1,1,99,0,0.794257," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c)),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
2,1,88,0,0.716888," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c)),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
3,1,74,0,0.611654," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - a \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\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
4,1,60,0,0.667034," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c)),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
5,1,36,0,1.644229," ","integrate(a+a*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
6,1,17,0,0.685741," ","integrate(cos(d*x+c)*(a+a*sec(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
7,1,29,0,1.663341," ","integrate(cos(d*x+c)^2*(a+a*sec(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
8,1,42,0,0.782097," ","integrate(cos(d*x+c)^3*(a+a*sec(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
9,1,53,0,0.653066," ","integrate(cos(d*x+c)^4*(a+a*sec(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
10,1,124,0,0.597677," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, a^{2} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, a^{2} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(24 \, a^{2} \cos\left(d x + c\right)^{4} + 15 \, a^{2} \cos\left(d x + c\right)^{3} + 12 \, a^{2} \cos\left(d x + c\right)^{2} + 10 \, a^{2} \cos\left(d x + c\right) + 4 \, a^{2}\right)} \sin\left(d x + c\right)}{40 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/40*(15*a^2*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*a^2*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(24*a^2*cos(d*x + c)^4 + 15*a^2*cos(d*x + c)^3 + 12*a^2*cos(d*x + c)^2 + 10*a^2*cos(d*x + c) + 4*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
11,1,111,0,0.796000," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^2,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
12,1,96,0,0.652632," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^2,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
13,1,83,0,0.694290," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^2,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
14,1,76,0,0.885824," ","integrate((a+a*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
15,1,53,0,0.639285," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^2,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
16,1,36,0,0.727890," ","integrate(cos(d*x+c)^2*(a+a*sec(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
17,1,49,0,0.554498," ","integrate(cos(d*x+c)^3*(a+a*sec(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
18,1,63,0,0.720950," ","integrate(cos(d*x+c)^4*(a+a*sec(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
19,1,76,0,0.543749," ","integrate(cos(d*x+c)^5*(a+a*sec(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
20,1,124,0,0.641986," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^3,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
21,1,111,0,0.816183," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^3,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
22,1,98,0,0.707063," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^3,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
23,1,98,0,0.830061," ","integrate((a+a*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
24,1,91,0,0.774474," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^3,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
25,1,65,0,0.604499," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^3,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
26,1,50,0,0.430731," ","integrate(cos(d*x+c)^3*(a+a*sec(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
27,1,63,0,0.578896," ","integrate(cos(d*x+c)^4*(a+a*sec(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
28,1,76,0,0.660116," ","integrate(cos(d*x+c)^5*(a+a*sec(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
29,1,89,0,0.637377," ","integrate(cos(d*x+c)^6*(a+a*sec(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
30,1,137,0,1.317147," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^4,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
31,1,124,0,0.706524," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^4,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
32,1,111,0,0.532572," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^4,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
33,1,110,0,7.104293," ","integrate((a+a*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
34,1,111,0,0.814244," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^4,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
35,1,105,0,0.895444," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^4,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
36,1,80,0,0.810963," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^4,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
37,1,63,0,0.898668," ","integrate(cos(d*x+c)^4*(a+a*sec(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
38,1,76,0,1.516168," ","integrate(cos(d*x+c)^5*(a+a*sec(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
39,1,89,0,0.781825," ","integrate(cos(d*x+c)^6*(a+a*sec(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
40,1,102,0,0.732658," ","integrate(cos(d*x+c)^7*(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{1155 \, a^{4} d x + {\left(60 \, a^{4} \cos\left(d x + c\right)^{6} + 280 \, a^{4} \cos\left(d x + c\right)^{5} + 576 \, a^{4} \cos\left(d x + c\right)^{4} + 770 \, a^{4} \cos\left(d x + c\right)^{3} + 908 \, a^{4} \cos\left(d x + c\right)^{2} + 1155 \, a^{4} \cos\left(d x + c\right) + 1816 \, a^{4}\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(1155*a^4*d*x + (60*a^4*cos(d*x + c)^6 + 280*a^4*cos(d*x + c)^5 + 576*a^4*cos(d*x + c)^4 + 770*a^4*cos(d*x + c)^3 + 908*a^4*cos(d*x + c)^2 + 1155*a^4*cos(d*x + c) + 1816*a^4)*sin(d*x + c))/d","A",0
41,1,150,0,0.787229," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^5,x, algorithm=""fricas"")","\frac{9765 \, a^{5} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 9765 \, a^{5} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(15328 \, a^{5} \cos\left(d x + c\right)^{6} + 9765 \, a^{5} \cos\left(d x + c\right)^{5} + 7664 \, a^{5} \cos\left(d x + c\right)^{4} + 5950 \, a^{5} \cos\left(d x + c\right)^{3} + 3648 \, a^{5} \cos\left(d x + c\right)^{2} + 1400 \, a^{5} \cos\left(d x + c\right) + 240 \, a^{5}\right)} \sin\left(d x + c\right)}{3360 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/3360*(9765*a^5*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 9765*a^5*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 2*(15328*a^5*cos(d*x + c)^6 + 9765*a^5*cos(d*x + c)^5 + 7664*a^5*cos(d*x + c)^4 + 5950*a^5*cos(d*x + c)^3 + 3648*a^5*cos(d*x + c)^2 + 1400*a^5*cos(d*x + c) + 240*a^5)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
42,1,124,0,0.628276," ","integrate(sec(d*x+c)^5/(a+a*sec(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
43,1,112,0,0.751835," ","integrate(sec(d*x+c)^4/(a+a*sec(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
44,1,97,0,0.669469," ","integrate(sec(d*x+c)^3/(a+a*sec(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
45,1,65,0,1.713341," ","integrate(sec(d*x+c)^2/(a+a*sec(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
46,1,22,0,0.688640," ","integrate(sec(d*x+c)/(a+a*sec(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
47,1,37,0,0.650275," ","integrate(1/(a+a*sec(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
48,1,46,0,0.509550," ","integrate(cos(d*x+c)/(a+a*sec(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
49,1,57,0,0.815524," ","integrate(cos(d*x+c)^2/(a+a*sec(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
50,1,70,0,0.482091," ","integrate(cos(d*x+c)^3/(a+a*sec(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
51,1,79,0,0.692840," ","integrate(cos(d*x+c)^4/(a+a*sec(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
52,1,162,0,0.706742," ","integrate(sec(d*x+c)^5/(a+a*sec(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
53,1,146,0,0.752705," ","integrate(sec(d*x+c)^4/(a+a*sec(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
54,1,114,0,1.372329," ","integrate(sec(d*x+c)^3/(a+a*sec(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
55,1,49,0,0.593006," ","integrate(sec(d*x+c)^2/(a+a*sec(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
56,1,51,0,0.790019," ","integrate(sec(d*x+c)/(a+a*sec(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
57,1,80,0,1.370129," ","integrate(1/(a+a*sec(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
58,1,90,0,0.820883," ","integrate(cos(d*x+c)/(a+a*sec(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
59,1,99,0,0.947898," ","integrate(cos(d*x+c)^2/(a+a*sec(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
60,1,108,0,1.402406," ","integrate(cos(d*x+c)^3/(a+a*sec(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
61,1,206,0,0.808942," ","integrate(sec(d*x+c)^6/(a+a*sec(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
62,1,190,0,0.873307," ","integrate(sec(d*x+c)^5/(a+a*sec(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
63,1,158,0,0.732044," ","integrate(sec(d*x+c)^4/(a+a*sec(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
64,1,75,0,0.583642," ","integrate(sec(d*x+c)^3/(a+a*sec(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
65,1,73,0,0.565242," ","integrate(sec(d*x+c)^2/(a+a*sec(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
66,1,75,0,0.579893," ","integrate(sec(d*x+c)/(a+a*sec(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
67,1,116,0,0.559842," ","integrate(1/(a+a*sec(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
68,1,126,0,1.298408," ","integrate(cos(d*x+c)/(a+a*sec(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
69,1,135,0,0.679644," ","integrate(cos(d*x+c)^2/(a+a*sec(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
70,1,250,0,0.527447," ","integrate(sec(d*x+c)^7/(a+a*sec(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
71,1,234,0,1.054473," ","integrate(sec(d*x+c)^6/(a+a*sec(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
72,1,202,0,0.591658," ","integrate(sec(d*x+c)^5/(a+a*sec(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
73,1,99,0,1.428226," ","integrate(sec(d*x+c)^4/(a+a*sec(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
74,1,99,0,0.899154," ","integrate(sec(d*x+c)^3/(a+a*sec(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
75,1,99,0,0.806180," ","integrate(sec(d*x+c)^2/(a+a*sec(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
76,1,99,0,0.647833," ","integrate(sec(d*x+c)/(a+a*sec(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
77,1,152,0,1.039075," ","integrate(1/(a+a*sec(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
78,1,162,0,0.893469," ","integrate(cos(d*x+c)/(a+a*sec(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
79,1,171,0,0.657696," ","integrate(cos(d*x+c)^2/(a+a*sec(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
80,1,278,0,1.305454," ","integrate(sec(d*x+c)^7/(a+a*sec(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
81,1,246,0,0.660050," ","integrate(sec(d*x+c)^6/(a+a*sec(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
82,1,123,0,1.695509," ","integrate(sec(d*x+c)^5/(a+a*sec(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
83,1,123,0,0.669032," ","integrate(sec(d*x+c)^4/(a+a*sec(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
84,1,123,0,0.574654," ","integrate(sec(d*x+c)^3/(a+a*sec(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
85,1,123,0,0.840373," ","integrate(sec(d*x+c)^2/(a+a*sec(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
86,1,123,0,0.659642," ","integrate(sec(d*x+c)/(a+a*sec(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
87,1,188,0,0.598617," ","integrate(1/(a+a*sec(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
88,1,198,0,0.579190," ","integrate(cos(d*x+c)/(a+a*sec(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
89,1,207,0,3.027205," ","integrate(cos(d*x+c)^2/(a+a*sec(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
90,1,82,0,1.255423," ","integrate(sec(d*x+c)^4*(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}"," ",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)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
91,1,72,0,0.694804," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 3\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}"," ",0,"2/15*(8*cos(d*x + c)^2 + 4*cos(d*x + c) + 3)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
92,1,60,0,0.652720," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\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)}}"," ",0,"2/3*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(2*cos(d*x + c) + 1)*sin(d*x + c)/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
93,1,41,0,0.752059," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
94,1,133,0,0.876023," ","integrate((a+a*sec(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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/d]","A",0
95,1,242,0,0.759427," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(sqrt(-a)*(cos(d*x + c) + 1)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c))/(d*cos(d*x + c) + d), -(sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
96,1,270,0,0.622763," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{-a} {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{3 \, \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/8*(3*sqrt(-a)*(cos(d*x + c) + 1)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(2*cos(d*x + c)^2 + 3*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/4*(3*sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (2*cos(d*x + c)^2 + 3*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
97,1,290,0,1.594370," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{-a} {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\left(8 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} + 15 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{15 \, \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(8 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} + 15 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/48*(15*sqrt(-a)*(cos(d*x + c) + 1)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(8*cos(d*x + c)^3 + 10*cos(d*x + c)^2 + 15*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/24*(15*sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (8*cos(d*x + c)^3 + 10*cos(d*x + c)^2 + 15*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
98,1,310,0,0.737344," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{-a} {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\left(48 \, \cos\left(d x + c\right)^{4} + 56 \, \cos\left(d x + c\right)^{3} + 70 \, \cos\left(d x + c\right)^{2} + 105 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{384 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{105 \, \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(48 \, \cos\left(d x + c\right)^{4} + 56 \, \cos\left(d x + c\right)^{3} + 70 \, \cos\left(d x + c\right)^{2} + 105 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/384*(105*sqrt(-a)*(cos(d*x + c) + 1)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(48*cos(d*x + c)^4 + 56*cos(d*x + c)^3 + 70*cos(d*x + c)^2 + 105*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/192*(105*sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (48*cos(d*x + c)^4 + 56*cos(d*x + c)^3 + 70*cos(d*x + c)^2 + 105*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
99,1,98,0,1.649441," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(272 \, a \cos\left(d x + c\right)^{4} + 136 \, a \cos\left(d x + c\right)^{3} + 102 \, a \cos\left(d x + c\right)^{2} + 85 \, a \cos\left(d x + c\right) + 35 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}"," ",0,"2/315*(272*a*cos(d*x + c)^4 + 136*a*cos(d*x + c)^3 + 102*a*cos(d*x + c)^2 + 85*a*cos(d*x + c) + 35*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
100,1,87,0,0.675599," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}"," ",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)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
101,1,74,0,0.523750," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}"," ",0,"2/5*(6*a*cos(d*x + c)^2 + 3*a*cos(d*x + c) + a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
102,1,61,0,0.576601," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, a \cos\left(d x + c\right) + a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}"," ",0,"2/3*(5*a*cos(d*x + c) + a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^2 + d*cos(d*x + c))","A",0
103,1,235,0,0.878821," ","integrate((a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}, -\frac{2 \, {\left({\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)\right)}}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[((a*cos(d*x + c) + a)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -2*((a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
104,1,248,0,0.610820," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(2*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*(a*cos(d*x + c) + a)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)))/(d*cos(d*x + c) + d), (a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))))/(d*cos(d*x + c) + d)]","A",0
105,1,278,0,0.637243," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{7 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\left(2 \, a \cos\left(d x + c\right)^{2} + 7 \, a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{7 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(2 \, a \cos\left(d x + c\right)^{2} + 7 \, a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/8*(7*(a*cos(d*x + c) + a)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(2*a*cos(d*x + c)^2 + 7*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/4*(7*(a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
106,1,300,0,0.839382," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{33 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{33 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/48*(33*(a*cos(d*x + c) + a)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/24*(33*(a*cos(d*x + c) + a)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
107,1,121,0,0.598307," ","integrate(sec(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1136 \, a^{2} \cos\left(d x + c\right)^{5} + 568 \, a^{2} \cos\left(d x + c\right)^{4} + 426 \, a^{2} \cos\left(d x + c\right)^{3} + 355 \, a^{2} \cos\left(d x + c\right)^{2} + 224 \, a^{2} \cos\left(d x + c\right) + 63 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{693 \, {\left(d \cos\left(d x + c\right)^{6} + d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"2/693*(1136*a^2*cos(d*x + c)^5 + 568*a^2*cos(d*x + c)^4 + 426*a^2*cos(d*x + c)^3 + 355*a^2*cos(d*x + c)^2 + 224*a^2*cos(d*x + c) + 63*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^6 + d*cos(d*x + c)^5)","A",0
108,1,108,0,0.693546," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}"," ",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)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)","A",0
109,1,95,0,0.667819," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}"," ",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)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)","A",0
110,1,82,0,0.829968," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2),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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}"," ",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)/cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)","A",0
111,1,310,0,2.808471," ","integrate((a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\left(8 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(8 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)\right)}}{3 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/3*(3*(a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(8*a^2*cos(d*x + c) + a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), -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)/cos(d*x + c))*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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
112,1,276,0,0.749126," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\left(a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{5 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(5*(a^2*cos(d*x + c) + a^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(a^2*cos(d*x + c) + 2*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -(5*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
113,1,294,0,0.559968," ","integrate(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{19 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} + 11 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{19 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} + 11 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/8*(19*(a^2*cos(d*x + c) + a^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(2*a^2*cos(d*x + c)^2 + 11*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/4*(19*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
114,1,320,0,0.749883," ","integrate(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{75 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{75 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/48*(75*(a^2*cos(d*x + c) + a^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/24*(75*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
115,1,346,0,0.525203," ","integrate(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{489 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{384 \, {\left(d \cos\left(d x + c\right) + d\right)}}, -\frac{489 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{192 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/384*(489*(a^2*cos(d*x + c) + a^2)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d), -1/192*(489*(a^2*cos(d*x + c) + a^2)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)/cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)]","A",0
116,1,44,0,0.956962," ","integrate(sec(d*x+c)*(a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) + 1\right)}}{d \sin\left(d x + c\right)}"," ",0,"2*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*(cos(d*x + c) + 1)/(d*sin(d*x + c))","A",0
117,1,182,0,0.880561," ","integrate((a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} \log\left(-\frac{4 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\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{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{{\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}\right)}{d}\right]"," ",0,"[1/2*sqrt(-a)*log(-(4*(2*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/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(2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))/((2*a*cos(d*x + c) + a)*sin(d*x + c)))/d]","B",0
118,1,294,0,0.899480," ","integrate(cos(d*x+c)*(a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} \log\left(\frac{4 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\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 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{4 \, d \sin\left(d x + c\right)}, \frac{\sqrt{a} \arctan\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{{\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}}}{2 \, d \sin\left(d x + c\right)}\right]"," ",0,"[1/4*(sqrt(-a)*log((4*(2*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/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*(cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/(d*sin(d*x + c)), 1/2*(sqrt(a)*arctan(2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))/((2*a*cos(d*x + c) + a)*sin(d*x + c)))*sin(d*x + c) - 2*(cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)))/(d*sin(d*x + c))]","B",0
119,1,347,0,0.823937," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \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) + 4 \, {\left(13 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 3\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{30 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, {\left(13 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 3\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) + \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{15 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/30*(15*sqrt(2)*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*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)) + 4*(13*cos(d*x + c)^2 - cos(d*x + c) + 3)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2), 1/15*(2*(13*cos(d*x + c)^2 - cos(d*x + c) + 3)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) + 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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)]","A",0
120,1,316,0,0.803535," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \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) - 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)}{6 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}, -\frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\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)^{2} + a \cos\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{3 \, {\left(a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/6*(3*sqrt(2)*(a*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*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)) - 4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 1)*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c)), -1/3*(2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 1)*sin(d*x + c) + 3*sqrt(2)*(a*cos(d*x + c)^2 + a*cos(d*x + c))*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))]","A",0
121,1,262,0,0.774694," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \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) + 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{\frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}} + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{a d \cos\left(d x + c\right) + a d}\right]"," ",0,"[1/2*(sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*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)) + 4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), (sqrt(2)*(a*cos(d*x + c) + a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
122,1,158,0,0.829647," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)/cos(d*x + c))*sqrt(-1/a)*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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/(sqrt(a)*d)]","A",0
123,1,294,0,0.695686," ","integrate(1/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \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 \, \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}{2 \, a d}, \frac{\sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{a d}\right]"," ",0,"[1/2*(sqrt(2)*a*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*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)) - 2*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)))/(a*d), (sqrt(2)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))))/(a*d)]","A",0
124,1,417,0,1.089060," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \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) - \sqrt{-a} {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{\sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - \frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{\sqrt{a}}}{a d \cos\left(d x + c\right) + a d}\right]"," ",0,"[1/2*(sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*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)) - sqrt(-a)*(cos(d*x + c) + 1)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), (sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - sqrt(2)*(a*cos(d*x + c) + a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)]","A",0
125,1,446,0,0.923850," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \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) - 7 \, \sqrt{-a} {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 2 \, {\left(2 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{8 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{7 \, \sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - {\left(2 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right) - \frac{4 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}\right]"," ",0,"[1/8*(4*sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*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)) - 7*sqrt(-a)*(cos(d*x + c) + 1)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 2*(2*cos(d*x + c)^2 - cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), -1/4*(7*sqrt(a)*(cos(d*x + c) + 1)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - (2*cos(d*x + c)^2 - cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c) - 4*sqrt(2)*(a*cos(d*x + c) + a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/sqrt(a))/(a*d*cos(d*x + c) + a*d)]","A",0
