left(d x + c\right) + 2 \, A b^{2}\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)^{4}}\right]"," ",0,"[1/12*(3*B*b^(5/2)*cos(d*x + c)^4*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(4*A*b^2*cos(d*x + c)^2 + 3*B*b^2*cos(d*x + c) + 2*A*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4), -1/6*(3*B*sqrt(-b)*b^2*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^4 - (4*A*b^2*cos(d*x + c)^2 + 3*B*b^2*cos(d*x + c) + 2*A*b^2)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4)]","A",0
866,1,236,0,2.003386," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, A \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, {\left(2 \, B \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, b d \cos\left(d x + c\right)}, \frac{3 \, A \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(2 \, B \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, b d \cos\left(d x + c\right)}\right]"," ",0,"[-1/12*(3*A*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*(2*B*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 4*B)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)), 1/6*(3*A*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (2*B*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 4*B)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c))]","A",0
867,1,210,0,0.944763," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{B \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, {\left(B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, b d \cos\left(d x + c\right)}, \frac{B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b d \cos\left(d x + c\right)}\right]"," ",0,"[-1/4*(B*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*(B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)), 1/2*(B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c))]","A",0
868,1,187,0,0.933435," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{A \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, \sqrt{b \cos\left(d x + c\right)} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b d \cos\left(d x + c\right)}, \frac{A \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + \sqrt{b \cos\left(d x + c\right)} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{b d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(A*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*sqrt(b*cos(d*x + c))*B*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)), (A*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + sqrt(b*cos(d*x + c))*B*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c))]","A",0
869,1,215,0,1.106943," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, A \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) + B \sqrt{-b} \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right)}{2 \, b d}, \frac{2 \, B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) + A \sqrt{b} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right)}{2 \, b d}\right]"," ",0,"[-1/2*(2*A*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c)))) + B*sqrt(-b)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b))/(b*d), 1/2*(2*B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2))) + A*sqrt(b)*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3))/(b*d)]","B",0
870,1,211,0,1.058162," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{B \sqrt{b} \cos\left(d x + c\right)^{2} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b d \cos\left(d x + c\right)^{2}}, -\frac{B \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{2} - \sqrt{b \cos\left(d x + c\right)} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{b d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/2*(B*sqrt(b)*cos(d*x + c)^2*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*sqrt(b*cos(d*x + c))*A*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)^2), -(B*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^2 - sqrt(b*cos(d*x + c))*A*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)^2)]","A",0
871,1,231,0,0.877631," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{b} \cos\left(d x + c\right)^{3} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, b d \cos\left(d x + c\right)^{3}}, -\frac{A \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{3} - {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/4*(A*sqrt(b)*cos(d*x + c)^3*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(2*B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)^3), -1/2*(A*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^3 - (2*B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)^3)]","A",0
872,1,259,0,0.850916," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, B \sqrt{b} \cos\left(d x + c\right)^{4} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(4 \, A \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, b d \cos\left(d x + c\right)^{4}}, -\frac{3 \, B \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{4} - {\left(4 \, A \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, b d \cos\left(d x + c\right)^{4}}\right]"," ",0,"[1/12*(3*B*sqrt(b)*cos(d*x + c)^4*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(4*A*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)^4), -1/6*(3*B*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^4 - (4*A*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b*d*cos(d*x + c)^4)]","A",0
873,1,236,0,1.177061," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, A \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, {\left(2 \, B \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, b^{2} d \cos\left(d x + c\right)}, \frac{3 \, A \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(2 \, B \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, b^{2} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/12*(3*A*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*(2*B*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 4*B)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)), 1/6*(3*A*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (2*B*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 4*B)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c))]","A",0