126,1,414,0,0.902097," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{75 \, \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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(49 \, \cos\left(d x + c\right)^{3} + 36 \, \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right) + 4\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{40 \, {\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)}}, \frac{75 \, \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left(49 \, \cos\left(d x + c\right)^{3} + 36 \, \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right) + 4\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{20 \, {\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)}}\right]"," ",0,"[-1/40*(75*sqrt(2)*(cos(d*x + c)^4 + 2*cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(49*cos(d*x + c)^3 + 36*cos(d*x + c)^2 - 4*cos(d*x + c) + 4)*sqrt((a*cos(d*x + c) + a)/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), 1/20*(75*sqrt(2)*(cos(d*x + c)^4 + 2*cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*(49*cos(d*x + c)^3 + 36*cos(d*x + c)^2 - 4*cos(d*x + c) + 4)*sqrt((a*cos(d*x + c) + a)/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
127,1,387,0,3.566268," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\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} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left(19 \, \cos\left(d x + c\right)^{2} + 12 \, \cos\left(d x + c\right) - 4\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{24 \, {\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left(19 \, \cos\left(d x + c\right)^{2} + 12 \, \cos\left(d x + c\right) - 4\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\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)}}\right]"," ",0,"[-1/24*(33*sqrt(2)*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(19*cos(d*x + c)^2 + 12*cos(d*x + c) - 4)*sqrt((a*cos(d*x + c) + a)/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)), -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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*(19*cos(d*x + c)^2 + 12*cos(d*x + c) - 4)*sqrt((a*cos(d*x + c) + a)/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
128,1,336,0,2.264575," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(5 \, \cos\left(d x + c\right) + 4\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)}}, \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(5 \, \cos\left(d x + c\right) + 4\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)}}\right]"," ",0,"[-1/8*(7*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(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), 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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(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
129,1,329,0,0.707914," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}\right]"," ",0,"[-1/8*(3*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), -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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)]","B",0
130,1,327,0,0.627660," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}\right]"," ",0,"[-1/8*(sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), -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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)]","B",0
131,1,491,0,1.153130," ","integrate(1/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 8 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\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)}}, \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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)}}\right]"," ",0,"[-1/8*(5*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 8*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), 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)/cos(d*x + c))*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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)]","B",0
132,1,518,0,1.080057," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{9 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 12 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) - 4 \, {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left(2 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\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)}}\right]"," ",0,"[-1/8*(9*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 12*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) - 4*(2*cos(d*x + c)^2 + 3*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -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)/cos(d*x + c))*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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*(2*cos(d*x + c)^2 + 3*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
133,1,536,0,0.869383," ","integrate(cos(d*x+c)^2/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[-\frac{13 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + 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)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) - 2 \, {\left(2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} - 7 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, \frac{13 \, \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 19 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + {\left(2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} - 7 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\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)}}\right]"," ",0,"[-1/8*(13*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 19*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) - 2*(2*cos(d*x + c)^3 - 3*cos(d*x + c)^2 - 7*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), 1/4*(13*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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 19*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*arctan(sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + (2*cos(d*x + c)^3 - 3*cos(d*x + c)^2 - 7*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
134,1,455,0,0.545783," ","integrate(sec(d*x+c)^5/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\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} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{192 \, {\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\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)}}\right]"," ",0,"[-1/192*(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)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(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)/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)), -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)/cos(d*x + c))*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)/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
135,1,404,0,0.758923," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(49 \, \cos\left(d x + c\right)^{2} + 85 \, \cos\left(d x + c\right) + 32\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left(49 \, \cos\left(d x + c\right)^{2} + 85 \, \cos\left(d x + c\right) + 32\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\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)}}\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(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(49*cos(d*x + c)^2 + 85*cos(d*x + c) + 32)*sqrt((a*cos(d*x + c) + a)/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), 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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*(49*cos(d*x + c)^2 + 85*cos(d*x + c) + 32)*sqrt((a*cos(d*x + c) + a)/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
136,1,403,0,1.195568," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, {\left(9 \, \cos\left(d x + c\right)^{2} + 13 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) + 2 \, {\left(9 \, \cos\left(d x + c\right)^{2} + 13 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\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)}}\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((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(9*cos(d*x + c)^2 + 13*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) + 2*(9*cos(d*x + c)^2 + 13*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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)]","B",0
137,1,399,0,0.741247," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - 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} + 5 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\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)}}\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((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(cos(d*x + c)^2 + 5*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*(cos(d*x + c)^2 + 5*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
138,1,403,0,0.689767," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 4 \, {\left(7 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left(7 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\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)}}\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((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(7*cos(d*x + c)^2 + 3*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*(7*cos(d*x + c)^2 + 3*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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)]","B",0
139,1,585,0,1.006994," ","integrate(1/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\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{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\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} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) + 4 \, {\left(15 \, \cos\left(d x + c\right)^{2} + 11 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, {\left(15 \, \cos\left(d x + c\right)^{2} + 11 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\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)}}\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(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) + a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 64*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(-a)*log((2*a*cos(d*x + c)^2 + 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) + 4*(15*cos(d*x + c)^2 + 11*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), 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)/cos(d*x + c))*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)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*(15*cos(d*x + c)^2 + 11*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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)]","B",0
140,1,606,0,0.975874," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[-\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} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\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} \log\left(\frac{2 \, a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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) - 4 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, -\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 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{\frac{a \cos\left(d x + c\right) + a}{\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)}}\right]"," ",0,"[-1/64*(115*sqrt(2)*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + 3*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) - a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 160*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(-a)*log((2*a*cos(d*x + c)^2 - 2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)*sin(d*x + c) + a*cos(d*x + c) - a)/(cos(d*x + c) + 1)) - 4*(16*cos(d*x + c)^3 + 55*cos(d*x + c)^2 + 35*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -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)/cos(d*x + c))*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)/cos(d*x + c))*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)/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
141,1,161,0,0.834758," ","integrate(sec(d*x+c)/(a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{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 \, d}, \frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \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)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*sqrt(-1/a) - (3*cos(d*x + c) + 1)*sin(d*x + c))/((cos(d*x + c) - 1)*sin(d*x + c)))/d, sqrt(2)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c)))/(sqrt(a)*d)]","A",0
142,1,301,0,1.249467," ","integrate(1/(a-a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{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 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\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}, \frac{\sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right) - 2 \, \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(d x + c\right) - a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)}{\sqrt{a} \sin\left(d x + c\right)}\right)}{a d}\right]"," ",0,"[1/2*(sqrt(2)*a*sqrt(-1/a)*log(-(2*sqrt(2)*(cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*sqrt(-1/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*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c)) - (2*a*cos(d*x + c) + a)*sin(d*x + c))/sin(d*x + c)))/(a*d), (sqrt(2)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))) - 2*sqrt(a)*arctan(sqrt((a*cos(d*x + c) - a)/cos(d*x + c))*cos(d*x + c)/(sqrt(a)*sin(d*x + c))))/(a*d)]","A",0
143,0,0,0,1.588729," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^3, x)","F",0
144,0,0,0,0.779786," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^2, x)","F",0
145,0,0,0,0.717209," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right), x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c), x)","F",0
146,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,0,0,0,1.217336," ","integrate(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((a*sec(d*x + c)^4 + a*sec(d*x + c)^3)*(a*sec(d*x + c) + a)^(2/3), x)","F",0
149,0,0,0,0.989758," ","integrate(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((a*sec(d*x + c)^3 + a*sec(d*x + c)^2)*(a*sec(d*x + c) + a)^(2/3), x)","F",0
150,0,0,0,0.885966," ","integrate(sec(d*x+c)*(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)\right)} {\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((a*sec(d*x + c)^2 + a*sec(d*x + c))*(a*sec(d*x + c) + a)^(2/3), x)","F",0
151,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,0,0,0,1.069214," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{4}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)^4/(a*sec(d*x + c) + a)^(1/3), x)","F",0
154,0,0,0,1.074801," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{3}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)^3/(a*sec(d*x + c) + a)^(1/3), x)","F",0
155,0,0,0,0.967229," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{2}}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)^2/(a*sec(d*x + c) + a)^(1/3), x)","F",0
156,0,0,0,1.220478," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)}{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)/(a*sec(d*x + c) + a)^(1/3), x)","F",0
157,-1,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,0,0,0,1.223371," ","integrate(sec(d*x+c)^4/(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{4}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^4/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
160,0,0,0,0.828615," ","integrate(sec(d*x+c)^3/(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{3}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^3/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
161,0,0,0,1.143180," ","integrate(sec(d*x+c)^2/(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{2}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^2/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
162,0,0,0,0.848850," ","integrate(sec(d*x+c)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(1/3)*sec(d*x + c)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
163,-1,0,0,0.000000," ","integrate(1/(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+a*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,0,0,0,1.333966," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a*sec(d*x + c)^3 + a*sec(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
166,0,0,0,1.061690," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a*sec(d*x + c)^2 + a*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
167,0,0,0,0.679238," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
168,0,0,0,1.914769," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(d x + c\right) + a}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
169,0,0,0,0.634050," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
170,0,0,0,2.023984," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
171,0,0,0,1.008527," ","integrate((a+a*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
172,0,0,0,1.775587," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(d x + c\right)^{4} + 2 \, a^{2} \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^4 + 2*a^2*sec(d*x + c)^3 + a^2*sec(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
173,0,0,0,0.846905," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(d x + c\right)^{3} + 2 \, a^{2} \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^3 + 2*a^2*sec(d*x + c)^2 + a^2*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
174,0,0,0,0.854893," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(sec(d*x + c)), x)","F",0
175,0,0,0,0.883921," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)/sqrt(sec(d*x + c)), x)","F",0
176,0,0,0,0.707839," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)/sec(d*x + c)^(3/2), x)","F",0
177,0,0,0,0.693247," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)/sec(d*x + c)^(5/2), x)","F",0
178,0,0,0,0.668169," ","integrate((a+a*sec(d*x+c))^2/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)/sec(d*x + c)^(7/2), x)","F",0
179,0,0,0,0.649739," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \sec\left(d x + c\right)^{4} + 3 \, a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^4 + 3*a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + a^3*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
180,0,0,0,0.766381," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)*sqrt(sec(d*x + c)), x)","F",0
181,0,0,0,0.997083," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)/sqrt(sec(d*x + c)), x)","F",0
182,0,0,0,0.528727," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)/sec(d*x + c)^(3/2), x)","F",0
183,0,0,0,1.018647," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)/sec(d*x + c)^(5/2), x)","F",0
184,0,0,0,0.607011," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)/sec(d*x + c)^(7/2), x)","F",0
185,0,0,0,0.642130," ","integrate((a+a*sec(d*x+c))^3/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)/sec(d*x + c)^(9/2), x)","F",0
186,0,0,0,0.670244," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \sec\left(d x + c\right)^{5} + 4 \, a^{4} \sec\left(d x + c\right)^{4} + 6 \, a^{4} \sec\left(d x + c\right)^{3} + 4 \, a^{4} \sec\left(d x + c\right)^{2} + a^{4} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^4*sec(d*x + c)^5 + 4*a^4*sec(d*x + c)^4 + 6*a^4*sec(d*x + c)^3 + 4*a^4*sec(d*x + c)^2 + a^4*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
187,0,0,0,1.021274," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4)*sqrt(sec(d*x + c)), x)","F",0
188,0,0,0,1.706350," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4)/sqrt(sec(d*x + c)), x)","F",0
189,0,0,0,0.730748," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4)/sec(d*x + c)^(3/2), x)","F",0
190,0,0,0,0.740397," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4)/sec(d*x + c)^(5/2), x)","F",0
191,0,0,0,0.666303," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4)/sec(d*x + c)^(7/2), x)","F",0
192,0,0,0,0.763503," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4)/sec(d*x + c)^(9/2), x)","F",0
193,0,0,0,0.673039," ","integrate((a+a*sec(d*x+c))^4/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} \sec\left(d x + c\right)^{4} + 4 \, a^{4} \sec\left(d x + c\right)^{3} + 6 \, a^{4} \sec\left(d x + c\right)^{2} + 4 \, a^{4} \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((a^4*sec(d*x + c)^4 + 4*a^4*sec(d*x + c)^3 + 6*a^4*sec(d*x + c)^2 + 4*a^4*sec(d*x + c) + a^4)/sec(d*x + c)^(11/2), x)","F",0
194,0,0,0,0.617135," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sec(d*x + c)^(7/2)/(a*sec(d*x + c) + a), x)","F",0
195,0,0,0,0.936782," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sec(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
196,0,0,0,0.729919," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sec(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
197,0,0,0,0.501184," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
198,0,0,0,0.566944," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
199,0,0,0,0.585369," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a*sec(d*x + c)^3 + a*sec(d*x + c)^2), x)","F",0
200,0,0,0,0.617231," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a*sec(d*x + c)^4 + a*sec(d*x + c)^3), x)","F",0
201,0,0,0,0.735845," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sec(d*x + c)^(9/2)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
202,0,0,0,0.791817," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sec(d*x + c)^(7/2)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
203,0,0,0,1.441264," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sec(d*x + c)^(5/2)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
204,0,0,0,0.558154," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sec(d*x + c)^(3/2)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
205,0,0,0,0.831276," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
206,0,0,0,0.757151," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{3} + 2 \, a^{2} \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^3 + 2*a^2*sec(d*x + c)^2 + a^2*sec(d*x + c)), x)","F",0
207,0,0,0,0.669015," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{4} + 2 \, a^{2} \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^4 + 2*a^2*sec(d*x + c)^3 + a^2*sec(d*x + c)^2), x)","F",0
208,0,0,0,1.474856," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{5} + 2 \, a^{2} \sec\left(d x + c\right)^{4} + a^{2} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^2*sec(d*x + c)^5 + 2*a^2*sec(d*x + c)^4 + a^2*sec(d*x + c)^3), x)","F",0
209,0,0,0,0.703621," ","integrate(sec(d*x+c)^(11/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{11}{2}}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sec(d*x + c)^(11/2)/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
210,0,0,0,0.570511," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{9}{2}}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sec(d*x + c)^(9/2)/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
211,0,0,0,0.638954," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{7}{2}}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sec(d*x + c)^(7/2)/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
212,0,0,0,0.762098," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{5}{2}}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sec(d*x + c)^(5/2)/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
213,0,0,0,0.727911," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{3}{2}}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sec(d*x + c)^(3/2)/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
214,0,0,0,1.398292," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
215,0,0,0,0.575516," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{4} + 3 \, a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^4 + 3*a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + a^3*sec(d*x + c)), x)","F",0
216,0,0,0,0.759698," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{5} + 3 \, a^{3} \sec\left(d x + c\right)^{4} + 3 \, a^{3} \sec\left(d x + c\right)^{3} + a^{3} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^5 + 3*a^3*sec(d*x + c)^4 + 3*a^3*sec(d*x + c)^3 + a^3*sec(d*x + c)^2), x)","F",0
217,0,0,0,0.795501," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{6} + 3 \, a^{3} \sec\left(d x + c\right)^{5} + 3 \, a^{3} \sec\left(d x + c\right)^{4} + a^{3} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(a^3*sec(d*x + c)^6 + 3*a^3*sec(d*x + c)^5 + 3*a^3*sec(d*x + c)^4 + a^3*sec(d*x + c)^3), x)","F",0
218,1,356,0,0.818009," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{3 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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))*(3*cos(d*x + c) + 2)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/8*(3*(cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(3*cos(d*x + c) + 2)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
219,1,302,0,0.639691," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, \frac{\sqrt{-a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/4*(sqrt(a)*(cos(d*x + c) + 1)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/2*(sqrt(-a)*(cos(d*x + c) + 1)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","B",0
220,1,189,0,0.643520," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2))/d, sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a))/d]","B",0
221,1,49,0,0.539661," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
222,1,66,0,0.554352," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3*(cos(d*x + c)^2 + 2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
223,1,78,0,0.588539," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} + 8 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/15*(3*cos(d*x + c)^3 + 4*cos(d*x + c)^2 + 8*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
224,1,88,0,0.803307," ","integrate((a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{3} + 8 \, \cos\left(d x + c\right)^{2} + 16 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{35 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/35*(5*cos(d*x + c)^4 + 6*cos(d*x + c)^3 + 8*cos(d*x + c)^2 + 16*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
225,1,400,0,1.670130," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{33 \, {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(33 \, a \cos\left(d x + c\right)^{2} + 22 \, a \cos\left(d x + c\right) + 8 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{33 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(33 \, a \cos\left(d x + c\right)^{2} + 22 \, a \cos\left(d x + c\right) + 8 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{48 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/96*(33*(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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/48*(33*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(33*a*cos(d*x + c)^2 + 22*a*cos(d*x + c) + 8*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
226,1,370,0,0.659858," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{7 \, {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(7 \, a \cos\left(d x + c\right) + 2 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{7 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(7 \, a \cos\left(d x + c\right) + 2 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(7*(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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/8*(7*(a*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(7*a*cos(d*x + c) + 2*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
227,1,310,0,0.647837," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, \frac{3 \, {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/4*(3*(a*cos(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/2*(3*(a*cos(d*x + c) + a)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","B",0
228,1,307,0,0.623408," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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 \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(4*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (a*cos(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c) + d), (2*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (a*cos(d*x + c) + a)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c) + d)]","B",0
229,1,69,0,0.626030," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a \cos\left(d x + c\right)^{2} + 5 \, a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/3*(a*cos(d*x + c)^2 + 5*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
230,1,80,0,0.563963," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)^{2} + 6 \, a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{5 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/5*(a*cos(d*x + c)^3 + 3*a*cos(d*x + c)^2 + 6*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
231,1,92,0,1.477977," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, a \cos\left(d x + c\right)^{4} + 39 \, a \cos\left(d x + c\right)^{3} + 52 \, a \cos\left(d x + c\right)^{2} + 104 \, a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/105*(15*a*cos(d*x + c)^4 + 39*a*cos(d*x + c)^3 + 52*a*cos(d*x + c)^2 + 104*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
232,1,103,0,0.464567," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a \cos\left(d x + c\right)^{5} + 85 \, a \cos\left(d x + c\right)^{4} + 102 \, a \cos\left(d x + c\right)^{3} + 136 \, a \cos\left(d x + c\right)^{2} + 272 \, a \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(35*a*cos(d*x + c)^5 + 85*a*cos(d*x + c)^4 + 102*a*cos(d*x + c)^3 + 136*a*cos(d*x + c)^2 + 272*a*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
233,1,446,0,0.650510," ","integrate(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{489 \, {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{768 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{489 \, {\left(a^{2} \cos\left(d x + c\right)^{4} + a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{384 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/768*(489*(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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3), 1/384*(489*(a^2*cos(d*x + c)^4 + a^2*cos(d*x + c)^3)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)]","A",0
234,1,420,0,1.602013," ","integrate(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{75 \, {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{75 \, {\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{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{48 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/96*(75*(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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/48*(75*(a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
235,1,386,0,0.691266," ","integrate(sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{19 \, {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(11 \, a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{19 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(11 \, a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{8 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(19*(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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/8*(19*(a^2*cos(d*x + c)^2 + a^2*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(11*a^2*cos(d*x + c) + 2*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
236,1,346,0,1.394209," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}, \frac{5 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/4*(5*(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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/2*(5*(a^2*cos(d*x + c) + a^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(2*a^2*cos(d*x + c) + a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","A",0
237,1,364,0,1.254749," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + 8 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{3 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + \frac{2 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + 8 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}\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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(a^2*cos(d*x + c)^2 + 8*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d), 1/3*(3*(a^2*cos(d*x + c) + a^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*(a^2*cos(d*x + c)^2 + 8*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)]","A",0
238,1,87,0,0.835171," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{3} + 14 \, a^{2} \cos\left(d x + c\right)^{2} + 43 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/15*(3*a^2*cos(d*x + c)^3 + 14*a^2*cos(d*x + c)^2 + 43*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
239,1,100,0,0.686481," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{4} + 12 \, a^{2} \cos\left(d x + c\right)^{3} + 23 \, a^{2} \cos\left(d x + c\right)^{2} + 46 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{21 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/21*(3*a^2*cos(d*x + c)^4 + 12*a^2*cos(d*x + c)^3 + 23*a^2*cos(d*x + c)^2 + 46*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
240,1,113,0,0.546194," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a^{2} \cos\left(d x + c\right)^{5} + 130 \, a^{2} \cos\left(d x + c\right)^{4} + 219 \, a^{2} \cos\left(d x + c\right)^{3} + 292 \, a^{2} \cos\left(d x + c\right)^{2} + 584 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/315*(35*a^2*cos(d*x + c)^5 + 130*a^2*cos(d*x + c)^4 + 219*a^2*cos(d*x + c)^3 + 292*a^2*cos(d*x + c)^2 + 584*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
241,1,126,0,1.514384," ","integrate((a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, a^{2} \cos\left(d x + c\right)^{6} + 224 \, a^{2} \cos\left(d x + c\right)^{5} + 355 \, a^{2} \cos\left(d x + c\right)^{4} + 426 \, a^{2} \cos\left(d x + c\right)^{3} + 568 \, a^{2} \cos\left(d x + c\right)^{2} + 1136 \, a^{2} \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{693 \, {\left(d \cos\left(d x + c\right) + d\right)} \sqrt{\cos\left(d x + c\right)}}"," ",0,"2/693*(63*a^2*cos(d*x + c)^6 + 224*a^2*cos(d*x + c)^5 + 355*a^2*cos(d*x + c)^4 + 426*a^2*cos(d*x + c)^3 + 568*a^2*cos(d*x + c)^2 + 1136*a^2*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/((d*cos(d*x + c) + d)*sqrt(cos(d*x + c)))","A",0
242,1,50,0,0.695227," ","integrate((a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/4),x, algorithm=""fricas"")","\frac{4 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \cos\left(d x + c\right)^{\frac{1}{4}} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"4*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*cos(d*x + c)^(1/4)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
243,1,189,0,0.767856," ","integrate(sec(f*x+e)^(1/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{a \cos\left(f x + e\right)^{3} - 7 \, a \cos\left(f x + e\right)^{2} - \frac{4 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{\sqrt{\cos\left(f x + e\right)}} + 8 \, a}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2}}\right)}{2 \, f}, \frac{\sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\cos\left(f x + e\right)} \sin\left(f x + e\right)}{a \cos\left(f x + e\right)^{2} - a \cos\left(f x + e\right) - 2 \, a}\right)}{f}\right]"," ",0,"[1/2*sqrt(a)*log((a*cos(f*x + e)^3 - 7*a*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 - 2*cos(f*x + e))*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e)/sqrt(cos(f*x + e)) + 8*a)/(cos(f*x + e)^3 + cos(f*x + e)^2))/f, sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(cos(f*x + e))*sin(f*x + e)/(a*cos(f*x + e)^2 - a*cos(f*x + e) - 2*a))/f]","B",0
244,1,215,0,0.698438," ","integrate((-sec(f*x+e))^(1/2)*(a-a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{4 \, {\left(\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{\cos\left(f x + e\right)}} + {\left(a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) + 8 \, a\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{2} \sin\left(f x + e\right)}\right)}{2 \, f}, -\frac{\sqrt{-a} \arctan\left(\frac{2 \, {\left(\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{\cos\left(f x + e\right)}}}{{\left(a \cos\left(f x + e\right) + 2 \, a\right)} \sin\left(f x + e\right)}\right)}{f}\right]"," ",0,"[1/2*sqrt(a)*log((4*(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + 2*cos(f*x + e))*sqrt(a)*sqrt((a*cos(f*x + e) - a)/cos(f*x + e))*sqrt(-1/cos(f*x + e)) + (a*cos(f*x + e)^2 + 8*a*cos(f*x + e) + 8*a)*sin(f*x + e))/(cos(f*x + e)^2*sin(f*x + e)))/f, -sqrt(-a)*arctan(2*(cos(f*x + e)^2 + cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) - a)/cos(f*x + e))*sqrt(-1/cos(f*x + e))/((a*cos(f*x + e) + 2*a)*sin(f*x + e)))/f]","B",0
245,1,481,0,1.156622," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + 1\right)} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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}} + \frac{4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{4 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{2 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + \sqrt{-a} {\left(\cos\left(d x + c\right) + 1\right)} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/4*(sqrt(a)*(cos(d*x + c) + 1)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 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)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d), -1/2*(2*sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + sqrt(-a)*(cos(d*x + c) + 1)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)]","A",0
246,1,351,0,0.643264," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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}, \frac{\sqrt{2} a \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{a d}\right]"," ",0,"[1/2*(sqrt(2)*sqrt(a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a*d), (sqrt(2)*a*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a*d)]","A",0
247,1,160,0,0.679184," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c))/d]","A",0
248,1,281,0,1.472903," ","integrate(1/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{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)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), (sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
249,1,318,0,0.511045," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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}} + \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{6 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, -\frac{3 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - \frac{2 \, {\left(\cos\left(d x + c\right)^{2} - \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{3 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/6*(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)/cos(d*x + c))*sqrt(cos(d*x + c))*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*(cos(d*x + c)^2 - cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d), -1/3*(3*sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*(cos(d*x + c)^2 - cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)]","A",0
250,1,342,0,0.629751," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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}} + \frac{4 \, {\left(3 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} + 13 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{30 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{15 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + \frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} + 13 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{15 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/30*(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)/cos(d*x + c))*sqrt(cos(d*x + c))*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*(3*cos(d*x + c)^3 - cos(d*x + c)^2 + 13*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d), 1/15*(15*sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*(3*cos(d*x + c)^3 - cos(d*x + c)^2 + 13*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(a*d*cos(d*x + c) + a*d)]","A",0
251,1,579,0,0.606340," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\frac{9 \, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)^{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} + \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 6 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 2\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)}}\right]"," ",0,"[1/8*(9*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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)^2 + 2*cos(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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))*(3*cos(d*x + c) + 2)*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), -1/4*(9*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 6*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(3*cos(d*x + c) + 2)*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
252,1,559,0,0.811137," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 4 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(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))*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), 1/4*(5*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 4*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)]","B",0
253,1,338,0,0.552959," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*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), -1/4*(sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
254,1,340,0,0.718046," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*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), -1/4*(3*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
255,1,378,0,0.546233," ","integrate(1/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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) + \frac{4 \, {\left(4 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(4 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)^2 + 5*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), 1/4*(7*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(4*cos(d*x + c)^2 + 5*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
256,1,398,0,0.732093," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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) + \frac{4 \, {\left(4 \, \cos\left(d x + c\right)^{3} - 12 \, \cos\left(d x + c\right)^{2} - 19 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, -\frac{33 \, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(4 \, \cos\left(d x + c\right)^{3} - 12 \, \cos\left(d x + c\right)^{2} - 19 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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 - 12*cos(d*x + c)^2 - 19*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -1/12*(33*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(4*cos(d*x + c)^3 - 12*cos(d*x + c)^2 - 19*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
257,1,418,0,0.681816," ","integrate(1/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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) + \frac{4 \, {\left(4 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{3} + 36 \, \cos\left(d x + c\right)^{2} + 49 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, \frac{75 \, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(4 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{3} + 36 \, \cos\left(d x + c\right)^{2} + 49 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{20 \, {\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)^4 - 4*cos(d*x + c)^3 + 36*cos(d*x + c)^2 + 49*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), 1/20*(75*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(4*cos(d*x + c)^4 - 4*cos(d*x + c)^3 + 36*cos(d*x + c)^2 + 49*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
258,1,667,0,1.417547," ","integrate(sec(d*x+c)^(9/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \log\left(-\frac{a \cos\left(d x + c\right)^{2} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)^{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} + \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + \frac{4 \, {\left(35 \, \cos\left(d x + c\right)^{2} + 55 \, \cos\left(d x + c\right) + 16\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 80 \, {\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{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, {\left(35 \, \cos\left(d x + c\right)^{2} + 55 \, \cos\left(d x + c\right) + 16\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}\right]"," ",0,"[1/64*(115*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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)^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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*(35*cos(d*x + c)^2 + 55*cos(d*x + c) + 16)*sqrt((a*cos(d*x + c) + a)/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), -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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 80*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*(35*cos(d*x + c)^2 + 55*cos(d*x + c) + 16)*sqrt((a*cos(d*x + c) + a)/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
259,1,665,0,0.990112," ","integrate(sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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} - \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right)\right)} \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - \frac{4 \, {\left(11 \, \cos\left(d x + c\right)^{2} + 15 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\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} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - \frac{2 \, {\left(11 \, \cos\left(d x + c\right)^{2} + 15 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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*(cos(d*x + c)^2 - 2*cos(d*x + c))*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)) + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*(11*cos(d*x + c)^2 + 15*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), 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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 32*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*(11*cos(d*x + c)^2 + 15*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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)]","B",0
260,1,426,0,1.149267," ","integrate(sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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) + \frac{4 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 7 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 7 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(3*cos(d*x + c)^2 + 7*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(3*cos(d*x + c)^2 + 7*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
261,1,422,0,0.766515," ","integrate(sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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) + \frac{4 \, {\left(5 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(5*cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(5*cos(d*x + c)^2 + cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
262,1,426,0,1.054544," ","integrate(sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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) - \frac{4 \, {\left(13 \, \cos\left(d x + c\right)^{2} + 9 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(13 \, \cos\left(d x + c\right)^{2} + 9 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 4*(13*cos(d*x + c)^2 + 9*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(13*cos(d*x + c)^2 + 9*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
263,1,446,0,1.536146," ","integrate(1/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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) + \frac{4 \, {\left(32 \, \cos\left(d x + c\right)^{3} + 85 \, \cos\left(d x + c\right)^{2} + 49 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + \frac{2 \, {\left(32 \, \cos\left(d x + c\right)^{3} + 85 \, \cos\left(d x + c\right)^{2} + 49 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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 + 85*cos(d*x + c)^2 + 49*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), 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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(32*cos(d*x + c)^3 + 85*cos(d*x + c)^2 + 49*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
264,1,466,0,0.969688," ","integrate(1/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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) + \frac{4 \, {\left(32 \, \cos\left(d x + c\right)^{4} - 160 \, \cos\left(d x + c\right)^{3} - 503 \, \cos\left(d x + c\right)^{2} - 299 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\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)}}, -\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - \frac{2 \, {\left(32 \, \cos\left(d x + c\right)^{4} - 160 \, \cos\left(d x + c\right)^{3} - 503 \, \cos\left(d x + c\right)^{2} - 299 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{96 \, {\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)^4 - 160*cos(d*x + c)^3 - 503*cos(d*x + c)^2 - 299*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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), -1/96*(489*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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(32*cos(d*x + c)^4 - 160*cos(d*x + c)^3 - 503*cos(d*x + c)^2 - 299*cos(d*x + c))*sqrt((a*cos(d*x + c) + a)/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
265,1,337,0,0.871208," ","integrate(sec(d*x+c)^(7/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{8 \, {\left(\sqrt{2} \cos\left(d x + c\right)^{2} + \sqrt{2} \cos\left(d x + c\right)\right)} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - 7 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + 2 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}{\cos\left(d x + c\right) + 1}\right) + 7 \, {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - 2 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}{\cos\left(d x + c\right) + 1}\right) - \frac{4 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{16 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}"," ",0,"1/16*(8*(sqrt(2)*cos(d*x + c)^2 + sqrt(2)*cos(d*x + c))*log(-(2*sqrt(2)*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + cos(d*x + c)^2 - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - 7*(cos(d*x + c)^2 + cos(d*x + c))*log(-(cos(d*x + c)^2 + 2*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c) - 2)/(cos(d*x + c) + 1)) + 7*(cos(d*x + c)^2 + cos(d*x + c))*log(-(cos(d*x + c)^2 - 2*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c) - 2)/(cos(d*x + c) + 1)) - 4*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*(cos(d*x + c) - 2)*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))","B",0
266,1,297,0,0.970806," ","integrate(sec(d*x+c)^(5/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + {\left(\cos\left(d x + c\right) + 1\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + 2 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}{\cos\left(d x + c\right) + 1}\right) - {\left(\cos\left(d x + c\right) + 1\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - 2 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}{\cos\left(d x + c\right) + 1}\right) + \frac{4 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\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*(2*(sqrt(2)*cos(d*x + c) + sqrt(2))*log((2*sqrt(2)*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c)^2 + 2*cos(d*x + c) + 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + (cos(d*x + c) + 1)*log(-(cos(d*x + c)^2 + 2*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c) - 2)/(cos(d*x + c) + 1)) - (cos(d*x + c) + 1)*log(-(cos(d*x + c)^2 - 2*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c) - 2)/(cos(d*x + c) + 1)) + 4*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","B",0
267,1,223,0,0.921842," ","integrate(sec(d*x+c)^(3/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) - \log\left(-\frac{\cos\left(d x + c\right)^{2} + 2 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}{\cos\left(d x + c\right) + 1}\right) + \log\left(-\frac{\cos\left(d x + c\right)^{2} - 2 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}{\cos\left(d x + c\right) + 1}\right)}{2 \, d}"," ",0,"1/2*(sqrt(2)*log(-(2*sqrt(2)*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + cos(d*x + c)^2 - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) - log(-(cos(d*x + c)^2 + 2*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c) - 2)/(cos(d*x + c) + 1)) + log(-(cos(d*x + c)^2 - 2*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c) - 2)/(cos(d*x + c) + 1)))/d","B",0
268,1,88,0,0.624626," ","integrate(sec(d*x+c)^(1/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{2} + 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 \, d}"," ",0,"1/2*sqrt(2)*log((2*sqrt(2)*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c)^2 + 2*cos(d*x + c) + 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/d","B",0
269,1,144,0,0.696982," ","integrate(1/sec(d*x+c)^(1/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + 4 \, \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/2*((sqrt(2)*cos(d*x + c) + sqrt(2))*log(-(2*sqrt(2)*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + cos(d*x + c)^2 - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c) + d)","B",0
270,1,163,0,1.216058," ","integrate(1/sec(d*x+c)^(3/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + \frac{4 \, {\left(\cos\left(d x + c\right)^{2} - \cos\left(d x + c\right)\right)} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/6*(3*(sqrt(2)*cos(d*x + c) + sqrt(2))*log((2*sqrt(2)*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - cos(d*x + c)^2 + 2*cos(d*x + c) + 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(cos(d*x + c)^2 - cos(d*x + c))*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
271,1,174,0,0.473284," ","integrate(1/sec(d*x+c)^(5/2)/(1+sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{15 \, {\left(\sqrt{2} \cos\left(d x + c\right) + \sqrt{2}\right)} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right) + \frac{4 \, {\left(3 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} + 13 \, \cos\left(d x + c\right)\right)} \sqrt{\frac{\cos\left(d x + c\right) + 1}{\cos\left(d x + c\right)}} \sin\left(d x + c\right)}{\sqrt{\cos\left(d x + c\right)}}}{30 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"1/30*(15*(sqrt(2)*cos(d*x + c) + sqrt(2))*log(-(2*sqrt(2)*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + cos(d*x + c)^2 - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(3*cos(d*x + c)^3 - cos(d*x + c)^2 + 13*cos(d*x + c))*sqrt((cos(d*x + c) + 1)/cos(d*x + c))*sin(d*x + c)/sqrt(cos(d*x + c)))/(d*cos(d*x + c) + d)","A",0
272,0,0,0,0.485508," ","integrate((e*sec(d*x+c))^(4/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}} e \sec\left(d x + c\right), x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(1/3)*e*sec(d*x + c), x)","F",0
273,0,0,0,0.501477," ","integrate((e*sec(d*x+c))^(1/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(1/3), x)","F",0
274,0,0,0,0.523139," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{e \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(1/3)/(e*sec(d*x + c)), x)","F",0
275,0,0,0,0.628381," ","integrate((e*sec(d*x+c))^(8/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}} e^{2} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(2/3)*e^2*sec(d*x + c)^2, x)","F",0
276,0,0,0,0.592320," ","integrate((e*sec(d*x+c))^(5/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}} e \sec\left(d x + c\right), x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(2/3)*e*sec(d*x + c), x)","F",0
277,0,0,0,0.544145," ","integrate((e*sec(d*x+c))^(2/3)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(2/3), x)","F",0
278,0,0,0,0.924510," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{e \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(2/3)/(e*sec(d*x + c)), x)","F",0
279,0,0,0,0.584557," ","integrate((a+a*sec(d*x+c))^(1/2)/(e*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{e^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(d*x + c) + a)*(e*sec(d*x + c))^(2/3)/(e^2*sec(d*x + c)^2), x)","F",0
280,-1,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(1/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(2/3)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,0,0,0,0.974842," ","integrate(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{\frac{4}{3}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^(4/3), x)","F",0
285,-2,0,0,0.000000," ","integrate(sec(d*x+c)^(4/3)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
286,0,0,0,0.489588," ","integrate(sec(d*x+c)^(5/3)*(a+a*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{\frac{5}{3}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^(5/3), x)","F",0
287,-1,0,0,0.000000," ","integrate((a+a*sec(d*x+c))^(4/3)/sec(d*x+c)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,0,0,0,0.661782," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} \sec\left(f x + e\right)^{4} + 4 \, a^{4} \sec\left(f x + e\right)^{3} + 6 \, a^{4} \sec\left(f x + e\right)^{2} + 4 \, a^{4} \sec\left(f x + e\right) + a^{4}\right)} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a^4*sec(f*x + e)^4 + 4*a^4*sec(f*x + e)^3 + 6*a^4*sec(f*x + e)^2 + 4*a^4*sec(f*x + e) + a^4)*sec(f*x + e)^n, x)","F",0
289,0,0,0,0.954051," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}\right)} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3)*sec(f*x + e)^n, x)","F",0
290,0,0,0,0.978834," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*sec(f*x + e)^n, x)","F",0
291,0,0,0,1.192853," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
292,0,0,0,1.383084," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(f x + e\right)^{n}}{a \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral(sec(f*x + e)^n/(a*sec(f*x + e) + a), x)","F",0
293,0,0,0,0.902577," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(f x + e\right)^{n}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sec(f*x + e)^n/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
294,0,0,0,0.549144," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(\sec\left(f x + e\right)^{2} + 2 \, \sec\left(f x + e\right) + 1\right)} \sec\left(f x + e\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}, x\right)"," ",0,"integral((sec(f*x + e)^2 + 2*sec(f*x + e) + 1)*sec(f*x + e)^n*sqrt(sec(f*x + e) + 1), x)","F",0
295,0,0,0,0.671518," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sec\left(f x + e\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral(sec(f*x + e)^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
296,0,0,0,0.587131," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sec\left(f x + e\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}, x\right)"," ",0,"integral(sec(f*x + e)^n*sqrt(sec(f*x + e) + 1), x)","F",0
297,0,0,0,0.529286," ","integrate(sec(f*x+e)^n/(1+sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(f x + e\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}, x\right)"," ",0,"integral(sec(f*x + e)^n/sqrt(sec(f*x + e) + 1), x)","F",0