874,1,210,0,1.160652," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{B \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, {\left(B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, b^{2} d \cos\left(d x + c\right)}, \frac{B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b^{2} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/4*(B*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*(B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)), 1/2*(B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c))]","A",0
875,1,187,0,1.101407," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{A \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, \sqrt{b \cos\left(d x + c\right)} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b^{2} d \cos\left(d x + c\right)}, \frac{A \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + \sqrt{b \cos\left(d x + c\right)} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{b^{2} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(A*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*sqrt(b*cos(d*x + c))*B*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)), (A*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + sqrt(b*cos(d*x + c))*B*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c))]","A",0
876,1,215,0,1.189406," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, A \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) + B \sqrt{-b} \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right)}{2 \, b^{2} d}, \frac{2 \, B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) + A \sqrt{b} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right)}{2 \, b^{2} d}\right]"," ",0,"[-1/2*(2*A*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c)))) + B*sqrt(-b)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b))/(b^2*d), 1/2*(2*B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2))) + A*sqrt(b)*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3))/(b^2*d)]","A",0
877,1,211,0,0.732063," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{B \sqrt{b} \cos\left(d x + c\right)^{2} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b^{2} d \cos\left(d x + c\right)^{2}}, -\frac{B \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{2} - \sqrt{b \cos\left(d x + c\right)} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{b^{2} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/2*(B*sqrt(b)*cos(d*x + c)^2*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*sqrt(b*cos(d*x + c))*A*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)^2), -(B*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^2 - sqrt(b*cos(d*x + c))*A*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)^2)]","A",0
878,1,231,0,0.884778," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{b} \cos\left(d x + c\right)^{3} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, b^{2} d \cos\left(d x + c\right)^{3}}, -\frac{A \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{3} - {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b^{2} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/4*(A*sqrt(b)*cos(d*x + c)^3*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(2*B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)^3), -1/2*(A*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^3 - (2*B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)^3)]","A",0
879,1,259,0,0.898651," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, B \sqrt{b} \cos\left(d x + c\right)^{4} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(4 \, A \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, b^{2} d \cos\left(d x + c\right)^{4}}, -\frac{3 \, B \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{4} - {\left(4 \, A \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, b^{2} d \cos\left(d x + c\right)^{4}}\right]"," ",0,"[1/12*(3*B*sqrt(b)*cos(d*x + c)^4*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(4*A*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)^4), -1/6*(3*B*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^4 - (4*A*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^2*d*cos(d*x + c)^4)]","A",0
880,1,236,0,0.810064," ","integrate(cos(d*x+c)^(9/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, A \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, {\left(2 \, B \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, b^{3} d \cos\left(d x + c\right)}, \frac{3 \, A \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(2 \, B \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 4 \, B\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, b^{3} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/12*(3*A*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*(2*B*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 4*B)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)), 1/6*(3*A*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (2*B*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 4*B)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c))]","A",0
881,1,210,0,1.024656," ","integrate(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{B \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, {\left(B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, b^{3} d \cos\left(d x + c\right)}, \frac{B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + {\left(B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b^{3} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/4*(B*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*(B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)), 1/2*(B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + (B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c))]","A",0