298,0,0,0,0.605979," ","integrate(sec(f*x+e)^n/(1+sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(f x + e\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}}{\sec\left(f x + e\right)^{2} + 2 \, \sec\left(f x + e\right) + 1}, x\right)"," ",0,"integral(sec(f*x + e)^n*sqrt(sec(f*x + e) + 1)/(sec(f*x + e)^2 + 2*sec(f*x + e) + 1), x)","F",0
299,0,0,0,0.606018," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(-\sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((-sec(f*x + e))^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
300,0,0,0,0.570902," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(-\sec\left(f x + e\right)\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}, x\right)"," ",0,"integral((-sec(f*x + e))^n*sqrt(sec(f*x + e) + 1), x)","F",0
301,0,0,0,0.588740," ","integrate((-sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-\sec\left(f x + e\right)\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}, x\right)"," ",0,"integral((-sec(f*x + e))^n/sqrt(sec(f*x + e) + 1), x)","F",0
302,0,0,0,0.547886," ","integrate((-sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-\sec\left(f x + e\right)\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}}{\sec\left(f x + e\right)^{2} + 2 \, \sec\left(f x + e\right) + 1}, x\right)"," ",0,"integral((-sec(f*x + e))^n*sqrt(sec(f*x + e) + 1)/(sec(f*x + e)^2 + 2*sec(f*x + e) + 1), x)","F",0
303,0,0,0,0.597172," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((d*sec(f*x + e))^n*(sec(f*x + e) + 1)^(3/2), x)","F",0
304,0,0,0,0.558120," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}, x\right)"," ",0,"integral((d*sec(f*x + e))^n*sqrt(sec(f*x + e) + 1), x)","F",0
305,0,0,0,0.576960," ","integrate((d*sec(f*x+e))^n/(1+sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{\sec\left(f x + e\right) + 1}}, x\right)"," ",0,"integral((d*sec(f*x + e))^n/sqrt(sec(f*x + e) + 1), x)","F",0
306,0,0,0,0.542689," ","integrate((d*sec(f*x+e))^n/(1+sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{n} \sqrt{\sec\left(f x + e\right) + 1}}{\sec\left(f x + e\right)^{2} + 2 \, \sec\left(f x + e\right) + 1}, x\right)"," ",0,"integral((d*sec(f*x + e))^n*sqrt(sec(f*x + e) + 1)/(sec(f*x + e)^2 + 2*sec(f*x + e) + 1), x)","F",0
307,0,0,0,0.473884," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*sqrt(a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
308,0,0,0,0.527665," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^(3/2)*sec(f*x + e)^n, x)","F",0
309,0,0,0,0.519735," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
310,0,0,0,0.580826," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(f x + e\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(sec(f*x + e)^n/sqrt(a*sec(f*x + e) + a), x)","F",0
311,0,0,0,0.570059," ","integrate(sec(f*x+e)^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*sec(f*x + e)^n/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
312,0,0,0,0.512864," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(-\sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^(3/2)*(-sec(f*x + e))^n, x)","F",0
313,0,0,0,0.511987," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*(-sec(f*x + e))^n, x)","F",0
314,0,0,0,0.508009," ","integrate((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-\sec\left(f x + e\right)\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((-sec(f*x + e))^n/sqrt(a*sec(f*x + e) + a), x)","F",0
315,0,0,0,0.570412," ","integrate((-sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*(-sec(f*x + e))^n/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
316,0,0,0,0.473847," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e))^n, x)","F",0
317,0,0,0,0.463348," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
318,0,0,0,0.899203," ","integrate((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((d*sec(f*x + e))^n/sqrt(a*sec(f*x + e) + a), x)","F",0
319,0,0,0,0.640662," ","integrate((d*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*(d*sec(f*x + e))^n/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
320,0,0,0,0.499810," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(f x + e\right)^{2} - 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sqrt{-a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 - 2*a^2*sec(f*x + e) + a^2)*sqrt(-a*sec(f*x + e) + a)*(-sec(f*x + e))^n, x)","F",0
321,0,0,0,0.546860," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a \sec\left(f x + e\right) - a\right)} \sqrt{-a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(a*sec(f*x + e) - a)*sqrt(-a*sec(f*x + e) + a)*(-sec(f*x + e))^n, x)","F",0
322,0,0,0,0.517671," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(sqrt(-a*sec(f*x + e) + a)*(-sec(f*x + e))^n, x)","F",0
323,0,0,0,0.466424," ","integrate((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}}{a \sec\left(f x + e\right) - a}, x\right)"," ",0,"integral(-sqrt(-a*sec(f*x + e) + a)*(-sec(f*x + e))^n/(a*sec(f*x + e) - a), x)","F",0
324,0,0,0,0.545707," ","integrate((-sec(f*x+e))^n/(a-a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a \sec\left(f x + e\right) + a} \left(-\sec\left(f x + e\right)\right)^{n}}{a^{2} \sec\left(f x + e\right)^{2} - 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(-a*sec(f*x + e) + a)*(-sec(f*x + e))^n/(a^2*sec(f*x + e)^2 - 2*a^2*sec(f*x + e) + a^2), x)","F",0
325,0,0,0,0.467129," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a \sec\left(f x + e\right) - a\right)} \sqrt{-a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral(-(a*sec(f*x + e) - a)*sqrt(-a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
326,0,0,0,0.531033," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a \sec\left(f x + e\right) + a} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral(sqrt(-a*sec(f*x + e) + a)*sec(f*x + e)^n, x)","F",0
327,0,0,0,0.514688," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a \sec\left(f x + e\right) - a\right)} \sqrt{-a \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(a*sec(f*x + e) - a)*sqrt(-a*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
328,0,0,0,0.455909," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(sqrt(-a*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
329,0,0,0,0.524585," ","integrate(sec(f*x+e)^n*(1+sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(\sec\left(f x + e\right) + 1\right)}^{m} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((sec(f*x + e) + 1)^m*sec(f*x + e)^n, x)","F",0
330,0,0,0,0.507546," ","integrate((1-sec(f*x+e))^m*sec(f*x+e)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-\sec\left(f x + e\right) + 1\right)}^{m} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((-sec(f*x + e) + 1)^m*sec(f*x + e)^n, x)","F",0
331,0,0,0,0.535293," ","integrate(sec(f*x+e)^n*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
332,0,0,0,0.487188," ","integrate(sec(f*x+e)^n*(a-a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(-a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((-a*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
333,0,0,0,0.551754," ","integrate((-sec(f*x+e))^n*(1+sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(-\sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{m}, x\right)"," ",0,"integral((-sec(f*x + e))^n*(sec(f*x + e) + 1)^m, x)","F",0
334,0,0,0,0.541989," ","integrate((1-sec(f*x+e))^m*(-sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(-\sec\left(f x + e\right)\right)^{n} {\left(-\sec\left(f x + e\right) + 1\right)}^{m}, x\right)"," ",0,"integral((-sec(f*x + e))^n*(-sec(f*x + e) + 1)^m, x)","F",0
335,0,0,0,0.543390," ","integrate((-sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(-\sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*(-sec(f*x + e))^n, x)","F",0
336,0,0,0,0.566308," ","integrate((-sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(-a \sec\left(f x + e\right) + a\right)}^{m} \left(-\sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((-a*sec(f*x + e) + a)^m*(-sec(f*x + e))^n, x)","F",0
337,0,0,0,0.563845," ","integrate((d*sec(f*x+e))^n*(1+sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{m}, x\right)"," ",0,"integral((d*sec(f*x + e))^n*(sec(f*x + e) + 1)^m, x)","F",0
338,0,0,0,0.575226," ","integrate((1-sec(f*x+e))^m*(d*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{n} {\left(-\sec\left(f x + e\right) + 1\right)}^{m}, x\right)"," ",0,"integral((d*sec(f*x + e))^n*(-sec(f*x + e) + 1)^m, x)","F",0
339,0,0,0,0.491002," ","integrate((d*sec(f*x+e))^n*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
340,0,0,0,0.567864," ","integrate((d*sec(f*x+e))^n*(a-a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(-a \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((-a*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
341,0,0,0,0.547525," ","integrate(sec(f*x+e)^4*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{4}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*sec(f*x + e)^4, x)","F",0
342,0,0,0,0.508224," ","integrate(sec(f*x+e)^3*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{3}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*sec(f*x + e)^3, x)","F",0
343,0,0,0,0.539914," ","integrate(sec(f*x+e)^2*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*sec(f*x + e)^2, x)","F",0
344,0,0,0,0.578669," ","integrate(sec(f*x+e)*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right), x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*sec(f*x + e), x)","F",0
345,0,0,0,0.694919," ","integrate((a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m, x)","F",0
346,0,0,0,0.631839," ","integrate(cos(f*x+e)*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right), x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*cos(f*x + e), x)","F",0
347,0,0,0,0.522059," ","integrate((d*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \sec\left(f x + e\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m} d \sec\left(f x + e\right), x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(a*sec(f*x + e) + a)^m*d*sec(f*x + e), x)","F",0
348,0,0,0,0.523334," ","integrate((d*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \sec\left(f x + e\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(a*sec(f*x + e) + a)^m, x)","F",0
349,0,0,0,0.532025," ","integrate((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(a*sec(f*x + e) + a)^m/(d*sec(f*x + e)), x)","F",0
350,0,0,0,0.537588," ","integrate((a+a*sec(f*x+e))^m/(d*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} {\left(a \sec\left(f x + e\right) + a\right)}^{m}}{d^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(a*sec(f*x + e) + a)^m/(d^2*sec(f*x + e)^2), x)","F",0
351,0,0,0,0.450375," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*cos(d*x + c)^3*sec(d*x + c) + a*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
352,0,0,0,0.444702," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + 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)^2*sec(d*x + c) + a*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
353,0,0,0,0.472708," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right) \sec\left(d x + c\right) + a \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*cos(d*x + c)*sec(d*x + c) + a*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
354,0,0,0,0.505007," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
355,0,0,0,0.526212," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(d x + c\right) + a}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
356,0,0,0,0.508845," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
357,0,0,0,0.500418," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
358,0,0,0,0.487949," ","integrate((a+a*sec(d*x+c))/cos(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((a*sec(d*x + c) + a)/cos(d*x + c)^(7/2), x)","F",0
359,0,0,0,0.475454," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^4*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^4*sec(d*x + c) + a^2*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
360,0,0,0,0.500946," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*cos(d*x + c)^3*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^3*sec(d*x + c) + a^2*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
361,0,0,0,0.528694," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + 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)^2*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^2*sec(d*x + c) + a^2*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
362,0,0,0,0.628716," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right) + 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)*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)*sec(d*x + c) + a^2*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
363,0,0,0,0.548583," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)*sqrt(cos(d*x + c)), x)","F",0
364,0,0,0,0.607312," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)/sqrt(cos(d*x + c)), x)","F",0
365,0,0,0,0.461738," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)/cos(d*x + c)^(3/2), x)","F",0
366,0,0,0,0.544619," ","integrate((a+a*sec(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2)/cos(d*x + c)^(5/2), x)","F",0
367,0,0,0,0.630810," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^4*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^4*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^4*sec(d*x + c) + a^3*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
368,0,0,0,0.458604," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^3*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^3*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^3*sec(d*x + c) + a^3*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
369,0,0,0,0.526992," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*cos(d*x + c)^2*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^2*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^2*sec(d*x + c) + a^3*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
370,0,0,0,0.654157," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right) + 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)*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)*sec(d*x + c) + a^3*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
371,0,0,0,0.518233," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)*sqrt(cos(d*x + c)), x)","F",0
372,0,0,0,0.493618," ","integrate((a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)/sqrt(cos(d*x + c)), x)","F",0
373,0,0,0,0.524265," ","integrate((a+a*sec(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3)/cos(d*x + c)^(3/2), x)","F",0
374,0,0,0,0.544806," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^(5/2)/(a*sec(d*x + c) + a), x)","F",0
375,0,0,0,0.697547," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/(a*sec(d*x + c) + a), x)","F",0
376,0,0,0,0.641680," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*sec(d*x + c) + a), x)","F",0
377,0,0,0,0.549083," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a \cos\left(d x + c\right) \sec\left(d x + c\right) + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*cos(d*x + c)*sec(d*x + c) + a*cos(d*x + c)), x)","F",0
378,0,0,0,0.690769," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(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} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*cos(d*x + c)^2*sec(d*x + c) + a*cos(d*x + c)^2), x)","F",0
379,0,0,0,0.887317," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(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} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*cos(d*x + c)^3*sec(d*x + c) + a*cos(d*x + c)^3), x)","F",0
380,0,0,0,0.972254," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(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} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a*cos(d*x + c)^4*sec(d*x + c) + a*cos(d*x + c)^4), x)","F",0
381,0,0,0,1.140857," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(cos(d*x + c)^(5/2)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
382,0,0,0,0.911428," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
383,0,0,0,0.853013," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{2} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*sec(d*x + c)^2 + 2*a^2*sec(d*x + c) + a^2), x)","F",0
384,0,0,0,0.705241," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(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) \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)*sec(d*x + c) + a^2*cos(d*x + c)), x)","F",0
385,0,0,0,0.769969," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(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} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^2*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^2*sec(d*x + c) + a^2*cos(d*x + c)^2), x)","F",0
386,0,0,0,0.731442," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(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} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^3*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^3*sec(d*x + c) + a^2*cos(d*x + c)^3), x)","F",0
387,0,0,0,0.586898," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(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} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^4*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^4*sec(d*x + c) + a^2*cos(d*x + c)^4), x)","F",0
388,0,0,0,0.698374," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(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} \sec\left(d x + c\right)^{2} + 2 \, a^{2} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^2*cos(d*x + c)^5*sec(d*x + c)^2 + 2*a^2*cos(d*x + c)^5*sec(d*x + c) + a^2*cos(d*x + c)^5), x)","F",0
389,0,0,0,0.537051," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(cos(d*x + c)^(5/2)/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
390,0,0,0,0.907120," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
391,0,0,0,0.994572," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{a^{3} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*sec(d*x + c)^3 + 3*a^3*sec(d*x + c)^2 + 3*a^3*sec(d*x + c) + a^3), x)","F",0
392,0,0,0,0.661436," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(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) \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)*sec(d*x + c) + a^3*cos(d*x + c)), x)","F",0
393,0,0,0,0.609144," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(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)^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^2*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^2*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^2*sec(d*x + c) + a^3*cos(d*x + c)^2), x)","F",0
394,0,0,0,0.750426," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(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} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^3*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^3*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^3*sec(d*x + c) + a^3*cos(d*x + c)^3), x)","F",0
395,0,0,0,0.954424," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(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} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{4}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^4*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^4*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^4*sec(d*x + c) + a^3*cos(d*x + c)^4), x)","F",0
396,0,0,0,0.785560," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(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} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{5} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{5}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^5*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^5*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^5*sec(d*x + c) + a^3*cos(d*x + c)^5), x)","F",0
397,0,0,0,0.566529," ","integrate(1/cos(d*x+c)^(11/2)/(a+a*sec(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} \sec\left(d x + c\right)^{3} + 3 \, a^{3} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right)^{2} + 3 \, a^{3} \cos\left(d x + c\right)^{6} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{6}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(a^3*cos(d*x + c)^6*sec(d*x + c)^3 + 3*a^3*cos(d*x + c)^6*sec(d*x + c)^2 + 3*a^3*cos(d*x + c)^6*sec(d*x + c) + a^3*cos(d*x + c)^6), x)","F",0
398,1,79,0,0.661628," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
399,1,69,0,0.844736," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right) + 8\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right) + d\right)}}"," ",0,"2/15*(3*cos(d*x + c)^2 + 4*cos(d*x + c) + 8)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
400,1,57,0,1.152678," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) + 2\right)} \sqrt{\cos\left(d x + c\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))*(cos(d*x + c) + 2)*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
401,1,49,0,1.265676," ","integrate(cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
402,1,180,0,0.732379," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2))/d, sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a))/d]","A",0
403,1,325,0,0.543332," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) + 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{{\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) + 4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/2*((cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
404,1,355,0,0.548949," ","integrate((a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/16*(4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))*sin(d*x + c) + 3*(cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/8*(2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))*sin(d*x + c) + 3*(cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
405,1,84,0,0.568197," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
406,1,72,0,0.583981," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
407,1,61,0,1.010661," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a \cos\left(d x + c\right) + 5 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
408,1,298,0,0.466264," ","integrate((a+a*sec(d*x+c))^(3/2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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 \cos\left(d x + c\right) + d}\right]"," ",0,"[1/2*(4*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (a*cos(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c) + d), (2*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + (a*cos(d*x + c) + a)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c) + d)]","A",0
409,1,337,0,0.747454," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{2 \, a \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*(a*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/2*(2*a*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*(a*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
410,1,369,0,0.554534," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(7 \, a \cos\left(d x + c\right) + 2 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, {\left(7 \, a \cos\left(d x + c\right) + 2 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 7 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/16*(4*(7*a*cos(d*x + c) + 2*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 7*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/8*(2*(7*a*cos(d*x + c) + 2*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 7*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
411,1,391,0,0.573322," ","integrate((a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(33 \, a \cos\left(d x + c\right)^{2} + 22 \, a \cos\left(d x + c\right) + 8 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{2 \, {\left(33 \, a \cos\left(d x + c\right)^{2} + 22 \, a \cos\left(d x + c\right) + 8 \, a\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 33 \, {\left(a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/96*(4*(33*a*cos(d*x + c)^2 + 22*a*cos(d*x + c) + 8*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 33*(a*cos(d*x + c)^4 + a*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3), 1/48*(2*(33*a*cos(d*x + c)^2 + 22*a*cos(d*x + c) + 8*a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 33*(a*cos(d*x + c)^4 + a*cos(d*x + c)^3)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)]","A",0
412,1,105,0,0.546817," ","integrate(cos(d*x+c)^(9/2)*(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
413,1,92,0,0.511056," ","integrate(cos(d*x+c)^(7/2)*(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
414,1,79,0,1.085547," ","integrate(cos(d*x+c)^(5/2)*(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
415,1,339,0,0.700259," ","integrate(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} \cos\left(d x + c\right) + 8 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{6 \, {\left(d \cos\left(d x + c\right) + d\right)}}, \frac{2 \, {\left(a^{2} \cos\left(d x + c\right) + 8 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 3 \, {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{3 \, {\left(d \cos\left(d x + c\right) + d\right)}}\right]"," ",0,"[1/6*(4*(a^2*cos(d*x + c) + 8*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*(a^2*cos(d*x + c) + a^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c) + d), 1/3*(2*(a^2*cos(d*x + c) + 8*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 3*(a^2*cos(d*x + c) + a^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c) + d)]","A",0
416,1,373,0,0.590164," ","integrate((a+a*sec(d*x+c))^(5/2)*cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}, \frac{2 \, {\left(2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(2*a^2*cos(d*x + c) + a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^2 + d*cos(d*x + c)), 1/2*(2*(2*a^2*cos(d*x + c) + a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^2 + d*cos(d*x + c))]","A",0
417,1,385,0,0.675247," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(11 \, a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}, \frac{2 \, {\left(11 \, a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 19 \, {\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{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/16*(4*(11*a^2*cos(d*x + c) + 2*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 19*(a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2), 1/8*(2*(11*a^2*cos(d*x + c) + 2*a^2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 19*(a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2)]","A",0
418,1,411,0,0.705081," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}, \frac{2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 75 \, {\left(a^{2} \cos\left(d x + c\right)^{4} + a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/96*(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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 75*(a^2*cos(d*x + c)^4 + a^2*cos(d*x + c)^3)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3), 1/48*(2*(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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 75*(a^2*cos(d*x + c)^4 + a^2*cos(d*x + c)^3)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^4 + d*cos(d*x + c)^3)]","A",0
419,1,437,0,0.577309," ","integrate((a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{768 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}, \frac{2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 489 \, {\left(a^{2} \cos\left(d x + c\right)^{5} + a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{384 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/768*(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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 489*(a^2*cos(d*x + c)^5 + a^2*cos(d*x + c)^4)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4), 1/384*(2*(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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 489*(a^2*cos(d*x + c)^5 + a^2*cos(d*x + c)^4)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4)]","A",0
420,1,324,0,0.952683," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 13\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)}}, \frac{15 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + 2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 13\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{15 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/30*(4*(3*cos(d*x + c)^2 - cos(d*x + c) + 13)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*sqrt(cos(d*x + c))*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), 1/15*(15*sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*(3*cos(d*x + c)^2 - cos(d*x + c) + 13)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
421,1,300,0,0.859567," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\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) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)}}, -\frac{3 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 1\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{3 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}\right]"," ",0,"[1/6*(4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 1)*sqrt(cos(d*x + c))*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)/cos(d*x + c))*sqrt(cos(d*x + c))*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), -1/3*(3*sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 1)*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
422,1,281,0,0.716881," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{2 \, {\left(a d \cos\left(d x + c\right) + a d\right)}}, \frac{\sqrt{2} {\left(a \cos\left(d x + c\right) + a\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{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)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d), (sqrt(2)*(a*cos(d*x + c) + a)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c) + a*d)]","A",0
423,1,160,0,0.622124," ","integrate(1/cos(d*x+c)^(1/2)/(a+a*sec(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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \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(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c))/d]","A",0
424,1,342,0,0.468268," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\cos\left(d x + c\right)^{2} + \frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right)}{2 \, a d}, \frac{\sqrt{2} a \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{a d}\right]"," ",0,"[1/2*(sqrt(2)*sqrt(a)*log(-(cos(d*x + c)^2 + 2*sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a*d), (sqrt(2)*a*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a*d)]","A",0
425,1,520,0,0.577425," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\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} + 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)}}, -\frac{2 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right)\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) + {\left(\cos\left(d x + c\right)^{2} + \cos\left(d x + c\right)\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}\right]"," ",0,"[1/4*((cos(d*x + c)^2 + cos(d*x + c))*sqrt(a)*log((a*cos(d*x + c)^3 + 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 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)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c)), -1/2*(2*sqrt(2)*(a*cos(d*x + c)^2 + a*cos(d*x + c))*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) + (cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c))/(a*d*cos(d*x + c)^2 + a*d*cos(d*x + c))]","A",0
426,1,550,0,0.876002," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)}}, \frac{8 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2}\right)} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{-\frac{1}{a}} \sqrt{\cos\left(d x + c\right)}}{\sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) + 7 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right)}{8 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/16*(4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*(cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(a)*log((a*cos(d*x + c)^3 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 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)/cos(d*x + c))*sqrt(cos(d*x + c))*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), 1/8*(8*sqrt(2)*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2)*sqrt(-1/a)*arctan(sqrt(2)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(-1/a)*sqrt(cos(d*x + c))/sin(d*x + c)) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) + 7*(cos(d*x + c)^3 + cos(d*x + c)^2)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2)]","A",0
427,1,400,0,0.488957," ","integrate(cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)}}, \frac{75 \, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{20 \, {\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*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), 1/20*(75*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(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)/cos(d*x + c))*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
428,1,380,0,0.663341," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)^{2} - 12 \, \cos\left(d x + c\right) - 19\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}, -\frac{33 \, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left(4 \, \cos\left(d x + c\right)^{2} - 12 \, \cos\left(d x + c\right) - 19\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)^2 - 12*cos(d*x + c) - 19)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), -1/12*(33*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(4*cos(d*x + c)^2 - 12*cos(d*x + c) - 19)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
429,1,360,0,0.714825," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(4 \, \cos\left(d x + c\right) + 5\right)} \sqrt{\cos\left(d x + c\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)}}, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(4 \, \cos\left(d x + c\right) + 5\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*(4*cos(d*x + c) + 5)*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), 1/4*(7*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(4*cos(d*x + c) + 5)*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
430,1,340,0,0.500475," ","integrate(1/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*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), -1/4*(3*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
431,1,338,0,0.471293," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*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), -1/4*(sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
432,1,550,0,0.506558," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\right) - 4 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 4 \, {\left(\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)^{2} + 2 \, a^{2} d \cos\left(d x + c\right) + a^{2} d\right)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)) - 4*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), 1/4*(5*sqrt(2)*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 4*(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
433,1,614,0,0.498752," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\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} + 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\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)}}, -\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\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} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*(3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))*sin(d*x + c) + 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 + 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c)), -1/4*(9*sqrt(2)*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(3*cos(d*x + c) + 2)*sqrt(cos(d*x + c))*sin(d*x + c) + 6*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(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
434,1,448,0,0.482765," ","integrate(cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)}}, -\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{96 \, {\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*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), -1/96*(489*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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(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)/cos(d*x + c))*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
435,1,428,0,0.463461," ","integrate(cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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)^{2} + 85 \, \cos\left(d x + c\right) + 49\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\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)}}, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, {\left(32 \, \cos\left(d x + c\right)^{2} + 85 \, \cos\left(d x + c\right) + 49\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)^2 + 85*cos(d*x + c) + 49)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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), 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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*(32*cos(d*x + c)^2 + 85*cos(d*x + c) + 49)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*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
436,1,408,0,0.527903," ","integrate(1/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(13 \, \cos\left(d x + c\right) + 9\right)} \sqrt{\cos\left(d x + c\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) + 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(13 \, \cos\left(d x + c\right) + 9\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*(13*cos(d*x + c) + 9)*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), -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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) + 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(13*cos(d*x + c) + 9)*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
437,1,408,0,0.499715," ","integrate(1/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(5 \, \cos\left(d x + c\right) + 1\right)} \sqrt{\cos\left(d x + c\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(5 \, \cos\left(d x + c\right) + 1\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*(5*cos(d*x + c) + 1)*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), -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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(5*cos(d*x + c) + 1)*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
438,1,408,0,0.485376," ","integrate(1/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 7\right)} \sqrt{\cos\left(d x + c\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)}}, -\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(3 \, \cos\left(d x + c\right) + 7\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*(3*cos(d*x + c) + 7)*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), -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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(3*cos(d*x + c) + 7)*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
439,1,638,0,0.529143," ","integrate(1/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(11 \, \cos\left(d x + c\right) + 15\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\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} - 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\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)}}, \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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(11 \, \cos\left(d x + c\right) + 15\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\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} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*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)/cos(d*x + c))*(11*cos(d*x + c) + 15)*sqrt(cos(d*x + c))*sin(d*x + c) + 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 - 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(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), 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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(11*cos(d*x + c) + 15)*sqrt(cos(d*x + c))*sin(d*x + c) + 32*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 + 3*cos(d*x + c) + 1)*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(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
440,1,702,0,0.532311," ","integrate(1/cos(d*x+c)^(9/2)/(a+a*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\left[\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} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \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(35 \, \cos\left(d x + c\right)^{2} + 55 \, \cos\left(d x + c\right) + 16\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\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} + 4 \, \sqrt{a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} {\left(\cos\left(d x + c\right) - 2\right)} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} + 8 \, a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2}}\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)}}, -\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} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)}}{a \sin\left(d x + c\right)}\right) - 2 \, {\left(35 \, \cos\left(d x + c\right)^{2} + 55 \, \cos\left(d x + c\right) + 16\right)} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\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} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(d x + c\right) + a}{\cos\left(d x + c\right)}} \sqrt{\cos\left(d x + c\right)} \sin\left(d x + c\right)}{a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - 2 \, a}\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)}}\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)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) - 2*a*cos(d*x + c) - 3*a)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1)) + 4*(35*cos(d*x + c)^2 + 55*cos(d*x + c) + 16)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 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 + 4*sqrt(a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*(cos(d*x + c) - 2)*sqrt(cos(d*x + c))*sin(d*x + c) - 7*a*cos(d*x + c)^2 + 8*a)/(cos(d*x + c)^3 + cos(d*x + c)^2)))/(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)), -1/32*(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)*arctan(sqrt(2)*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))/(a*sin(d*x + c))) - 2*(35*cos(d*x + c)^2 + 55*cos(d*x + c) + 16)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c) + 80*(cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + cos(d*x + c))*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*cos(d*x + c) + a)/cos(d*x + c))*sqrt(cos(d*x + c))*sin(d*x + c)/(a*cos(d*x + c)^2 - a*cos(d*x + c) - 2*a)))/(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
441,0,0,0,0.464943," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}\right)} \left(d \cos\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3)*(d*cos(f*x + e))^n, x)","F",0
442,0,0,0,0.488242," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \left(d \cos\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*(d*cos(f*x + e))^n, x)","F",0
443,0,0,0,0.460951," ","integrate((d*cos(f*x+e))^n*(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)*(d*cos(f*x + e))^n, x)","F",0
444,0,0,0,0.464869," ","integrate((d*cos(f*x+e))^n/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \cos\left(f x + e\right)\right)^{n}}{a \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*cos(f*x + e))^n/(a*sec(f*x + e) + a), x)","F",0
445,0,0,0,0.482519," ","integrate((d*cos(f*x+e))^n/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \cos\left(f x + e\right)\right)^{n}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*cos(f*x + e))^n/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
446,1,99,0,0.469216," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, b \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, b \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 \, b \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) + 6 \, b\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(9*b*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 9*b*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(16*a*cos(d*x + c)^3 + 9*b*cos(d*x + c)^2 + 8*a*cos(d*x + c) + 6*b)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
447,1,88,0,0.501990," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c)),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 \, b \cos\left(d x + c\right)^{2} + 3 \, a \cos\left(d x + c\right) + 2 \, b\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*b*cos(d*x + c)^2 + 3*a*cos(d*x + c) + 2*b)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
448,1,74,0,0.513769," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{b \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - b \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) + b\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(b*cos(d*x + c)^2*log(sin(d*x + c) + 1) - b*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*a*cos(d*x + c) + b)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
449,1,60,0,0.460363," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c)),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 \, b \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*b*sin(d*x + c))/(d*cos(d*x + c))","B",0
450,1,36,0,0.473220," ","integrate(a+b*sec(d*x+c),x, algorithm=""fricas"")","\frac{2 \, a d x + b \log\left(\sin\left(d x + c\right) + 1\right) - b \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"1/2*(2*a*d*x + b*log(sin(d*x + c) + 1) - b*log(-sin(d*x + c) + 1))/d","B",0
451,1,17,0,0.538234," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{b d x + a \sin\left(d x + c\right)}{d}"," ",0,"(b*d*x + a*sin(d*x + c))/d","A",0
452,1,29,0,0.447810," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{a d x + {\left(a \cos\left(d x + c\right) + 2 \, b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*d*x + (a*cos(d*x + c) + 2*b)*sin(d*x + c))/d","A",0
453,1,42,0,0.481899," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, b d x + {\left(2 \, a \cos\left(d x + c\right)^{2} + 3 \, b \cos\left(d x + c\right) + 4 \, a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*b*d*x + (2*a*cos(d*x + c)^2 + 3*b*cos(d*x + c) + 4*a)*sin(d*x + c))/d","A",0
454,1,53,0,0.467324," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, a d x + {\left(6 \, a \cos\left(d x + c\right)^{3} + 8 \, b \cos\left(d x + c\right)^{2} + 9 \, a \cos\left(d x + c\right) + 16 \, b\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(9*a*d*x + (6*a*cos(d*x + c)^3 + 8*b*cos(d*x + c)^2 + 9*a*cos(d*x + c) + 16*b)*sin(d*x + c))/d","A",0
455,1,64,0,0.535596," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\frac{45 \, b d x + {\left(24 \, a \cos\left(d x + c\right)^{4} + 30 \, b \cos\left(d x + c\right)^{3} + 32 \, a \cos\left(d x + c\right)^{2} + 45 \, b \cos\left(d x + c\right) + 64 \, a\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(45*b*d*x + (24*a*cos(d*x + c)^4 + 30*b*cos(d*x + c)^3 + 32*a*cos(d*x + c)^2 + 45*b*cos(d*x + c) + 64*a)*sin(d*x + c))/d","A",0
456,1,136,0,0.511576," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^2,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(5 \, a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 30 \, a b \cos\left(d x + c\right) + 4 \, {\left(5 \, a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 12 \, b^{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*(5*a^2 + 4*b^2)*cos(d*x + c)^4 + 30*a*b*cos(d*x + c) + 4*(5*a^2 + 4*b^2)*cos(d*x + c)^2 + 12*b^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
457,1,133,0,0.501775," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, a^{2} + 3 \, 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(4 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 6 \, b^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(3*(4*a^2 + 3*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*a^2 + 3*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*(4*a^2 + 3*b^2)*cos(d*x + c)^2 + 6*b^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
458,1,100,0,0.483448," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^2,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(3 \, a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{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) + (3*a^2 + 2*b^2)*cos(d*x + c)^2 + b^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
459,1,93,0,0.485271," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, a^{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) + b^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((2*a^2 + b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*a^2 + b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(4*a*b*cos(d*x + c) + b^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
460,1,74,0,0.468062," ","integrate((a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{a^{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) + b^{2} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)}"," ",0,"(a^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) + b^2*sin(d*x + c))/(d*cos(d*x + c))","B",0
461,1,52,0,0.453927," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a b d x + b^{2} \log\left(\sin\left(d x + c\right) + 1\right) - b^{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*b*d*x + b^2*log(sin(d*x + c) + 1) - b^2*log(-sin(d*x + c) + 1) + 2*a^2*sin(d*x + c))/d","A",0
462,1,40,0,0.446149," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} + 2 \, b^{2}\right)} d x + {\left(a^{2} \cos\left(d x + c\right) + 4 \, a b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((a^2 + 2*b^2)*d*x + (a^2*cos(d*x + c) + 4*a*b)*sin(d*x + c))/d","A",0
463,1,52,0,0.453751," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a b d x + {\left(a^{2} \cos\left(d x + c\right)^{2} + 3 \, a b \cos\left(d x + c\right) + 2 \, a^{2} + 3 \, b^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(3*a*b*d*x + (a^2*cos(d*x + c)^2 + 3*a*b*cos(d*x + c) + 2*a^2 + 3*b^2)*sin(d*x + c))/d","A",0
464,1,77,0,0.460461," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{2} + 4 \, b^{2}\right)} d x + {\left(6 \, a^{2} \cos\left(d x + c\right)^{3} + 16 \, a b \cos\left(d x + c\right)^{2} + 32 \, a b + 3 \, {\left(3 \, a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*a^2 + 4*b^2)*d*x + (6*a^2*cos(d*x + c)^3 + 16*a*b*cos(d*x + c)^2 + 32*a*b + 3*(3*a^2 + 4*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
465,1,86,0,0.453907," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{45 \, a b d x + {\left(12 \, a^{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(4 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 32 \, a^{2} + 40 \, b^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(45*a*b*d*x + (12*a^2*cos(d*x + c)^4 + 30*a*b*cos(d*x + c)^3 + 45*a*b*cos(d*x + c) + 4*(4*a^2 + 5*b^2)*cos(d*x + c)^2 + 32*a^2 + 40*b^2)*sin(d*x + c))/d","A",0
466,1,170,0,0.462292," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(16 \, {\left(15 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + 90 \, a b^{2} \cos\left(d x + c\right) + 15 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 24 \, b^{3} + 8 \, {\left(15 \, a^{2} b + 4 \, b^{3}\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*(4*a^3 + 9*a*b^2)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*a^3 + 9*a*b^2)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(16*(15*a^2*b + 4*b^3)*cos(d*x + c)^4 + 90*a*b^2*cos(d*x + c) + 15*(4*a^3 + 9*a*b^2)*cos(d*x + c)^3 + 24*b^3 + 8*(15*a^2*b + 4*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
467,1,140,0,0.481087," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(4 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, a b^{2} \cos\left(d x + c\right) + 8 \, {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 2 \, b^{3} + 3 \, {\left(4 \, a^{2} b + b^{3}\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*(4*a^2*b + b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*a^2*b + b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(8*a*b^2*cos(d*x + c) + 8*(a^3 + 2*a*b^2)*cos(d*x + c)^3 + 2*b^3 + 3*(4*a^2*b + b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
468,1,126,0,0.451424," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(9 \, a b^{2} \cos\left(d x + c\right) + 2 \, b^{3} + 2 \, {\left(9 \, a^{2} b + 2 \, b^{3}\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*(2*a^3 + 3*a*b^2)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*a^3 + 3*a*b^2)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(9*a*b^2*cos(d*x + c) + 2*b^3 + 2*(9*a^2*b + 2*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
469,1,112,0,0.489179," ","integrate((a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{3} d x \cos\left(d x + c\right)^{2} + {\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, a b^{2} \cos\left(d x + c\right) + b^{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 + (6*a^2*b + b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (6*a^2*b + b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(6*a*b^2*cos(d*x + c) + b^3)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
470,1,94,0,0.485886," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, a^{2} b d x \cos\left(d x + c\right) + 3 \, a b^{2} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a b^{2} \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) + b^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(6*a^2*b*d*x*cos(d*x + c) + 3*a*b^2*cos(d*x + c)*log(sin(d*x + c) + 1) - 3*a*b^2*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(a^3*cos(d*x + c) + b^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
471,1,72,0,0.481545," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{b^{3} \log\left(\sin\left(d x + c\right) + 1\right) - b^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(a^{3} + 6 \, a b^{2}\right)} d x + {\left(a^{3} \cos\left(d x + c\right) + 6 \, a^{2} b\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b^3*log(sin(d*x + c) + 1) - b^3*log(-sin(d*x + c) + 1) + (a^3 + 6*a*b^2)*d*x + (a^3*cos(d*x + c) + 6*a^2*b)*sin(d*x + c))/d","A",0
472,1,66,0,0.460922," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} d x + {\left(2 \, a^{3} \cos\left(d x + c\right)^{2} + 9 \, a^{2} b \cos\left(d x + c\right) + 4 \, a^{3} + 18 \, a b^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(3*a^2*b + 2*b^3)*d*x + (2*a^3*cos(d*x + c)^2 + 9*a^2*b*cos(d*x + c) + 4*a^3 + 18*a*b^2)*sin(d*x + c))/d","A",0
473,1,84,0,0.439216," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{3} + 4 \, a b^{2}\right)} d x + {\left(2 \, a^{3} \cos\left(d x + c\right)^{3} + 8 \, a^{2} b \cos\left(d x + c\right)^{2} + 16 \, a^{2} b + 8 \, b^{3} + 3 \, {\left(a^{3} + 4 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(3*(a^3 + 4*a*b^2)*d*x + (2*a^3*cos(d*x + c)^3 + 8*a^2*b*cos(d*x + c)^2 + 16*a^2*b + 8*b^3 + 3*(a^3 + 4*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
474,1,110,0,0.487690," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(9 \, a^{2} b + 4 \, b^{3}\right)} d x + {\left(24 \, a^{3} \cos\left(d x + c\right)^{4} + 90 \, a^{2} b \cos\left(d x + c\right)^{3} + 64 \, a^{3} + 240 \, a b^{2} + 8 \, {\left(4 \, a^{3} + 15 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(9 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(15*(9*a^2*b + 4*b^3)*d*x + (24*a^3*cos(d*x + c)^4 + 90*a^2*b*cos(d*x + c)^3 + 64*a^3 + 240*a*b^2 + 8*(4*a^3 + 15*a*b^2)*cos(d*x + c)^2 + 15*(9*a^2*b + 4*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
475,1,132,0,0.493699," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(5 \, a^{3} + 18 \, a b^{2}\right)} d x + {\left(40 \, a^{3} \cos\left(d x + c\right)^{5} + 144 \, a^{2} b \cos\left(d x + c\right)^{4} + 10 \, {\left(5 \, a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 384 \, a^{2} b + 160 \, b^{3} + 16 \, {\left(12 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(5 \, a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(5*a^3 + 18*a*b^2)*d*x + (40*a^3*cos(d*x + c)^5 + 144*a^2*b*cos(d*x + c)^4 + 10*(5*a^3 + 18*a*b^2)*cos(d*x + c)^3 + 384*a^2*b + 160*b^3 + 16*(12*a^2*b + 5*b^3)*cos(d*x + c)^2 + 15*(5*a^3 + 18*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
476,1,217,0,0.505317," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(8 \, a^{4} + 36 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(8 \, a^{4} + 36 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(128 \, {\left(5 \, a^{3} b + 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} + 192 \, a b^{3} \cos\left(d x + c\right) + 15 \, {\left(8 \, a^{4} + 36 \, a^{2} b^{2} + 5 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 40 \, b^{4} + 64 \, {\left(5 \, a^{3} b + 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} + 10 \, {\left(36 \, a^{2} b^{2} + 5 \, b^{4}\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*(8*a^4 + 36*a^2*b^2 + 5*b^4)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(8*a^4 + 36*a^2*b^2 + 5*b^4)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 2*(128*(5*a^3*b + 4*a*b^3)*cos(d*x + c)^5 + 192*a*b^3*cos(d*x + c) + 15*(8*a^4 + 36*a^2*b^2 + 5*b^4)*cos(d*x + c)^4 + 40*b^4 + 64*(5*a^3*b + 4*a*b^3)*cos(d*x + c)^3 + 10*(36*a^2*b^2 + 5*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
477,1,182,0,0.488765," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(4 \, a^{3} b + 3 \, 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 b^{3} \cos\left(d x + c\right) + 2 \, {\left(15 \, a^{4} + 60 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 6 \, b^{4} + 15 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{2} b^{2} + 2 \, b^{4}\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*(4*a^3*b + 3*a*b^3)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*a^3*b + 3*a*b^3)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 2*(30*a*b^3*cos(d*x + c) + 2*(15*a^4 + 60*a^2*b^2 + 8*b^4)*cos(d*x + c)^4 + 6*b^4 + 15*(4*a^3*b + 3*a*b^3)*cos(d*x + c)^3 + 4*(15*a^2*b^2 + 2*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
478,1,163,0,0.510531," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, a^{4} + 24 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, a^{4} + 24 \, a^{2} b^{2} + 3 \, b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(32 \, a b^{3} \cos\left(d x + c\right) + 6 \, b^{4} + 32 \, {\left(3 \, a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(8 \, a^{2} b^{2} + b^{4}\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*(8*a^4 + 24*a^2*b^2 + 3*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*a^4 + 24*a^2*b^2 + 3*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(32*a*b^3*cos(d*x + c) + 6*b^4 + 32*(3*a^3*b + 2*a*b^3)*cos(d*x + c)^3 + 9*(8*a^2*b^2 + b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
479,1,138,0,0.534626," ","integrate((a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, a^{4} d x \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, a b^{3} \cos\left(d x + c\right) + b^{4} + 2 \, {\left(9 \, a^{2} b^{2} + b^{4}\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*a^4*d*x*cos(d*x + c)^3 + 3*(2*a^3*b + a*b^3)*cos(d*x + c)^3*log(sin(d*x + c) + 1) - 3*(2*a^3*b + a*b^3)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + (6*a*b^3*cos(d*x + c) + b^4 + 2*(9*a^2*b^2 + b^4)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","A",0