882,1,187,0,1.533913," ","integrate(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{A \sqrt{-b} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right) - 2 \, \sqrt{b \cos\left(d x + c\right)} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b^{3} d \cos\left(d x + c\right)}, \frac{A \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) \cos\left(d x + c\right) + \sqrt{b \cos\left(d x + c\right)} B \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{b^{3} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(A*sqrt(-b)*cos(d*x + c)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b) - 2*sqrt(b*cos(d*x + c))*B*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)), (A*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2)))*cos(d*x + c) + sqrt(b*cos(d*x + c))*B*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c))]","A",0
883,1,215,0,0.872446," ","integrate(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\frac{2 \, A \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) + B \sqrt{-b} \log\left(2 \, b \cos\left(d x + c\right)^{2} + 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - b\right)}{2 \, b^{3} d}, \frac{2 \, B \sqrt{b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sin\left(d x + c\right)}{\sqrt{b} \cos\left(d x + c\right)^{\frac{3}{2}}}\right) + A \sqrt{b} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right)}{2 \, b^{3} d}\right]"," ",0,"[-1/2*(2*A*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c)))) + B*sqrt(-b)*log(2*b*cos(d*x + c)^2 + 2*sqrt(b*cos(d*x + c))*sqrt(-b)*sqrt(cos(d*x + c))*sin(d*x + c) - b))/(b^3*d), 1/2*(2*B*sqrt(b)*arctan(sqrt(b*cos(d*x + c))*sin(d*x + c)/(sqrt(b)*cos(d*x + c)^(3/2))) + A*sqrt(b)*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3))/(b^3*d)]","A",0
884,1,211,0,0.924760," ","integrate(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{B \sqrt{b} \cos\left(d x + c\right)^{2} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, \sqrt{b \cos\left(d x + c\right)} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b^{3} d \cos\left(d x + c\right)^{2}}, -\frac{B \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{2} - \sqrt{b \cos\left(d x + c\right)} A \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{b^{3} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/2*(B*sqrt(b)*cos(d*x + c)^2*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*sqrt(b*cos(d*x + c))*A*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)^2), -(B*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^2 - sqrt(b*cos(d*x + c))*A*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)^2)]","A",0
885,1,231,0,0.886978," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{b} \cos\left(d x + c\right)^{3} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, b^{3} d \cos\left(d x + c\right)^{3}}, -\frac{A \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{3} - {\left(2 \, B \cos\left(d x + c\right) + A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, b^{3} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/4*(A*sqrt(b)*cos(d*x + c)^3*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(2*B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)^3), -1/2*(A*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^3 - (2*B*cos(d*x + c) + A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)^3)]","A",0
886,1,259,0,0.944290," ","integrate((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, B \sqrt{b} \cos\left(d x + c\right)^{4} \log\left(-\frac{b \cos\left(d x + c\right)^{3} - 2 \, \sqrt{b \cos\left(d x + c\right)} \sqrt{b} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 2 \, b \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{3}}\right) + 2 \, {\left(4 \, A \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{12 \, b^{3} d \cos\left(d x + c\right)^{4}}, -\frac{3 \, B \sqrt{-b} \arctan\left(\frac{\sqrt{b \cos\left(d x + c\right)} \sqrt{-b} \sin\left(d x + c\right)}{b \sqrt{\cos\left(d x + c\right)}}\right) \cos\left(d x + c\right)^{4} - {\left(4 \, A \cos\left(d x + c\right)^{2} + 3 \, B \cos\left(d x + c\right) + 2 \, A\right)} \sqrt{b \cos\left(d x + c\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{6 \, b^{3} d \cos\left(d x + c\right)^{4}}\right]"," ",0,"[1/12*(3*B*sqrt(b)*cos(d*x + c)^4*log(-(b*cos(d*x + c)^3 - 2*sqrt(b*cos(d*x + c))*sqrt(b)*sqrt(cos(d*x + c))*sin(d*x + c) - 2*b*cos(d*x + c))/cos(d*x + c)^3) + 2*(4*A*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)^4), -1/6*(3*B*sqrt(-b)*arctan(sqrt(b*cos(d*x + c))*sqrt(-b)*sin(d*x + c)/(b*sqrt(cos(d*x + c))))*cos(d*x + c)^4 - (4*A*cos(d*x + c)^2 + 3*B*cos(d*x + c) + 2*A)*sqrt(b*cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(b^3*d*cos(d*x + c)^4)]","A",0
887,0,0,0,0.989964," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*(b*cos(d*x + c))^(1/3), x)","F",0
888,0,0,0,0.615582," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*(b*cos(d*x + c))^(1/3), x)","F",0
889,0,0,0,0.557115," ","integrate((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3), x)","F",0
890,0,0,0,0.701118," ","integrate((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right), x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c), x)","F",0
891,0,0,0,0.644370," ","integrate((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c)^2, x)","F",0
892,0,0,0,1.671585," ","integrate((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c)^3, x)","F",0
893,0,0,0,0.955003," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{4} + A b \cos\left(d x + c\right)^{3}\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^4 + A*b*cos(d*x + c)^3)*(b*cos(d*x + c))^(1/3), x)","F",0
894,0,0,0,0.628522," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{3} + A b \cos\left(d x + c\right)^{2}\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^3 + A*b*cos(d*x + c)^2)*(b*cos(d*x + c))^(1/3), x)","F",0