480,1,130,0,0.494569," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{16 \, a^{3} b d x \cos\left(d x + c\right)^{2} + {\left(12 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(12 \, a^{2} b^{2} + b^{4}\right)} \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 b^{3} \cos\left(d x + c\right) + b^{4}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(16*a^3*b*d*x*cos(d*x + c)^2 + (12*a^2*b^2 + b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (12*a^2*b^2 + b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(2*a^4*cos(d*x + c)^2 + 8*a*b^3*cos(d*x + c) + b^4)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
481,1,116,0,0.485173," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{4 \, a b^{3} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, a b^{3} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(a^{4} + 12 \, a^{2} b^{2}\right)} d x \cos\left(d x + c\right) + {\left(a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{3} b \cos\left(d x + c\right) + 2 \, b^{4}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(4*a*b^3*cos(d*x + c)*log(sin(d*x + c) + 1) - 4*a*b^3*cos(d*x + c)*log(-sin(d*x + c) + 1) + (a^4 + 12*a^2*b^2)*d*x*cos(d*x + c) + (a^4*cos(d*x + c)^2 + 8*a^3*b*cos(d*x + c) + 2*b^4)*sin(d*x + c))/(d*cos(d*x + c))","A",0
482,1,98,0,0.483318," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, b^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 12 \, {\left(a^{3} b + 2 \, a b^{3}\right)} d x + 2 \, {\left(a^{4} \cos\left(d x + c\right)^{2} + 6 \, a^{3} b \cos\left(d x + c\right) + 2 \, a^{4} + 18 \, a^{2} b^{2}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*b^4*log(sin(d*x + c) + 1) - 3*b^4*log(-sin(d*x + c) + 1) + 12*(a^3*b + 2*a*b^3)*d*x + 2*(a^4*cos(d*x + c)^2 + 6*a^3*b*cos(d*x + c) + 2*a^4 + 18*a^2*b^2)*sin(d*x + c))/d","A",0
483,1,96,0,0.471286," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{4} + 24 \, a^{2} b^{2} + 8 \, b^{4}\right)} d x + {\left(6 \, a^{4} \cos\left(d x + c\right)^{3} + 32 \, a^{3} b \cos\left(d x + c\right)^{2} + 64 \, a^{3} b + 96 \, a b^{3} + 9 \, {\left(a^{4} + 8 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(3*(3*a^4 + 24*a^2*b^2 + 8*b^4)*d*x + (6*a^4*cos(d*x + c)^3 + 32*a^3*b*cos(d*x + c)^2 + 64*a^3*b + 96*a*b^3 + 9*(a^4 + 8*a^2*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
484,1,121,0,0.477362," ","integrate(cos(d*x+c)^5*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, a^{3} b + 4 \, a b^{3}\right)} d x + {\left(6 \, a^{4} \cos\left(d x + c\right)^{4} + 30 \, a^{3} b \cos\left(d x + c\right)^{3} + 16 \, a^{4} + 120 \, a^{2} b^{2} + 30 \, b^{4} + 4 \, {\left(2 \, a^{4} + 15 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(3 \, a^{3} b + 4 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(15*(3*a^3*b + 4*a*b^3)*d*x + (6*a^4*cos(d*x + c)^4 + 30*a^3*b*cos(d*x + c)^3 + 16*a^4 + 120*a^2*b^2 + 30*b^4 + 4*(2*a^4 + 15*a^2*b^2)*cos(d*x + c)^2 + 15*(3*a^3*b + 4*a*b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
485,1,150,0,0.536991," ","integrate(cos(d*x+c)^6*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{15 \, {\left(5 \, a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} d x + {\left(40 \, a^{4} \cos\left(d x + c\right)^{5} + 192 \, a^{3} b \cos\left(d x + c\right)^{4} + 512 \, a^{3} b + 640 \, a b^{3} + 10 \, {\left(5 \, a^{4} + 36 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 64 \, {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(5 \, a^{4} + 36 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(15*(5*a^4 + 36*a^2*b^2 + 8*b^4)*d*x + (40*a^4*cos(d*x + c)^5 + 192*a^3*b*cos(d*x + c)^4 + 512*a^3*b + 640*a*b^3 + 10*(5*a^4 + 36*a^2*b^2)*cos(d*x + c)^3 + 64*(4*a^3*b + 5*a*b^3)*cos(d*x + c)^2 + 15*(5*a^4 + 36*a^2*b^2 + 8*b^4)*cos(d*x + c))*sin(d*x + c))/d","A",0
486,1,183,0,0.486623," ","integrate((a+b*sec(d*x+c))^5,x, algorithm=""fricas"")","\frac{48 \, a^{5} d x \cos\left(d x + c\right)^{4} + 3 \, {\left(40 \, a^{4} b + 40 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(40 \, a^{4} b + 40 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(40 \, a b^{4} \cos\left(d x + c\right) + 6 \, b^{5} + 80 \, {\left(3 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(40 \, a^{2} b^{3} + 3 \, b^{5}\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*(48*a^5*d*x*cos(d*x + c)^4 + 3*(40*a^4*b + 40*a^2*b^3 + 3*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(40*a^4*b + 40*a^2*b^3 + 3*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(40*a*b^4*cos(d*x + c) + 6*b^5 + 80*(3*a^3*b^2 + a*b^4)*cos(d*x + c)^3 + 3*(40*a^2*b^3 + 3*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
487,1,557,0,0.664335," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{a^{2} - b^{2}} a^{4} \cos\left(d x + c\right)^{3} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 3 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{2} b^{3} - 2 \, b^{5} + 2 \, {\left(3 \, a^{4} b - a^{2} b^{3} - 2 \, 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)}{12 \, {\left(a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}, \frac{12 \, \sqrt{-a^{2} + b^{2}} a^{4} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, a^{5} - a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{2} b^{3} - 2 \, b^{5} + 2 \, {\left(3 \, a^{4} b - a^{2} b^{3} - 2 \, 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)}{12 \, {\left(a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[1/12*(6*sqrt(a^2 - b^2)*a^4*cos(d*x + c)^3*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 3*(2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*a^2*b^3 - 2*b^5 + 2*(3*a^4*b - a^2*b^3 - 2*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*cos(d*x + c)^3), 1/12*(12*sqrt(-a^2 + b^2)*a^4*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^3 - 3*(2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c)^3*log(sin(d*x + c) + 1) + 3*(2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c)^3*log(-sin(d*x + c) + 1) + 2*(2*a^2*b^3 - 2*b^5 + 2*(3*a^4*b - a^2*b^3 - 2*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*cos(d*x + c)^3)]","A",0
488,1,485,0,0.670228," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{a^{2} - b^{2}} a^{3} \cos\left(d x + c\right)^{2} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{2} b^{2} - b^{4} - 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^{2} b^{3} - b^{5}\right)} d \cos\left(d x + c\right)^{2}}, -\frac{4 \, \sqrt{-a^{2} + b^{2}} a^{3} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right)^{2} - {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{2} b^{2} - b^{4} - 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^{2} b^{3} - b^{5}\right)} d \cos\left(d x + c\right)^{2}}\right]"," ",0,"[1/4*(2*sqrt(a^2 - b^2)*a^3*cos(d*x + c)^2*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (2*a^4 - a^2*b^2 - b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*a^4 - a^2*b^2 - b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(a^2*b^2 - b^4 - 2*(a^3*b - a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c)^2), -1/4*(4*sqrt(-a^2 + b^2)*a^3*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*cos(d*x + c)^2 - (2*a^4 - a^2*b^2 - b^4)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*a^4 - a^2*b^2 - b^4)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*(a^2*b^2 - b^4 - 2*(a^3*b - a*b^3)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d*cos(d*x + c)^2)]","B",0
489,1,392,0,0.548747," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a^{2} - b^{2}} a^{2} \cos\left(d x + c\right) \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(d x + c\right)}, \frac{2 \, \sqrt{-a^{2} + b^{2}} a^{2} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) \cos\left(d x + c\right) - {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(a^2 - b^2)*a^2*cos(d*x + c)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - (a^3 - a*b^2)*cos(d*x + c)*log(sin(d*x + c) + 1) + (a^3 - a*b^2)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(a^2*b - b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c)), 1/2*(2*sqrt(-a^2 + b^2)*a^2*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))*cos(d*x + c) - (a^3 - a*b^2)*cos(d*x + c)*log(sin(d*x + c) + 1) + (a^3 - a*b^2)*cos(d*x + c)*log(-sin(d*x + c) + 1) + 2*(a^2*b - b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d*cos(d*x + c))]","B",0
490,1,290,0,0.573029," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a^{2} - b^{2}} a \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{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^{2} b - b^{3}\right)} d}, -\frac{2 \, \sqrt{-a^{2} + b^{2}} a \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \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^{2} b - b^{3}\right)} d}\right]"," ",0,"[1/2*(sqrt(a^2 - b^2)*a*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (a^2 - b^2)*log(sin(d*x + c) + 1) - (a^2 - b^2)*log(-sin(d*x + c) + 1))/((a^2*b - b^3)*d), -1/2*(2*sqrt(-a^2 + b^2)*a*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((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^2*b - b^3)*d)]","A",0
491,1,185,0,0.462920," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right)}{2 \, \sqrt{a^{2} - b^{2}} d}, \frac{\sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right)}{{\left(a^{2} - b^{2}\right)} d}\right]"," ",0,"[1/2*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2))/(sqrt(a^2 - b^2)*d), sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c)))/((a^2 - b^2)*d)]","A",0
492,1,230,0,0.526066," ","integrate(1/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} - b^{2}\right)} d x + \sqrt{a^{2} - b^{2}} b \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}, \frac{{\left(a^{2} - b^{2}\right)} d x - \sqrt{-a^{2} + b^{2}} b \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right)}{{\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[1/2*(2*(a^2 - b^2)*d*x + sqrt(a^2 - b^2)*b*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)))/((a^3 - a*b^2)*d), ((a^2 - b^2)*d*x - sqrt(-a^2 + b^2)*b*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))))/((a^3 - a*b^2)*d)]","A",0
493,1,277,0,0.491428," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a^{2} - b^{2}} b^{2} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(a^{2} b - b^{3}\right)} d x + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d}, \frac{\sqrt{-a^{2} + b^{2}} b^{2} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{2} b - b^{3}\right)} d x + {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{4} - a^{2} b^{2}\right)} d}\right]"," ",0,"[1/2*(sqrt(a^2 - b^2)*b^2*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(a^2*b - b^3)*d*x + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d), (sqrt(-a^2 + b^2)*b^2*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^2*b - b^3)*d*x + (a^3 - a*b^2)*sin(d*x + c))/((a^4 - a^2*b^2)*d)]","A",0
494,1,334,0,0.503103," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{a^{2} - b^{2}} b^{3} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} d x - {\left(2 \, a^{3} b - 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{5} - a^{3} b^{2}\right)} d}, -\frac{2 \, \sqrt{-a^{2} + b^{2}} b^{3} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{4} + a^{2} b^{2} - 2 \, b^{4}\right)} d x + {\left(2 \, a^{3} b - 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{5} - a^{3} b^{2}\right)} d}\right]"," ",0,"[1/2*(sqrt(a^2 - b^2)*b^3*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (a^4 + a^2*b^2 - 2*b^4)*d*x - (2*a^3*b - 2*a*b^3 - (a^4 - a^2*b^2)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d), -1/2*(2*sqrt(-a^2 + b^2)*b^3*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^4 + a^2*b^2 - 2*b^4)*d*x + (2*a^3*b - 2*a*b^3 - (a^4 - a^2*b^2)*cos(d*x + c))*sin(d*x + c))/((a^5 - a^3*b^2)*d)]","A",0
495,1,401,0,0.568612," ","integrate(cos(d*x+c)^3/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a^{2} - b^{2}} b^{4} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 3 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} d x + {\left(4 \, a^{5} + 2 \, a^{3} b^{2} - 6 \, a b^{4} + 2 \, {\left(a^{5} - a^{3} b^{2}\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)}{6 \, {\left(a^{6} - a^{4} b^{2}\right)} d}, \frac{6 \, \sqrt{-a^{2} + b^{2}} b^{4} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - 3 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} d x + {\left(4 \, a^{5} + 2 \, a^{3} b^{2} - 6 \, a b^{4} + 2 \, {\left(a^{5} - a^{3} b^{2}\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)}{6 \, {\left(a^{6} - a^{4} b^{2}\right)} d}\right]"," ",0,"[1/6*(3*sqrt(a^2 - b^2)*b^4*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 3*(a^4*b + a^2*b^3 - 2*b^5)*d*x + (4*a^5 + 2*a^3*b^2 - 6*a*b^4 + 2*(a^5 - a^3*b^2)*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), 1/6*(6*sqrt(-a^2 + b^2)*b^4*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - 3*(a^4*b + a^2*b^3 - 2*b^5)*d*x + (4*a^5 + 2*a^3*b^2 - 6*a*b^4 + 2*(a^5 - a^3*b^2)*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)]","A",0
496,1,482,0,0.510971," ","integrate(cos(d*x+c)^4/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{a^{2} - b^{2}} b^{5} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 3 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} d x - {\left(16 \, a^{5} b + 8 \, a^{3} b^{3} - 24 \, a b^{5} - 6 \, {\left(a^{6} - a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(3 \, a^{6} + a^{4} b^{2} - 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{7} - a^{5} b^{2}\right)} d}, -\frac{24 \, \sqrt{-a^{2} + b^{2}} b^{5} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - 3 \, {\left(3 \, a^{6} + a^{4} b^{2} + 4 \, a^{2} b^{4} - 8 \, b^{6}\right)} d x + {\left(16 \, a^{5} b + 8 \, a^{3} b^{3} - 24 \, a b^{5} - 6 \, {\left(a^{6} - a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 8 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(3 \, a^{6} + a^{4} b^{2} - 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(a^{7} - a^{5} b^{2}\right)} d}\right]"," ",0,"[1/24*(12*sqrt(a^2 - b^2)*b^5*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 3*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*d*x - (16*a^5*b + 8*a^3*b^3 - 24*a*b^5 - 6*(a^6 - a^4*b^2)*cos(d*x + c)^3 + 8*(a^5*b - a^3*b^3)*cos(d*x + c)^2 - 3*(3*a^6 + a^4*b^2 - 4*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d), -1/24*(24*sqrt(-a^2 + b^2)*b^5*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - 3*(3*a^6 + a^4*b^2 + 4*a^2*b^4 - 8*b^6)*d*x + (16*a^5*b + 8*a^3*b^3 - 24*a*b^5 - 6*(a^6 - a^4*b^2)*cos(d*x + c)^3 + 8*(a^5*b - a^3*b^3)*cos(d*x + c)^2 - 3*(3*a^6 + a^4*b^2 - 4*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^7 - a^5*b^2)*d)]","A",0
497,1,909,0,1.247154," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(3 \, a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left({\left(6 \, a^{7} - 11 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(6 \, a^{7} - 11 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} - 2 \, {\left(3 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\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)}{4 \, {\left({\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2}\right)}}, -\frac{4 \, {\left({\left(3 \, a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left({\left(6 \, a^{7} - 11 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(6 \, a^{7} - 11 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} - 2 \, {\left(3 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\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)}{4 \, {\left({\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/4*(2*((3*a^6 - 4*a^4*b^2)*cos(d*x + c)^3 + (3*a^5*b - 4*a^3*b^3)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + ((6*a^7 - 11*a^5*b^2 + 4*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + (6*a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((6*a^7 - 11*a^5*b^2 + 4*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + (6*a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(a^4*b^3 - 2*a^2*b^5 + b^7 - 2*(3*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*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^5*b^4 - 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3 + (a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c)^2), -1/4*(4*((3*a^6 - 4*a^4*b^2)*cos(d*x + c)^3 + (3*a^5*b - 4*a^3*b^3)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - ((6*a^7 - 11*a^5*b^2 + 4*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + (6*a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + b^7)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((6*a^7 - 11*a^5*b^2 + 4*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + (6*a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + b^7)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^4*b^3 - 2*a^2*b^5 + b^7 - 2*(3*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*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^5*b^4 - 2*a^3*b^6 + a*b^8)*d*cos(d*x + c)^3 + (a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c)^2)]","B",0
498,1,760,0,0.843893," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} \cos\left(d x + c\right)^{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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left({\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\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^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\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^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)\right)}}, \frac{{\left({\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} \cos\left(d x + c\right)^{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{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left({\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\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^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\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^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(((2*a^5 - 3*a^3*b^2)*cos(d*x + c)^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) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*((a^6 - 2*a^4*b^2 + a^2*b^4)*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)*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 + (2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^5*b^3 - 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)^2 + (a^4*b^4 - 2*a^2*b^6 + b^8)*d*cos(d*x + c)), (((2*a^5 - 3*a^3*b^2)*cos(d*x + c)^2 + (2*a^4*b - 3*a^2*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - ((a^6 - 2*a^4*b^2 + a^2*b^4)*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)*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 + (2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^5*b^3 - 2*a^3*b^5 + a*b^7)*d*cos(d*x + c)^2 + (a^4*b^4 - 2*a^2*b^6 + b^8)*d*cos(d*x + c))]","B",0
499,1,596,0,0.811861," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{3} b - 2 \, a b^{3} + {\left(a^{4} - 2 \, a^{2} b^{2}\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d\right)}}, -\frac{2 \, {\left(a^{3} b - 2 \, a b^{3} + {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d\right)}}\right]"," ",0,"[1/2*((a^3*b - 2*a*b^3 + (a^4 - 2*a^2*b^2)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + (a^4*b - 2*a^2*b^3 + b^5 + (a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) - (a^4*b - 2*a^2*b^3 + b^5 + (a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) - 2*(a^4*b - a^2*b^3)*sin(d*x + c))/((a^5*b^2 - 2*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^4*b^3 - 2*a^2*b^5 + b^7)*d), -1/2*(2*(a^3*b - 2*a*b^3 + (a^4 - 2*a^2*b^2)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^4*b - 2*a^2*b^3 + b^5 + (a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) + (a^4*b - 2*a^2*b^3 + b^5 + (a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(a^4*b - a^2*b^3)*sin(d*x + c))/((a^5*b^2 - 2*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^4*b^3 - 2*a^2*b^5 + b^7)*d)]","B",0
500,1,329,0,0.490304," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(a b \cos\left(d x + c\right) + b^{2}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d\right)}}, -\frac{{\left(a b \cos\left(d x + c\right) + b^{2}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d}\right]"," ",0,"[-1/2*((a*b*cos(d*x + c) + b^2)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(a^3 - a*b^2)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*d), -((a*b*cos(d*x + c) + b^2)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^3 - a*b^2)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*d)]","A",0
501,1,332,0,0.515440," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(a^{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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d\right)}}, \frac{{\left(a^{2} \cos\left(d x + c\right) + a b\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d}\right]"," ",0,"[-1/2*((a^2*cos(d*x + c) + a*b)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(a^2*b - b^3)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*d), ((a^2*cos(d*x + c) + a*b)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^2*b - b^3)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*d)]","A",0
502,1,484,0,0.539263," ","integrate(1/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x + {\left(2 \, a^{2} b^{2} - b^{4} + {\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)}}, \frac{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d x - {\left(2 \, a^{2} b^{2} - b^{4} + {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d}\right]"," ",0,"[1/2*(2*(a^5 - 2*a^3*b^2 + a*b^4)*d*x*cos(d*x + c) + 2*(a^4*b - 2*a^2*b^3 + b^5)*d*x + (2*a^2*b^2 - b^4 + (2*a^3*b - a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(a^3*b^2 - a*b^4)*sin(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d), ((a^5 - 2*a^3*b^2 + a*b^4)*d*x*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*d*x - (2*a^2*b^2 - b^4 + (2*a^3*b - a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (a^3*b^2 - a*b^4)*sin(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c) + (a^6*b - 2*a^4*b^3 + a^2*b^5)*d)]","B",0
503,1,565,0,0.571016," ","integrate(cos(d*x+c)/(a+b*sec(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^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d x - {\left(3 \, a^{2} b^{3} - 2 \, b^{5} + {\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5} + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\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^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d x - {\left(3 \, a^{2} b^{3} - 2 \, b^{5} + {\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{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5} + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\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^4*b^2 - 2*a^2*b^4 + b^6)*d*x - (3*a^2*b^3 - 2*b^5 + (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) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(a^5*b - 3*a^3*b^3 + 2*a*b^5 + (a^6 - 2*a^4*b^2 + a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(d*x + c) + (a^7*b - 2*a^5*b^3 + a^3*b^5)*d), -(2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x*cos(d*x + c) + 2*(a^4*b^2 - 2*a^2*b^4 + b^6)*d*x - (3*a^2*b^3 - 2*b^5 + (3*a^3*b^2 - 2*a*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^5*b - 3*a^3*b^3 + 2*a*b^5 + (a^6 - 2*a^4*b^2 + a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^8 - 2*a^6*b^2 + a^4*b^4)*d*cos(d*x + c) + (a^7*b - 2*a^5*b^3 + a^3*b^5)*d)]","A",0
504,1,660,0,0.560826," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(a^{6} b + 4 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 6 \, b^{7}\right)} d x + {\left(4 \, a^{2} b^{4} - 3 \, b^{6} + {\left(4 \, a^{3} b^{3} - 3 \, a 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - {\left(4 \, a^{5} b^{2} - 10 \, a^{3} b^{4} + 6 \, a b^{6} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\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)}{2 \, {\left({\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d\right)}}, \frac{{\left(a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(a^{6} b + 4 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 6 \, b^{7}\right)} d x - 2 \, {\left(4 \, a^{2} b^{4} - 3 \, b^{6} + {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(4 \, a^{5} b^{2} - 10 \, a^{3} b^{4} + 6 \, a b^{6} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\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)}{2 \, {\left({\left(a^{9} - 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d\right)}}\right]"," ",0,"[1/2*((a^7 + 4*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*d*x*cos(d*x + c) + (a^6*b + 4*a^4*b^3 - 11*a^2*b^5 + 6*b^7)*d*x + (4*a^2*b^4 - 3*b^6 + (4*a^3*b^3 - 3*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - (4*a^5*b^2 - 10*a^3*b^4 + 6*a*b^6 - (a^7 - 2*a^5*b^2 + a^3*b^4)*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^9 - 2*a^7*b^2 + a^5*b^4)*d*cos(d*x + c) + (a^8*b - 2*a^6*b^3 + a^4*b^5)*d), 1/2*((a^7 + 4*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*d*x*cos(d*x + c) + (a^6*b + 4*a^4*b^3 - 11*a^2*b^5 + 6*b^7)*d*x - 2*(4*a^2*b^4 - 3*b^6 + (4*a^3*b^3 - 3*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (4*a^5*b^2 - 10*a^3*b^4 + 6*a*b^6 - (a^7 - 2*a^5*b^2 + a^3*b^4)*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^9 - 2*a^7*b^2 + a^5*b^4)*d*cos(d*x + c) + (a^8*b - 2*a^6*b^3 + a^4*b^5)*d)]","A",0
505,1,757,0,0.564564," ","integrate(cos(d*x+c)^3/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(a^{7} b + 2 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 4 \, a b^{7}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + 4 \, b^{8}\right)} d x - 3 \, {\left(5 \, a^{2} b^{5} - 4 \, b^{7} + {\left(5 \, a^{3} b^{4} - 4 \, 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(2 \, a^{7} b + 5 \, a^{5} b^{3} - 19 \, a^{3} b^{5} + 12 \, a b^{7} + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + 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)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d\right)}}, -\frac{3 \, {\left(a^{7} b + 2 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 4 \, a b^{7}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + 4 \, b^{8}\right)} d x - 3 \, {\left(5 \, a^{2} b^{5} - 4 \, b^{7} + {\left(5 \, a^{3} b^{4} - 4 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{7} b + 5 \, a^{5} b^{3} - 19 \, a^{3} b^{5} + 12 \, a b^{7} + {\left(a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + 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)\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{10} - 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d\right)}}\right]"," ",0,"[-1/6*(6*(a^7*b + 2*a^5*b^3 - 7*a^3*b^5 + 4*a*b^7)*d*x*cos(d*x + c) + 6*(a^6*b^2 + 2*a^4*b^4 - 7*a^2*b^6 + 4*b^8)*d*x - 3*(5*a^2*b^5 - 4*b^7 + (5*a^3*b^4 - 4*a*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(2*a^7*b + 5*a^5*b^3 - 19*a^3*b^5 + 12*a*b^7 + (a^8 - 2*a^6*b^2 + a^4*b^4)*cos(d*x + c)^3 - 2*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c)^2 + 2*(a^8 + a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c) + (a^9*b - 2*a^7*b^3 + a^5*b^5)*d), -1/3*(3*(a^7*b + 2*a^5*b^3 - 7*a^3*b^5 + 4*a*b^7)*d*x*cos(d*x + c) + 3*(a^6*b^2 + 2*a^4*b^4 - 7*a^2*b^6 + 4*b^8)*d*x - 3*(5*a^2*b^5 - 4*b^7 + (5*a^3*b^4 - 4*a*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (2*a^7*b + 5*a^5*b^3 - 19*a^3*b^5 + 12*a*b^7 + (a^8 - 2*a^6*b^2 + a^4*b^4)*cos(d*x + c)^3 - 2*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c)^2 + 2*(a^8 + a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^10 - 2*a^8*b^2 + a^6*b^4)*d*cos(d*x + c) + (a^9*b - 2*a^7*b^3 + a^5*b^5)*d)]","A",0
506,1,1354,0,1.447479," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(2 \, a^{8} - 5 \, a^{6} b^{2} + 4 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{7} b - 5 \, a^{5} b^{3} + 4 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + 4 \, 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 6 \, {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + 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)^{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)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 6 \, {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + 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)^{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)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{6} b^{3} - 6 \, a^{4} b^{5} + 6 \, a^{2} b^{7} - 2 \, b^{9} + {\left(6 \, a^{8} b - 17 \, a^{6} b^{3} + 13 \, a^{4} b^{5} - 2 \, a^{2} b^{7}\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^{8} b^{4} - 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + {\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)\right)}}, \frac{3 \, {\left({\left(2 \, a^{8} - 5 \, a^{6} b^{2} + 4 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{7} b - 5 \, a^{5} b^{3} + 4 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + 4 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - 3 \, {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + 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)^{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)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} \cos\left(d x + c\right)^{3} + 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)^{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)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(2 \, a^{6} b^{3} - 6 \, a^{4} b^{5} + 6 \, a^{2} b^{7} - 2 \, b^{9} + {\left(6 \, a^{8} b - 17 \, a^{6} b^{3} + 13 \, a^{4} b^{5} - 2 \, a^{2} b^{7}\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^{8} b^{4} - 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} - a^{2} b^{10}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + {\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)\right)}}\right]"," ",0,"[1/4*(3*((2*a^8 - 5*a^6*b^2 + 4*a^4*b^4)*cos(d*x + c)^3 + 2*(2*a^7*b - 5*a^5*b^3 + 4*a^3*b^5)*cos(d*x + c)^2 + (2*a^6*b^2 - 5*a^4*b^4 + 4*a^2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 6*((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*cos(d*x + c)^3 + 2*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c)^2 + (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*cos(d*x + c))*log(sin(d*x + c) + 1) + 6*((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*cos(d*x + c)^3 + 2*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c)^2 + (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*cos(d*x + c))*log(-sin(d*x + c) + 1) + 2*(2*a^6*b^3 - 6*a^4*b^5 + 6*a^2*b^7 - 2*b^9 + (6*a^8*b - 17*a^6*b^3 + 13*a^4*b^5 - 2*a^2*b^7)*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^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10)*d*cos(d*x + c)^3 + 2*(a^7*b^5 - 3*a^5*b^7 + 3*a^3*b^9 - a*b^11)*d*cos(d*x + c)^2 + (a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*d*cos(d*x + c)), 1/2*(3*((2*a^8 - 5*a^6*b^2 + 4*a^4*b^4)*cos(d*x + c)^3 + 2*(2*a^7*b - 5*a^5*b^3 + 4*a^3*b^5)*cos(d*x + c)^2 + (2*a^6*b^2 - 5*a^4*b^4 + 4*a^2*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - 3*((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*cos(d*x + c)^3 + 2*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c)^2 + (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*cos(d*x + c)^3 + 2*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*cos(d*x + c)^2 + (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*cos(d*x + c))*log(-sin(d*x + c) + 1) + (2*a^6*b^3 - 6*a^4*b^5 + 6*a^2*b^7 - 2*b^9 + (6*a^8*b - 17*a^6*b^3 + 13*a^4*b^5 - 2*a^2*b^7)*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^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10)*d*cos(d*x + c)^3 + 2*(a^7*b^5 - 3*a^5*b^7 + 3*a^3*b^9 - a*b^11)*d*cos(d*x + c)^2 + (a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12)*d*cos(d*x + c))]","B",0
507,1,1153,0,1.449258," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 6 \, a b^{6} + {\left(2 \, a^{7} - 5 \, a^{5} b^{2} + 6 \, a^{3} b^{4}\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8} + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8} + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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(3 \, a^{6} b^{2} - 9 \, a^{4} b^{4} + 6 \, a^{2} b^{6} + {\left(2 \, a^{7} b - 7 \, a^{5} b^{3} + 5 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{3} - 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} - a^{2} b^{9}\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^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} d\right)}}, -\frac{{\left(2 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 6 \, a b^{6} + {\left(2 \, a^{7} - 5 \, a^{5} b^{2} + 6 \, a^{3} b^{4}\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{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8} + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8} + {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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(3 \, a^{6} b^{2} - 9 \, a^{4} b^{4} + 6 \, a^{2} b^{6} + {\left(2 \, a^{7} b - 7 \, a^{5} b^{3} + 5 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{3} - 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} - a^{2} b^{9}\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^{6} b^{5} - 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} - b^{11}\right)} d\right)}}\right]"," ",0,"[1/4*((2*a^5*b^2 - 5*a^3*b^4 + 6*a*b^6 + (2*a^7 - 5*a^5*b^2 + 6*a^3*b^4)*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) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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*(3*a^6*b^2 - 9*a^4*b^4 + 6*a^2*b^6 + (2*a^7*b - 7*a^5*b^3 + 5*a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 3*a^6*b^5 + 3*a^4*b^7 - a^2*b^9)*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^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*d), -1/2*((2*a^5*b^2 - 5*a^3*b^4 + 6*a*b^6 + (2*a^7 - 5*a^5*b^2 + 6*a^3*b^4)*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(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + (a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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) + (3*a^6*b^2 - 9*a^4*b^4 + 6*a^2*b^6 + (2*a^7*b - 7*a^5*b^3 + 5*a^3*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*b^3 - 3*a^6*b^5 + 3*a^4*b^7 - a^2*b^9)*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^6*b^5 - 3*a^4*b^7 + 3*a^2*b^9 - b^11)*d)]","B",0
508,1,594,0,0.520222," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} b^{2} + 2 \, b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2}\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(a^{5} - 5 \, a^{3} b^{2} + 4 \, a b^{4} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}, \frac{{\left(a^{2} b^{2} + 2 \, b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2}\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{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(a^{5} - 5 \, a^{3} b^{2} + 4 \, a b^{4} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*((a^2*b^2 + 2*b^4 + (a^4 + 2*a^2*b^2)*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) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(a^5 - 5*a^3*b^2 + 4*a*b^4 - 3*(a^4*b - a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d), 1/2*((a^2*b^2 + 2*b^4 + (a^4 + 2*a^2*b^2)*cos(d*x + c)^2 + 2*(a^3*b + 2*a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (a^5 - 5*a^3*b^2 + 4*a*b^4 - 3*(a^4*b - a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d)]","A",0
509,1,565,0,0.531463," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{3} b \cos\left(d x + c\right)^{2} + 2 \, a^{2} b^{2} \cos\left(d x + c\right) + a b^{3}\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5} + {\left(2 \, a^{5} - 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^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}, -\frac{3 \, {\left(a^{3} b \cos\left(d x + c\right)^{2} + 2 \, a^{2} b^{2} \cos\left(d x + c\right) + a b^{3}\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5} + {\left(2 \, a^{5} - 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^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*(3*(a^3*b*cos(d*x + c)^2 + 2*a^2*b^2*cos(d*x + c) + a*b^3)*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(a^4*b + a^2*b^3 - 2*b^5 + (2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d), -1/2*(3*(a^3*b*cos(d*x + c)^2 + 2*a^2*b^2*cos(d*x + c) + a*b^3)*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (a^4*b + a^2*b^3 - 2*b^5 + (2*a^5 - a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d)]","B",0
510,1,595,0,0.508939," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a^{2} b^{2} + b^{4} + {\left(2 \, a^{4} + a^{2} b^{2}\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(3 \, a^{3} b^{2} - 3 \, a b^{4} + {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}, \frac{{\left(2 \, a^{2} b^{2} + b^{4} + {\left(2 \, a^{4} + a^{2} b^{2}\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{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(3 \, a^{3} b^{2} - 3 \, a b^{4} + {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*((2*a^2*b^2 + b^4 + (2*a^4 + a^2*b^2)*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) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(3*a^3*b^2 - 3*a*b^4 + (4*a^4*b - 5*a^2*b^3 + b^5)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d), 1/2*((2*a^2*b^2 + b^4 + (2*a^4 + a^2*b^2)*cos(d*x + c)^2 + 2*(2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (3*a^3*b^2 - 3*a*b^4 + (4*a^4*b - 5*a^2*b^3 + b^5)*cos(d*x + c))*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d)]","B",0
511,1,919,0,0.564034," ","integrate(1/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d x + {\left(6 \, a^{4} b^{3} - 5 \, a^{2} b^{5} + 2 \, b^{7} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(5 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 2 \, a b^{7} + 3 \, {\left(2 \, a^{6} b^{2} - 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\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^{9} b^{2} - 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} - a^{3} b^{8}\right)} d\right)}}, \frac{2 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\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^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d x - {\left(6 \, a^{4} b^{3} - 5 \, a^{2} b^{5} + 2 \, b^{7} + {\left(6 \, a^{6} b - 5 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\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{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(5 \, a^{5} b^{3} - 7 \, a^{3} b^{5} + 2 \, a b^{7} + 3 \, {\left(2 \, a^{6} b^{2} - 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\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^{9} b^{2} - 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} - a^{3} b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*(4*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*x + (6*a^4*b^3 - 5*a^2*b^5 + 2*b^7 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*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) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(5*a^5*b^3 - 7*a^3*b^5 + 2*a*b^7 + 3*(2*a^6*b^2 - 3*a^4*b^4 + a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*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^9*b^2 - 3*a^7*b^4 + 3*a^5*b^6 - a^3*b^8)*d), 1/2*(2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*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^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*x - (6*a^4*b^3 - 5*a^2*b^5 + 2*b^7 + (6*a^6*b - 5*a^4*b^3 + 2*a^2*b^5)*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(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (5*a^5*b^3 - 7*a^3*b^5 + 2*a*b^7 + 3*(2*a^6*b^2 - 3*a^4*b^4 + a^2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*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^9*b^2 - 3*a^7*b^4 + 3*a^5*b^6 - a^3*b^8)*d)]","B",0
512,1,1037,0,0.602226," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{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)^{2} + 24 \, {\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) + 12 \, {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d x - 3 \, {\left(4 \, a^{4} b^{4} - 5 \, a^{2} b^{6} + 2 \, b^{8} + {\left(4 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 2 \, a 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(2 \, a^{7} b^{2} - 13 \, a^{5} b^{4} + 17 \, a^{3} b^{6} - 6 \, a b^{8} + 2 \, {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\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^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 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) + {\left(a^{10} b^{2} - 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} - a^{4} b^{8}\right)} d\right)}}, -\frac{6 \, {\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)^{2} + 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) + 6 \, {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d x - 3 \, {\left(4 \, a^{4} b^{4} - 5 \, a^{2} b^{6} + 2 \, b^{8} + {\left(4 \, a^{6} b^{2} - 5 \, a^{4} b^{4} + 2 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 2 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{7} b^{2} - 13 \, a^{5} b^{4} + 17 \, a^{3} b^{6} - 6 \, a b^{8} + 2 \, {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\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^{12} - 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} - a^{6} b^{6}\right)} d \cos\left(d x + c\right)^{2} + 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) + {\left(a^{10} b^{2} - 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} - a^{4} b^{8}\right)} d\right)}}\right]"," ",0,"[-1/4*(12*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*d*x*cos(d*x + c)^2 + 24*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d*x*cos(d*x + c) + 12*(a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d*x - 3*(4*a^4*b^4 - 5*a^2*b^6 + 2*b^8 + (4*a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6)*cos(d*x + c)^2 + 2*(4*a^5*b^3 - 5*a^3*b^5 + 2*a*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(2*a^7*b^2 - 13*a^5*b^4 + 17*a^3*b^6 - 6*a*b^8 + 2*(a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*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^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*d*cos(d*x + c)^2 + 2*(a^11*b - 3*a^9*b^3 + 3*a^7*b^5 - a^5*b^7)*d*cos(d*x + c) + (a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8)*d), -1/2*(6*(a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*d*x*cos(d*x + c)^2 + 12*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d*x*cos(d*x + c) + 6*(a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d*x - 3*(4*a^4*b^4 - 5*a^2*b^6 + 2*b^8 + (4*a^6*b^2 - 5*a^4*b^4 + 2*a^2*b^6)*cos(d*x + c)^2 + 2*(4*a^5*b^3 - 5*a^3*b^5 + 2*a*b^7)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (2*a^7*b^2 - 13*a^5*b^4 + 17*a^3*b^6 - 6*a*b^8 + 2*(a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*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^12 - 3*a^10*b^2 + 3*a^8*b^4 - a^6*b^6)*d*cos(d*x + c)^2 + 2*(a^11*b - 3*a^9*b^3 + 3*a^7*b^5 - a^5*b^7)*d*cos(d*x + c) + (a^10*b^2 - 3*a^8*b^4 + 3*a^6*b^6 - a^4*b^8)*d)]","B",0
513,1,1158,0,0.608838," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{10} + 9 \, a^{8} b^{2} - 33 \, a^{6} b^{4} + 35 \, a^{4} b^{6} - 12 \, a^{2} b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{9} b + 9 \, a^{7} b^{3} - 33 \, a^{5} b^{5} + 35 \, a^{3} b^{7} - 12 \, a b^{9}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{8} b^{2} + 9 \, a^{6} b^{4} - 33 \, a^{4} b^{6} + 35 \, a^{2} b^{8} - 12 \, b^{10}\right)} d x + {\left(20 \, a^{4} b^{5} - 29 \, a^{2} b^{7} + 12 \, b^{9} + {\left(20 \, a^{6} b^{3} - 29 \, a^{4} b^{5} + 12 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{5} b^{4} - 29 \, a^{3} b^{6} + 12 \, a 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(6 \, a^{7} b^{3} - 27 \, a^{5} b^{5} + 33 \, a^{3} b^{7} - 12 \, a b^{9} - {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + {\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)\right)} \sin\left(d x + c\right)}{4 \, {\left({\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} + 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) + {\left(a^{11} b^{2} - 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} - a^{5} b^{8}\right)} d\right)}}, \frac{{\left(a^{10} + 9 \, a^{8} b^{2} - 33 \, a^{6} b^{4} + 35 \, a^{4} b^{6} - 12 \, a^{2} b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 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)} d x \cos\left(d x + c\right) + {\left(a^{8} b^{2} + 9 \, a^{6} b^{4} - 33 \, a^{4} b^{6} + 35 \, a^{2} b^{8} - 12 \, b^{10}\right)} d x - {\left(20 \, a^{4} b^{5} - 29 \, a^{2} b^{7} + 12 \, b^{9} + {\left(20 \, a^{6} b^{3} - 29 \, a^{4} b^{5} + 12 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{5} b^{4} - 29 \, a^{3} b^{6} + 12 \, a b^{8}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(6 \, a^{7} b^{3} - 27 \, a^{5} b^{5} + 33 \, a^{3} b^{7} - 12 \, a b^{9} - {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + {\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)\right)} \sin\left(d x + c\right)}{2 \, {\left({\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} + 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) + {\left(a^{11} b^{2} - 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} - a^{5} b^{8}\right)} d\right)}}\right]"," ",0,"[1/4*(2*(a^10 + 9*a^8*b^2 - 33*a^6*b^4 + 35*a^4*b^6 - 12*a^2*b^8)*d*x*cos(d*x + c)^2 + 4*(a^9*b + 9*a^7*b^3 - 33*a^5*b^5 + 35*a^3*b^7 - 12*a*b^9)*d*x*cos(d*x + c) + 2*(a^8*b^2 + 9*a^6*b^4 - 33*a^4*b^6 + 35*a^2*b^8 - 12*b^10)*d*x + (20*a^4*b^5 - 29*a^2*b^7 + 12*b^9 + (20*a^6*b^3 - 29*a^4*b^5 + 12*a^2*b^7)*cos(d*x + c)^2 + 2*(20*a^5*b^4 - 29*a^3*b^6 + 12*a*b^8)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(6*a^7*b^3 - 27*a^5*b^5 + 33*a^3*b^7 - 12*a*b^9 - (a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*cos(d*x + c)^3 + 4*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*cos(d*x + c)^2 + (11*a^8*b^2 - 43*a^6*b^4 + 50*a^4*b^6 - 18*a^2*b^8)*cos(d*x + c))*sin(d*x + c))/((a^13 - 3*a^11*b^2 + 3*a^9*b^4 - a^7*b^6)*d*cos(d*x + c)^2 + 2*(a^12*b - 3*a^10*b^3 + 3*a^8*b^5 - a^6*b^7)*d*cos(d*x + c) + (a^11*b^2 - 3*a^9*b^4 + 3*a^7*b^6 - a^5*b^8)*d), 1/2*((a^10 + 9*a^8*b^2 - 33*a^6*b^4 + 35*a^4*b^6 - 12*a^2*b^8)*d*x*cos(d*x + c)^2 + 2*(a^9*b + 9*a^7*b^3 - 33*a^5*b^5 + 35*a^3*b^7 - 12*a*b^9)*d*x*cos(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)*d*x - (20*a^4*b^5 - 29*a^2*b^7 + 12*b^9 + (20*a^6*b^3 - 29*a^4*b^5 + 12*a^2*b^7)*cos(d*x + c)^2 + 2*(20*a^5*b^4 - 29*a^3*b^6 + 12*a*b^8)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (6*a^7*b^3 - 27*a^5*b^5 + 33*a^3*b^7 - 12*a*b^9 - (a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*cos(d*x + c)^3 + 4*(a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*cos(d*x + c)^2 + (11*a^8*b^2 - 43*a^6*b^4 + 50*a^4*b^6 - 18*a^2*b^8)*cos(d*x + c))*sin(d*x + c))/((a^13 - 3*a^11*b^2 + 3*a^9*b^4 - a^7*b^6)*d*cos(d*x + c)^2 + 2*(a^12*b - 3*a^10*b^3 + 3*a^8*b^5 - a^6*b^7)*d*cos(d*x + c) + (a^11*b^2 - 3*a^9*b^4 + 3*a^7*b^6 - a^5*b^8)*d)]","A",0
514,1,2058,0,3.028139," ","integrate(sec(d*x+c)^6/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, a^{11} - 28 \, a^{9} b^{2} + 35 \, a^{7} b^{4} - 20 \, a^{5} b^{6}\right)} \cos\left(d x + c\right)^{4} + 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)^{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} + {\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)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 24 \, {\left({\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\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)^{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^{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)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 24 \, {\left({\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\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)^{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^{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)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, a^{8} b^{4} - 24 \, a^{6} b^{6} + 36 \, a^{4} b^{8} - 24 \, a^{2} b^{10} + 6 \, b^{12} + {\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}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + {\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)\right)} \sin\left(d x + c\right)}{12 \, {\left({\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 \cos\left(d x + c\right)^{4} + 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)^{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} + {\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)\right)}}, \frac{3 \, {\left({\left(8 \, a^{11} - 28 \, a^{9} b^{2} + 35 \, a^{7} b^{4} - 20 \, a^{5} b^{6}\right)} \cos\left(d x + c\right)^{4} + 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)^{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} + {\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)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - 12 \, {\left({\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\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)^{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^{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)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 12 \, {\left({\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\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)^{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^{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)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(6 \, a^{8} b^{4} - 24 \, a^{6} b^{6} + 36 \, a^{4} b^{8} - 24 \, a^{2} b^{10} + 6 \, b^{12} + {\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}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + {\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)\right)} \sin\left(d x + c\right)}{6 \, {\left({\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 \cos\left(d x + c\right)^{4} + 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)^{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} + {\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)\right)}}\right]"," ",0,"[1/12*(3*((8*a^11 - 28*a^9*b^2 + 35*a^7*b^4 - 20*a^5*b^6)*cos(d*x + c)^4 + 3*(8*a^10*b - 28*a^8*b^3 + 35*a^6*b^5 - 20*a^4*b^7)*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 + (8*a^8*b^3 - 28*a^6*b^5 + 35*a^4*b^7 - 20*a^2*b^9)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 24*((a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*cos(d*x + c)^4 + 3*(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)^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^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))*log(sin(d*x + c) + 1) + 24*((a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*cos(d*x + c)^4 + 3*(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)^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^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))*log(-sin(d*x + c) + 1) + 2*(6*a^8*b^4 - 24*a^6*b^6 + 36*a^4*b^8 - 24*a^2*b^10 + 6*b^12 + (24*a^11*b - 92*a^9*b^3 + 133*a^7*b^5 - 71*a^5*b^7 + 6*a^3*b^9)*cos(d*x + c)^3 + 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)^2 + (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))*sin(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*cos(d*x + c)^4 + 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)^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 + (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)), 1/6*(3*((8*a^11 - 28*a^9*b^2 + 35*a^7*b^4 - 20*a^5*b^6)*cos(d*x + c)^4 + 3*(8*a^10*b - 28*a^8*b^3 + 35*a^6*b^5 - 20*a^4*b^7)*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 + (8*a^8*b^3 - 28*a^6*b^5 + 35*a^4*b^7 - 20*a^2*b^9)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - 12*((a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*cos(d*x + c)^4 + 3*(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)^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^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))*log(sin(d*x + c) + 1) + 12*((a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*cos(d*x + c)^4 + 3*(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)^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^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))*log(-sin(d*x + c) + 1) + (6*a^8*b^4 - 24*a^6*b^6 + 36*a^4*b^8 - 24*a^2*b^10 + 6*b^12 + (24*a^11*b - 92*a^9*b^3 + 133*a^7*b^5 - 71*a^5*b^7 + 6*a^3*b^9)*cos(d*x + c)^3 + 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)^2 + (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))*sin(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*cos(d*x + c)^4 + 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)^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 + (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))]","B",0
515,1,1822,0,3.202880," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, a^{7} b^{3} - 7 \, a^{5} b^{5} + 8 \, a^{3} b^{7} - 8 \, a b^{9} + {\left(2 \, a^{10} - 7 \, a^{8} b^{2} + 8 \, a^{6} b^{4} - 8 \, a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + 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)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 6 \, {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11} + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + 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)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11} + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + 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)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(11 \, a^{8} b^{3} - 43 \, a^{6} b^{5} + 68 \, a^{4} b^{7} - 36 \, a^{2} b^{9} + {\left(6 \, a^{10} b - 23 \, a^{8} b^{3} + 43 \, a^{6} b^{5} - 26 \, a^{4} b^{7}\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^{11} b^{4} - 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} - 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d\right)}}, -\frac{3 \, {\left(2 \, a^{7} b^{3} - 7 \, a^{5} b^{5} + 8 \, a^{3} b^{7} - 8 \, a b^{9} + {\left(2 \, a^{10} - 7 \, a^{8} b^{2} + 8 \, a^{6} b^{4} - 8 \, a^{4} b^{6}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + 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)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - 3 \, {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11} + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + 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)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11} + {\left(a^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + 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)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + {\left(11 \, a^{8} b^{3} - 43 \, a^{6} b^{5} + 68 \, a^{4} b^{7} - 36 \, a^{2} b^{9} + {\left(6 \, a^{10} b - 23 \, a^{8} b^{3} + 43 \, a^{6} b^{5} - 26 \, a^{4} b^{7}\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^{11} b^{4} - 4 \, a^{9} b^{6} + 6 \, a^{7} b^{8} - 4 \, a^{5} b^{10} + a^{3} b^{12}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{7} - 4 \, a^{6} b^{9} + 6 \, a^{4} b^{11} - 4 \, a^{2} b^{13} + b^{15}\right)} d\right)}}\right]"," ",0,"[1/12*(3*(2*a^7*b^3 - 7*a^5*b^5 + 8*a^3*b^7 - 8*a*b^9 + (2*a^10 - 7*a^8*b^2 + 8*a^6*b^4 - 8*a^4*b^6)*cos(d*x + c)^3 + 3*(2*a^9*b - 7*a^7*b^3 + 8*a^5*b^5 - 8*a^3*b^7)*cos(d*x + c)^2 + 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))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 6*(a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11 + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*cos(d*x + c)^3 + 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)^2 + 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))*log(sin(d*x + c) + 1) - 6*(a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11 + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*cos(d*x + c)^3 + 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)^2 + 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))*log(-sin(d*x + c) + 1) - 2*(11*a^8*b^3 - 43*a^6*b^5 + 68*a^4*b^7 - 36*a^2*b^9 + (6*a^10*b - 23*a^8*b^3 + 43*a^6*b^5 - 26*a^4*b^7)*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^11*b^4 - 4*a^9*b^6 + 6*a^7*b^8 - 4*a^5*b^10 + a^3*b^12)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d), -1/6*(3*(2*a^7*b^3 - 7*a^5*b^5 + 8*a^3*b^7 - 8*a*b^9 + (2*a^10 - 7*a^8*b^2 + 8*a^6*b^4 - 8*a^4*b^6)*cos(d*x + c)^3 + 3*(2*a^9*b - 7*a^7*b^3 + 8*a^5*b^5 - 8*a^3*b^7)*cos(d*x + c)^2 + 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))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - 3*(a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11 + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*cos(d*x + c)^3 + 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)^2 + 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))*log(sin(d*x + c) + 1) + 3*(a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11 + (a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*cos(d*x + c)^3 + 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)^2 + 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))*log(-sin(d*x + c) + 1) + (11*a^8*b^3 - 43*a^6*b^5 + 68*a^4*b^7 - 36*a^2*b^9 + (6*a^10*b - 23*a^8*b^3 + 43*a^6*b^5 - 26*a^4*b^7)*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^11*b^4 - 4*a^9*b^6 + 6*a^7*b^8 - 4*a^5*b^10 + a^3*b^12)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^7 - 4*a^6*b^9 + 6*a^4*b^11 - 4*a^2*b^13 + b^15)*d)]","B",0
516,1,903,0,0.609453," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, a^{2} b^{4} + 2 \, b^{6} + {\left(3 \, a^{5} b + 2 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{3} b^{3} + 2 \, a 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(2 \, a^{7} - 7 \, a^{5} b^{2} + 23 \, a^{3} b^{4} - 18 \, a b^{6} + {\left(4 \, a^{7} + 7 \, a^{5} b^{2} - 11 \, a^{3} b^{4}\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^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}, -\frac{3 \, {\left(3 \, a^{2} b^{4} + 2 \, b^{6} + {\left(3 \, a^{5} b + 2 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{7} - 7 \, a^{5} b^{2} + 23 \, a^{3} b^{4} - 18 \, a b^{6} + {\left(4 \, a^{7} + 7 \, a^{5} b^{2} - 11 \, a^{3} b^{4}\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^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(3*a^2*b^4 + 2*b^6 + (3*a^5*b + 2*a^3*b^3)*cos(d*x + c)^3 + 3*(3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c)^2 + 3*(3*a^3*b^3 + 2*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(2*a^7 - 7*a^5*b^2 + 23*a^3*b^4 - 18*a*b^6 + (4*a^7 + 7*a^5*b^2 - 11*a^3*b^4)*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^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d), -1/6*(3*(3*a^2*b^4 + 2*b^6 + (3*a^5*b + 2*a^3*b^3)*cos(d*x + c)^3 + 3*(3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c)^2 + 3*(3*a^3*b^3 + 2*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (2*a^7 - 7*a^5*b^2 + 23*a^3*b^4 - 18*a*b^6 + (4*a^7 + 7*a^5*b^2 - 11*a^3*b^4)*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^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d)]","B",0