895,0,0,0,0.779436," ","integrate((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*(b*cos(d*x + c))^(1/3), x)","F",0
896,0,0,0,0.809475," ","integrate((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right), x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*(b*cos(d*x + c))^(1/3)*sec(d*x + c), x)","F",0
897,0,0,0,0.674096," ","integrate((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*(b*cos(d*x + c))^(1/3)*sec(d*x + c)^2, x)","F",0
898,0,0,0,0.770347," ","integrate((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*(b*cos(d*x + c))^(1/3)*sec(d*x + c)^3, x)","F",0
899,0,0,0,0.907574," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}{b}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*(b*cos(d*x + c))^(1/3)/b, x)","F",0
900,0,0,0,0.914792," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}{b}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)/b, x)","F",0
901,0,0,0,0.811148," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}}}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)/(b*cos(d*x + c)), x)","F",0
902,0,0,0,0.771065," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c)/(b*cos(d*x + c)), x)","F",0
903,0,0,0,0.704433," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{2}}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c)^2/(b*cos(d*x + c)), x)","F",0
904,0,0,0,1.093242," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \sec\left(d x + c\right)^{3}}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*sec(d*x + c)^3/(b*cos(d*x + c)), x)","F",0
905,0,0,0,0.650871," ","integrate(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)/b^2, x)","F",0
906,0,0,0,0.616260," ","integrate(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)/(b^2*cos(d*x + c)), x)","F",0
907,0,0,0,0.775645," ","integrate((A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}}}{b^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)/(b^2*cos(d*x + c)^2), x)","F",0
908,0,0,0,0.819844," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)}{b^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)*sec(d*x + c)/(b^2*cos(d*x + c)^2), x)","F",0
909,0,0,0,0.575668," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{2}}{b^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)*sec(d*x + c)^2/(b^2*cos(d*x + c)^2), x)","F",0
910,0,0,0,0.651880," ","integrate((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \sec\left(d x + c\right)^{3}}{b^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)*sec(d*x + c)^3/(b^2*cos(d*x + c)^2), x)","F",0
911,0,0,0,0.658150," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*cos(d*x + c)^m, x)","F",0
912,0,0,0,0.690998," ","integrate(cos(d*x+c)^2*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \left(b \cos\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*(b*cos(d*x + c))^n, x)","F",0
913,0,0,0,0.765664," ","integrate(cos(d*x+c)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*(b*cos(d*x + c))^n, x)","F",0
914,0,0,0,0.645807," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n, x)","F",0
915,0,0,0,0.787292," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right), x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sec(d*x + c), x)","F",0
916,0,0,0,0.936305," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sec(d*x + c)^2, x)","F",0
917,0,0,0,0.747555," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sec(d*x + c)^3, x)","F",0
918,0,0,0,0.772219," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sec(d*x + c)^4, x)","F",0
919,0,0,0,0.902850," ","integrate(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{3} + A \cos\left(d x + c\right)^{2}\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)^3 + A*cos(d*x + c)^2)*(b*cos(d*x + c))^n*sqrt(cos(d*x + c)), x)","F",0
920,0,0,0,0.846358," ","integrate(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right)^{2} + A \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c)^2 + A*cos(d*x + c))*(b*cos(d*x + c))^n*sqrt(cos(d*x + c)), x)","F",0
921,0,0,0,0.785717," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n*sqrt(cos(d*x + c)), x)","F",0
922,0,0,0,0.669903," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/sqrt(cos(d*x + c)), x)","F",0
923,0,0,0,0.981136," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/cos(d*x + c)^(3/2), x)","F",0
924,0,0,0,0.669805," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/cos(d*x + c)^(5/2), x)","F",0
925,0,0,0,0.986334," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/cos(d*x + c)^(7/2), x)","F",0
926,0,0,0,0.501657," ","integrate((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{n}}{\cos\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^n/cos(d*x + c)^(9/2), x)","F",0
927,0,0,0,0.747369," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b \cos\left(d x + c\right)^{2} + A b \cos\left(d x + c\right)\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*b*cos(d*x + c)^2 + A*b*cos(d*x + c))*(b*cos(d*x + c))^(1/3)*cos(d*x + c)^m, x)","F",0
928,0,0,0,0.901630," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)*cos(d*x + c)^m, x)","F",0
929,0,0,0,0.825086," ","integrate(cos(d*x+c)^m*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{m}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*cos(d*x + c)^m, x)","F",0
930,0,0,0,0.875084," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)*cos(d*x + c)^m/(b*cos(d*x + c)), x)","F",0
931,0,0,0,0.688883," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{1}{3}} \cos\left(d x + c\right)^{m}}{b \cos\left(d x + c\right)}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(1/3)*cos(d*x + c)^m/(b*cos(d*x + c)), x)","F",0
932,0,0,0,0.871417," ","integrate(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \cos\left(d x + c\right) + A\right)} \left(b \cos\left(d x + c\right)\right)^{\frac{2}{3}} \cos\left(d x + c\right)^{m}}{b^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral((B*cos(d*x + c) + A)*(b*cos(d*x + c))^(2/3)*cos(d*x + c)^m/(b^2*cos(d*x + c)^2), x)","F",0