517,1,902,0,0.559207," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a^{3} b^{3} + 4 \, a b^{5} + {\left(a^{6} + 4 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b + 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{4} b^{2} + 4 \, 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + 6 \, b^{7} - {\left(13 \, a^{6} b - 11 \, a^{4} b^{3} - 2 \, a^{2} b^{5}\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^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}, \frac{3 \, {\left(a^{3} b^{3} + 4 \, a b^{5} + {\left(a^{6} + 4 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b + 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(a^{6} b - 11 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + 6 \, b^{7} - {\left(13 \, a^{6} b - 11 \, a^{4} b^{3} - 2 \, a^{2} b^{5}\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^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(a^3*b^3 + 4*a*b^5 + (a^6 + 4*a^4*b^2)*cos(d*x + c)^3 + 3*(a^5*b + 4*a^3*b^3)*cos(d*x + c)^2 + 3*(a^4*b^2 + 4*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + 6*b^7 - (13*a^6*b - 11*a^4*b^3 - 2*a^2*b^5)*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^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d), 1/6*(3*(a^3*b^3 + 4*a*b^5 + (a^6 + 4*a^4*b^2)*cos(d*x + c)^3 + 3*(a^5*b + 4*a^3*b^3)*cos(d*x + c)^2 + 3*(a^4*b^2 + 4*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (a^6*b - 11*a^4*b^3 + 4*a^2*b^5 + 6*b^7 - (13*a^6*b - 11*a^4*b^3 - 2*a^2*b^5)*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^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d)]","B",0
518,1,901,0,0.577734," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(4 \, a^{2} b^{4} + b^{6} + {\left(4 \, a^{5} b + a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, a^{3} b^{3} + a 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(2 \, a^{5} b^{2} + 11 \, a^{3} b^{4} - 13 \, a b^{6} + {\left(6 \, a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 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^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}, -\frac{3 \, {\left(4 \, a^{2} b^{4} + b^{6} + {\left(4 \, a^{5} b + a^{3} b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(4 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(2 \, a^{5} b^{2} + 11 \, a^{3} b^{4} - 13 \, a b^{6} + {\left(6 \, a^{7} + 4 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 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^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(4*a^2*b^4 + b^6 + (4*a^5*b + a^3*b^3)*cos(d*x + c)^3 + 3*(4*a^4*b^2 + a^2*b^4)*cos(d*x + c)^2 + 3*(4*a^3*b^3 + a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(2*a^5*b^2 + 11*a^3*b^4 - 13*a*b^6 + (6*a^7 + 4*a^5*b^2 - 11*a^3*b^4 + 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^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d), -1/6*(3*(4*a^2*b^4 + b^6 + (4*a^5*b + a^3*b^3)*cos(d*x + c)^3 + 3*(4*a^4*b^2 + a^2*b^4)*cos(d*x + c)^2 + 3*(4*a^3*b^3 + a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (2*a^5*b^2 + 11*a^3*b^4 - 13*a*b^6 + (6*a^7 + 4*a^5*b^2 - 11*a^3*b^4 + 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^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d)]","B",0
519,1,905,0,0.591476," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, a^{3} b^{3} + 3 \, a b^{5} + {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{4} b^{2} + 3 \, 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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7} + {\left(18 \, a^{6} b - 23 \, a^{4} b^{3} + 7 \, a^{2} b^{5} - 2 \, 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^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}, \frac{3 \, {\left(2 \, a^{3} b^{3} + 3 \, a b^{5} + {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{5} b + 3 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7} + {\left(18 \, a^{6} b - 23 \, a^{4} b^{3} + 7 \, a^{2} b^{5} - 2 \, 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^{11} - 4 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + a^{3} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[-1/12*(3*(2*a^3*b^3 + 3*a*b^5 + (2*a^6 + 3*a^4*b^2)*cos(d*x + c)^3 + 3*(2*a^5*b + 3*a^3*b^3)*cos(d*x + c)^2 + 3*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(11*a^4*b^3 - 7*a^2*b^5 - 4*b^7 + (18*a^6*b - 23*a^4*b^3 + 7*a^2*b^5 - 2*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^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d), 1/6*(3*(2*a^3*b^3 + 3*a*b^5 + (2*a^6 + 3*a^4*b^2)*cos(d*x + c)^3 + 3*(2*a^5*b + 3*a^3*b^3)*cos(d*x + c)^2 + 3*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (11*a^4*b^3 - 7*a^2*b^5 - 4*b^7 + (18*a^6*b - 23*a^4*b^3 + 7*a^2*b^5 - 2*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^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d)]","B",0
520,1,1456,0,0.653587," ","integrate(1/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{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 \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + 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 + 3 \, {\left(8 \, a^{6} b^{4} - 8 \, a^{4} b^{6} + 7 \, a^{2} b^{8} - 2 \, b^{10} + {\left(8 \, a^{9} b - 8 \, a^{7} b^{3} + 7 \, a^{5} b^{5} - 2 \, a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + 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)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) + 2 \, {\left(26 \, a^{7} b^{4} - 43 \, a^{5} b^{6} + 23 \, a^{3} b^{8} - 6 \, a b^{10} + {\left(36 \, a^{9} b^{2} - 68 \, a^{7} b^{4} + 43 \, a^{5} b^{6} - 11 \, a^{3} b^{8}\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^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\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\right)}}, \frac{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 \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + 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 - 3 \, {\left(8 \, a^{6} b^{4} - 8 \, a^{4} b^{6} + 7 \, a^{2} b^{8} - 2 \, b^{10} + {\left(8 \, a^{9} b - 8 \, a^{7} b^{3} + 7 \, a^{5} b^{5} - 2 \, a^{3} b^{7}\right)} \cos\left(d x + c\right)^{3} + 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)^{2} + 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)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) + {\left(26 \, a^{7} b^{4} - 43 \, a^{5} b^{6} + 23 \, a^{3} b^{8} - 6 \, a b^{10} + {\left(36 \, a^{9} b^{2} - 68 \, a^{7} b^{4} + 43 \, a^{5} b^{6} - 11 \, a^{3} b^{8}\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^{15} - 4 \, a^{13} b^{2} + 6 \, a^{11} b^{4} - 4 \, a^{9} b^{6} + a^{7} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 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)^{2} + 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) + {\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\right)}}\right]"," ",0,"[1/12*(12*(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*x*cos(d*x + c)^3 + 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)^2 + 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) + 12*(a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*x + 3*(8*a^6*b^4 - 8*a^4*b^6 + 7*a^2*b^8 - 2*b^10 + (8*a^9*b - 8*a^7*b^3 + 7*a^5*b^5 - 2*a^3*b^7)*cos(d*x + c)^3 + 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)^2 + 3*(8*a^7*b^3 - 8*a^5*b^5 + 7*a^3*b^7 - 2*a*b^9)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) + 2*(26*a^7*b^4 - 43*a^5*b^6 + 23*a^3*b^8 - 6*a*b^10 + (36*a^9*b^2 - 68*a^7*b^4 + 43*a^5*b^6 - 11*a^3*b^8)*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^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^12*b^3 - 4*a^10*b^5 + 6*a^8*b^7 - 4*a^6*b^9 + a^4*b^11)*d), 1/6*(6*(a^11 - 4*a^9*b^2 + 6*a^7*b^4 - 4*a^5*b^6 + a^3*b^8)*d*x*cos(d*x + c)^3 + 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)^2 + 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) + 6*(a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*d*x - 3*(8*a^6*b^4 - 8*a^4*b^6 + 7*a^2*b^8 - 2*b^10 + (8*a^9*b - 8*a^7*b^3 + 7*a^5*b^5 - 2*a^3*b^7)*cos(d*x + c)^3 + 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)^2 + 3*(8*a^7*b^3 - 8*a^5*b^5 + 7*a^3*b^7 - 2*a*b^9)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) + (26*a^7*b^4 - 43*a^5*b^6 + 23*a^3*b^8 - 6*a*b^10 + (36*a^9*b^2 - 68*a^7*b^4 + 43*a^5*b^6 - 11*a^3*b^8)*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^15 - 4*a^13*b^2 + 6*a^11*b^4 - 4*a^9*b^6 + a^7*b^8)*d*cos(d*x + c)^3 + 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)^2 + 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) + (a^12*b^3 - 4*a^10*b^5 + 6*a^8*b^7 - 4*a^6*b^9 + a^4*b^11)*d)]","B",0
521,1,1603,0,0.681690," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[-\frac{48 \, {\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)^{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^{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) + 48 \, {\left(a^{8} b^{4} - 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} d x - 3 \, {\left(20 \, a^{6} b^{5} - 35 \, a^{4} b^{7} + 28 \, a^{2} b^{9} - 8 \, b^{11} + {\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)^{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} + 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)\right)} \sqrt{a^{2} - b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) - {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\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} + 6 \, {\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(d x + c\right)^{3} + {\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)^{2} + 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)\right)} \sin\left(d x + c\right)}{12 \, {\left({\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)^{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} + 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) + {\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\right)}}, -\frac{24 \, {\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)^{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^{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) + 24 \, {\left(a^{8} b^{4} - 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} - 4 \, a^{2} b^{10} + b^{12}\right)} d x - 3 \, {\left(20 \, a^{6} b^{5} - 35 \, a^{4} b^{7} + 28 \, a^{2} b^{9} - 8 \, b^{11} + {\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)^{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} + 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)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\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} + 6 \, {\left(a^{12} - 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} - 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} \cos\left(d x + c\right)^{3} + {\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)^{2} + 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)\right)} \sin\left(d x + c\right)}{6 \, {\left({\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)^{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} + 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) + {\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\right)}}\right]"," ",0,"[-1/12*(48*(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)^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^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) + 48*(a^8*b^4 - 4*a^6*b^6 + 6*a^4*b^8 - 4*a^2*b^10 + b^12)*d*x - 3*(20*a^6*b^5 - 35*a^4*b^7 + 28*a^2*b^9 - 8*b^11 + (20*a^9*b^2 - 35*a^7*b^4 + 28*a^5*b^6 - 8*a^3*b^8)*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 + 3*(20*a^7*b^4 - 35*a^5*b^6 + 28*a^3*b^8 - 8*a*b^10)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 + 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(6*a^9*b^3 - 71*a^7*b^5 + 133*a^5*b^7 - 92*a^3*b^9 + 24*a*b^11 + 6*(a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*cos(d*x + c)^3 + (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)^2 + 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))*sin(d*x + c))/((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)^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 + 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) + (a^13*b^3 - 4*a^11*b^5 + 6*a^9*b^7 - 4*a^7*b^9 + a^5*b^11)*d), -1/6*(24*(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)^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^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) + 24*(a^8*b^4 - 4*a^6*b^6 + 6*a^4*b^8 - 4*a^2*b^10 + b^12)*d*x - 3*(20*a^6*b^5 - 35*a^4*b^7 + 28*a^2*b^9 - 8*b^11 + (20*a^9*b^2 - 35*a^7*b^4 + 28*a^5*b^6 - 8*a^3*b^8)*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 + 3*(20*a^7*b^4 - 35*a^5*b^6 + 28*a^3*b^8 - 8*a*b^10)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (6*a^9*b^3 - 71*a^7*b^5 + 133*a^5*b^7 - 92*a^3*b^9 + 24*a*b^11 + 6*(a^12 - 4*a^10*b^2 + 6*a^8*b^4 - 4*a^6*b^6 + a^4*b^8)*cos(d*x + c)^3 + (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)^2 + 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))*sin(d*x + c))/((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)^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 + 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) + (a^13*b^3 - 4*a^11*b^5 + 6*a^9*b^7 - 4*a^7*b^9 + a^5*b^11)*d)]","B",0
522,1,1767,0,0.748345," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(a^{13} + 16 \, a^{11} b^{2} - 74 \, a^{9} b^{4} + 116 \, a^{7} b^{6} - 79 \, a^{5} b^{8} + 20 \, a^{3} b^{10}\right)} d x \cos\left(d x + c\right)^{3} + 18 \, {\left(a^{12} b + 16 \, a^{10} b^{3} - 74 \, a^{8} b^{5} + 116 \, a^{6} b^{7} - 79 \, a^{4} b^{9} + 20 \, a^{2} b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 18 \, {\left(a^{11} b^{2} + 16 \, a^{9} b^{4} - 74 \, a^{7} b^{6} + 116 \, a^{5} b^{8} - 79 \, a^{3} b^{10} + 20 \, a b^{12}\right)} d x \cos\left(d x + c\right) + 6 \, {\left(a^{10} b^{3} + 16 \, a^{8} b^{5} - 74 \, a^{6} b^{7} + 116 \, a^{4} b^{9} - 79 \, a^{2} b^{11} + 20 \, b^{13}\right)} d x + 3 \, {\left(40 \, a^{6} b^{6} - 84 \, a^{4} b^{8} + 69 \, a^{2} b^{10} - 20 \, b^{12} + {\left(40 \, a^{9} b^{3} - 84 \, a^{7} b^{5} + 69 \, a^{5} b^{7} - 20 \, a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(40 \, a^{8} b^{4} - 84 \, a^{6} b^{6} + 69 \, a^{4} b^{8} - 20 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(40 \, a^{7} b^{5} - 84 \, a^{5} b^{7} + 69 \, a^{3} b^{9} - 20 \, a b^{11}\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(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} - b^{2}} {\left(b \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a^{2} - b^{2}}{a^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) + b^{2}}\right) - 2 \, {\left(24 \, a^{9} b^{4} - 170 \, a^{7} b^{6} + 313 \, a^{5} b^{8} - 227 \, a^{3} b^{10} + 60 \, a b^{12} - 3 \, {\left(a^{13} - 4 \, a^{11} b^{2} + 6 \, a^{9} b^{4} - 4 \, a^{7} b^{6} + a^{5} b^{8}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(a^{12} b - 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} - 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(63 \, a^{11} b^{2} - 342 \, a^{9} b^{4} + 590 \, a^{7} b^{6} - 421 \, a^{5} b^{8} + 110 \, a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(23 \, a^{10} b^{3} - 146 \, a^{8} b^{5} + 263 \, a^{6} b^{7} - 190 \, a^{4} b^{9} + 50 \, a^{2} b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{17} - 4 \, a^{15} b^{2} + 6 \, a^{13} b^{4} - 4 \, a^{11} b^{6} + a^{9} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{16} b - 4 \, a^{14} b^{3} + 6 \, a^{12} b^{5} - 4 \, a^{10} b^{7} + a^{8} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{15} b^{2} - 4 \, a^{13} b^{4} + 6 \, a^{11} b^{6} - 4 \, a^{9} b^{8} + a^{7} b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{14} b^{3} - 4 \, a^{12} b^{5} + 6 \, a^{10} b^{7} - 4 \, a^{8} b^{9} + a^{6} b^{11}\right)} d\right)}}, \frac{3 \, {\left(a^{13} + 16 \, a^{11} b^{2} - 74 \, a^{9} b^{4} + 116 \, a^{7} b^{6} - 79 \, a^{5} b^{8} + 20 \, a^{3} b^{10}\right)} d x \cos\left(d x + c\right)^{3} + 9 \, {\left(a^{12} b + 16 \, a^{10} b^{3} - 74 \, a^{8} b^{5} + 116 \, a^{6} b^{7} - 79 \, a^{4} b^{9} + 20 \, a^{2} b^{11}\right)} d x \cos\left(d x + c\right)^{2} + 9 \, {\left(a^{11} b^{2} + 16 \, a^{9} b^{4} - 74 \, a^{7} b^{6} + 116 \, a^{5} b^{8} - 79 \, a^{3} b^{10} + 20 \, a b^{12}\right)} d x \cos\left(d x + c\right) + 3 \, {\left(a^{10} b^{3} + 16 \, a^{8} b^{5} - 74 \, a^{6} b^{7} + 116 \, a^{4} b^{9} - 79 \, a^{2} b^{11} + 20 \, b^{13}\right)} d x - 3 \, {\left(40 \, a^{6} b^{6} - 84 \, a^{4} b^{8} + 69 \, a^{2} b^{10} - 20 \, b^{12} + {\left(40 \, a^{9} b^{3} - 84 \, a^{7} b^{5} + 69 \, a^{5} b^{7} - 20 \, a^{3} b^{9}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(40 \, a^{8} b^{4} - 84 \, a^{6} b^{6} + 69 \, a^{4} b^{8} - 20 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(40 \, a^{7} b^{5} - 84 \, a^{5} b^{7} + 69 \, a^{3} b^{9} - 20 \, a b^{11}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \arctan\left(-\frac{\sqrt{-a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) + a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}\right) - {\left(24 \, a^{9} b^{4} - 170 \, a^{7} b^{6} + 313 \, a^{5} b^{8} - 227 \, a^{3} b^{10} + 60 \, a b^{12} - 3 \, {\left(a^{13} - 4 \, a^{11} b^{2} + 6 \, a^{9} b^{4} - 4 \, a^{7} b^{6} + a^{5} b^{8}\right)} \cos\left(d x + c\right)^{4} + 15 \, {\left(a^{12} b - 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} - 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} \cos\left(d x + c\right)^{3} + {\left(63 \, a^{11} b^{2} - 342 \, a^{9} b^{4} + 590 \, a^{7} b^{6} - 421 \, a^{5} b^{8} + 110 \, a^{3} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(23 \, a^{10} b^{3} - 146 \, a^{8} b^{5} + 263 \, a^{6} b^{7} - 190 \, a^{4} b^{9} + 50 \, a^{2} b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{17} - 4 \, a^{15} b^{2} + 6 \, a^{13} b^{4} - 4 \, a^{11} b^{6} + a^{9} b^{8}\right)} d \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{16} b - 4 \, a^{14} b^{3} + 6 \, a^{12} b^{5} - 4 \, a^{10} b^{7} + a^{8} b^{9}\right)} d \cos\left(d x + c\right)^{2} + 3 \, {\left(a^{15} b^{2} - 4 \, a^{13} b^{4} + 6 \, a^{11} b^{6} - 4 \, a^{9} b^{8} + a^{7} b^{10}\right)} d \cos\left(d x + c\right) + {\left(a^{14} b^{3} - 4 \, a^{12} b^{5} + 6 \, a^{10} b^{7} - 4 \, a^{8} b^{9} + a^{6} b^{11}\right)} d\right)}}\right]"," ",0,"[1/12*(6*(a^13 + 16*a^11*b^2 - 74*a^9*b^4 + 116*a^7*b^6 - 79*a^5*b^8 + 20*a^3*b^10)*d*x*cos(d*x + c)^3 + 18*(a^12*b + 16*a^10*b^3 - 74*a^8*b^5 + 116*a^6*b^7 - 79*a^4*b^9 + 20*a^2*b^11)*d*x*cos(d*x + c)^2 + 18*(a^11*b^2 + 16*a^9*b^4 - 74*a^7*b^6 + 116*a^5*b^8 - 79*a^3*b^10 + 20*a*b^12)*d*x*cos(d*x + c) + 6*(a^10*b^3 + 16*a^8*b^5 - 74*a^6*b^7 + 116*a^4*b^9 - 79*a^2*b^11 + 20*b^13)*d*x + 3*(40*a^6*b^6 - 84*a^4*b^8 + 69*a^2*b^10 - 20*b^12 + (40*a^9*b^3 - 84*a^7*b^5 + 69*a^5*b^7 - 20*a^3*b^9)*cos(d*x + c)^3 + 3*(40*a^8*b^4 - 84*a^6*b^6 + 69*a^4*b^8 - 20*a^2*b^10)*cos(d*x + c)^2 + 3*(40*a^7*b^5 - 84*a^5*b^7 + 69*a^3*b^9 - 20*a*b^11)*cos(d*x + c))*sqrt(a^2 - b^2)*log((2*a*b*cos(d*x + c) - (a^2 - 2*b^2)*cos(d*x + c)^2 - 2*sqrt(a^2 - b^2)*(b*cos(d*x + c) + a)*sin(d*x + c) + 2*a^2 - b^2)/(a^2*cos(d*x + c)^2 + 2*a*b*cos(d*x + c) + b^2)) - 2*(24*a^9*b^4 - 170*a^7*b^6 + 313*a^5*b^8 - 227*a^3*b^10 + 60*a*b^12 - 3*(a^13 - 4*a^11*b^2 + 6*a^9*b^4 - 4*a^7*b^6 + a^5*b^8)*cos(d*x + c)^4 + 15*(a^12*b - 4*a^10*b^3 + 6*a^8*b^5 - 4*a^6*b^7 + a^4*b^9)*cos(d*x + c)^3 + (63*a^11*b^2 - 342*a^9*b^4 + 590*a^7*b^6 - 421*a^5*b^8 + 110*a^3*b^10)*cos(d*x + c)^2 + 3*(23*a^10*b^3 - 146*a^8*b^5 + 263*a^6*b^7 - 190*a^4*b^9 + 50*a^2*b^11)*cos(d*x + c))*sin(d*x + c))/((a^17 - 4*a^15*b^2 + 6*a^13*b^4 - 4*a^11*b^6 + a^9*b^8)*d*cos(d*x + c)^3 + 3*(a^16*b - 4*a^14*b^3 + 6*a^12*b^5 - 4*a^10*b^7 + a^8*b^9)*d*cos(d*x + c)^2 + 3*(a^15*b^2 - 4*a^13*b^4 + 6*a^11*b^6 - 4*a^9*b^8 + a^7*b^10)*d*cos(d*x + c) + (a^14*b^3 - 4*a^12*b^5 + 6*a^10*b^7 - 4*a^8*b^9 + a^6*b^11)*d), 1/6*(3*(a^13 + 16*a^11*b^2 - 74*a^9*b^4 + 116*a^7*b^6 - 79*a^5*b^8 + 20*a^3*b^10)*d*x*cos(d*x + c)^3 + 9*(a^12*b + 16*a^10*b^3 - 74*a^8*b^5 + 116*a^6*b^7 - 79*a^4*b^9 + 20*a^2*b^11)*d*x*cos(d*x + c)^2 + 9*(a^11*b^2 + 16*a^9*b^4 - 74*a^7*b^6 + 116*a^5*b^8 - 79*a^3*b^10 + 20*a*b^12)*d*x*cos(d*x + c) + 3*(a^10*b^3 + 16*a^8*b^5 - 74*a^6*b^7 + 116*a^4*b^9 - 79*a^2*b^11 + 20*b^13)*d*x - 3*(40*a^6*b^6 - 84*a^4*b^8 + 69*a^2*b^10 - 20*b^12 + (40*a^9*b^3 - 84*a^7*b^5 + 69*a^5*b^7 - 20*a^3*b^9)*cos(d*x + c)^3 + 3*(40*a^8*b^4 - 84*a^6*b^6 + 69*a^4*b^8 - 20*a^2*b^10)*cos(d*x + c)^2 + 3*(40*a^7*b^5 - 84*a^5*b^7 + 69*a^3*b^9 - 20*a*b^11)*cos(d*x + c))*sqrt(-a^2 + b^2)*arctan(-sqrt(-a^2 + b^2)*(b*cos(d*x + c) + a)/((a^2 - b^2)*sin(d*x + c))) - (24*a^9*b^4 - 170*a^7*b^6 + 313*a^5*b^8 - 227*a^3*b^10 + 60*a*b^12 - 3*(a^13 - 4*a^11*b^2 + 6*a^9*b^4 - 4*a^7*b^6 + a^5*b^8)*cos(d*x + c)^4 + 15*(a^12*b - 4*a^10*b^3 + 6*a^8*b^5 - 4*a^6*b^7 + a^4*b^9)*cos(d*x + c)^3 + (63*a^11*b^2 - 342*a^9*b^4 + 590*a^7*b^6 - 421*a^5*b^8 + 110*a^3*b^10)*cos(d*x + c)^2 + 3*(23*a^10*b^3 - 146*a^8*b^5 + 263*a^6*b^7 - 190*a^4*b^9 + 50*a^2*b^11)*cos(d*x + c))*sin(d*x + c))/((a^17 - 4*a^15*b^2 + 6*a^13*b^4 - 4*a^11*b^6 + a^9*b^8)*d*cos(d*x + c)^3 + 3*(a^16*b - 4*a^14*b^3 + 6*a^12*b^5 - 4*a^10*b^7 + a^8*b^9)*d*cos(d*x + c)^2 + 3*(a^15*b^2 - 4*a^13*b^4 + 6*a^11*b^6 - 4*a^9*b^8 + a^7*b^10)*d*cos(d*x + c) + (a^14*b^3 - 4*a^12*b^5 + 6*a^10*b^7 - 4*a^8*b^9 + a^6*b^11)*d)]","B",0
523,1,33,0,0.469301," ","integrate(1/(3+5*sec(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, d x + 5 \, \arctan\left(\frac{5 \, \cos\left(d x + c\right) + 3}{4 \, \sin\left(d x + c\right)}\right)}{12 \, d}"," ",0,"1/12*(4*d*x + 5*arctan(1/4*(5*cos(d*x + c) + 3)/sin(d*x + c)))/d","A",0
524,1,73,0,0.465655," ","integrate(1/(3+5*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{192 \, d x \cos\left(d x + c\right) + 320 \, d x + 35 \, {\left(3 \, \cos\left(d x + c\right) + 5\right)} \arctan\left(\frac{5 \, \cos\left(d x + c\right) + 3}{4 \, \sin\left(d x + c\right)}\right) - 300 \, \sin\left(d x + c\right)}{576 \, {\left(3 \, d \cos\left(d x + c\right) + 5 \, d\right)}}"," ",0,"1/576*(192*d*x*cos(d*x + c) + 320*d*x + 35*(3*cos(d*x + c) + 5)*arctan(1/4*(5*cos(d*x + c) + 3)/sin(d*x + c)) - 300*sin(d*x + c))/(3*d*cos(d*x + c) + 5*d)","A",0
525,1,116,0,0.544458," ","integrate(1/(3+5*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{18432 \, d x \cos\left(d x + c\right)^{2} + 61440 \, d x \cos\left(d x + c\right) + 51200 \, d x + 3055 \, {\left(9 \, \cos\left(d x + c\right)^{2} + 30 \, \cos\left(d x + c\right) + 25\right)} \arctan\left(\frac{5 \, \cos\left(d x + c\right) + 3}{4 \, \sin\left(d x + c\right)}\right) - 300 \, {\left(63 \, \cos\left(d x + c\right) + 25\right)} \sin\left(d x + c\right)}{55296 \, {\left(9 \, d \cos\left(d x + c\right)^{2} + 30 \, d \cos\left(d x + c\right) + 25 \, d\right)}}"," ",0,"1/55296*(18432*d*x*cos(d*x + c)^2 + 61440*d*x*cos(d*x + c) + 51200*d*x + 3055*(9*cos(d*x + c)^2 + 30*cos(d*x + c) + 25)*arctan(1/4*(5*cos(d*x + c) + 3)/sin(d*x + c)) - 300*(63*cos(d*x + c) + 25)*sin(d*x + c))/(9*d*cos(d*x + c)^2 + 30*d*cos(d*x + c) + 25*d)","A",0
526,1,159,0,0.470452," ","integrate(1/(3+5*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{884736 \, d x \cos\left(d x + c\right)^{3} + 4423680 \, d x \cos\left(d x + c\right)^{2} + 7372800 \, d x \cos\left(d x + c\right) + 4096000 \, d x + 11215 \, {\left(27 \, \cos\left(d x + c\right)^{3} + 135 \, \cos\left(d x + c\right)^{2} + 225 \, \cos\left(d x + c\right) + 125\right)} \arctan\left(\frac{5 \, \cos\left(d x + c\right) + 3}{4 \, \sin\left(d x + c\right)}\right) - 300 \, {\left(7773 \, \cos\left(d x + c\right)^{2} + 20550 \, \cos\left(d x + c\right) + 16925\right)} \sin\left(d x + c\right)}{2654208 \, {\left(27 \, d \cos\left(d x + c\right)^{3} + 135 \, d \cos\left(d x + c\right)^{2} + 225 \, d \cos\left(d x + c\right) + 125 \, d\right)}}"," ",0,"1/2654208*(884736*d*x*cos(d*x + c)^3 + 4423680*d*x*cos(d*x + c)^2 + 7372800*d*x*cos(d*x + c) + 4096000*d*x + 11215*(27*cos(d*x + c)^3 + 135*cos(d*x + c)^2 + 225*cos(d*x + c) + 125)*arctan(1/4*(5*cos(d*x + c) + 3)/sin(d*x + c)) - 300*(7773*cos(d*x + c)^2 + 20550*cos(d*x + c) + 16925)*sin(d*x + c))/(27*d*cos(d*x + c)^3 + 135*d*cos(d*x + c)^2 + 225*d*cos(d*x + c) + 125*d)","A",0
527,1,52,0,0.506620," ","integrate(1/(5+3*sec(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, d x - 3 \, \log\left(\frac{3}{2} \, \cos\left(d x + c\right) + 2 \, \sin\left(d x + c\right) + \frac{5}{2}\right) + 3 \, \log\left(\frac{3}{2} \, \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right) + \frac{5}{2}\right)}{40 \, d}"," ",0,"1/40*(8*d*x - 3*log(3/2*cos(d*x + c) + 2*sin(d*x + c) + 5/2) + 3*log(3/2*cos(d*x + c) - 2*sin(d*x + c) + 5/2))/d","A",0
528,1,102,0,0.459142," ","integrate(1/(5+3*sec(d*x+c))^2,x, algorithm=""fricas"")","\frac{640 \, d x \cos\left(d x + c\right) + 384 \, d x - 123 \, {\left(5 \, \cos\left(d x + c\right) + 3\right)} \log\left(\frac{3}{2} \, \cos\left(d x + c\right) + 2 \, \sin\left(d x + c\right) + \frac{5}{2}\right) + 123 \, {\left(5 \, \cos\left(d x + c\right) + 3\right)} \log\left(\frac{3}{2} \, \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right) + \frac{5}{2}\right) + 360 \, \sin\left(d x + c\right)}{3200 \, {\left(5 \, d \cos\left(d x + c\right) + 3 \, d\right)}}"," ",0,"1/3200*(640*d*x*cos(d*x + c) + 384*d*x - 123*(5*cos(d*x + c) + 3)*log(3/2*cos(d*x + c) + 2*sin(d*x + c) + 5/2) + 123*(5*cos(d*x + c) + 3)*log(3/2*cos(d*x + c) - 2*sin(d*x + c) + 5/2) + 360*sin(d*x + c))/(5*d*cos(d*x + c) + 3*d)","A",0
529,1,155,0,0.488803," ","integrate(1/(5+3*sec(d*x+c))^3,x, algorithm=""fricas"")","\frac{102400 \, d x \cos\left(d x + c\right)^{2} + 122880 \, d x \cos\left(d x + c\right) + 36864 \, d x - 8361 \, {\left(25 \, \cos\left(d x + c\right)^{2} + 30 \, \cos\left(d x + c\right) + 9\right)} \log\left(\frac{3}{2} \, \cos\left(d x + c\right) + 2 \, \sin\left(d x + c\right) + \frac{5}{2}\right) + 8361 \, {\left(25 \, \cos\left(d x + c\right)^{2} + 30 \, \cos\left(d x + c\right) + 9\right)} \log\left(\frac{3}{2} \, \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right) + \frac{5}{2}\right) + 1080 \, {\left(205 \, \cos\left(d x + c\right) + 107\right)} \sin\left(d x + c\right)}{512000 \, {\left(25 \, d \cos\left(d x + c\right)^{2} + 30 \, d \cos\left(d x + c\right) + 9 \, d\right)}}"," ",0,"1/512000*(102400*d*x*cos(d*x + c)^2 + 122880*d*x*cos(d*x + c) + 36864*d*x - 8361*(25*cos(d*x + c)^2 + 30*cos(d*x + c) + 9)*log(3/2*cos(d*x + c) + 2*sin(d*x + c) + 5/2) + 8361*(25*cos(d*x + c)^2 + 30*cos(d*x + c) + 9)*log(3/2*cos(d*x + c) - 2*sin(d*x + c) + 5/2) + 1080*(205*cos(d*x + c) + 107)*sin(d*x + c))/(25*d*cos(d*x + c)^2 + 30*d*cos(d*x + c) + 9*d)","A",0
530,1,208,0,0.525059," ","integrate(1/(5+3*sec(d*x+c))^4,x, algorithm=""fricas"")","\frac{8192000 \, d x \cos\left(d x + c\right)^{3} + 14745600 \, d x \cos\left(d x + c\right)^{2} + 8847360 \, d x \cos\left(d x + c\right) + 1769472 \, d x - 278151 \, {\left(125 \, \cos\left(d x + c\right)^{3} + 225 \, \cos\left(d x + c\right)^{2} + 135 \, \cos\left(d x + c\right) + 27\right)} \log\left(\frac{3}{2} \, \cos\left(d x + c\right) + 2 \, \sin\left(d x + c\right) + \frac{5}{2}\right) + 278151 \, {\left(125 \, \cos\left(d x + c\right)^{3} + 225 \, \cos\left(d x + c\right)^{2} + 135 \, \cos\left(d x + c\right) + 27\right)} \log\left(\frac{3}{2} \, \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right) + \frac{5}{2}\right) + 1080 \, {\left(44975 \, \cos\left(d x + c\right)^{2} + 47650 \, \cos\left(d x + c\right) + 12911\right)} \sin\left(d x + c\right)}{40960000 \, {\left(125 \, d \cos\left(d x + c\right)^{3} + 225 \, d \cos\left(d x + c\right)^{2} + 135 \, d \cos\left(d x + c\right) + 27 \, d\right)}}"," ",0,"1/40960000*(8192000*d*x*cos(d*x + c)^3 + 14745600*d*x*cos(d*x + c)^2 + 8847360*d*x*cos(d*x + c) + 1769472*d*x - 278151*(125*cos(d*x + c)^3 + 225*cos(d*x + c)^2 + 135*cos(d*x + c) + 27)*log(3/2*cos(d*x + c) + 2*sin(d*x + c) + 5/2) + 278151*(125*cos(d*x + c)^3 + 225*cos(d*x + c)^2 + 135*cos(d*x + c) + 27)*log(3/2*cos(d*x + c) - 2*sin(d*x + c) + 5/2) + 1080*(44975*cos(d*x + c)^2 + 47650*cos(d*x + c) + 12911)*sin(d*x + c))/(125*d*cos(d*x + c)^3 + 225*d*cos(d*x + c)^2 + 135*d*cos(d*x + c) + 27*d)","A",0
531,0,0,0,0.468745," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
532,0,0,0,0.445326," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2, x)","F",0
533,0,0,0,0.503765," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right), x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c), x)","F",0
534,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,0,0,0,2.035711," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right), x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c), x)","F",0
536,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,0,0,0,1.260876," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{5} + a \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)^5 + a*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
538,0,0,0,0.655547," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)^4 + a*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
539,0,0,0,0.777975," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)^3 + a*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
540,0,0,0,0.898955," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*sec(d*x + c)^2 + a*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
541,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,0,0,0,2.259118," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) \sec\left(d x + c\right) + a \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*cos(d*x + c)*sec(d*x + c) + a*cos(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
543,0,0,0,1.839647," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*cos(d*x + c)^2*sec(d*x + c) + a*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
544,0,0,0,0.607623," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{6} + 2 \, a b \sec\left(d x + c\right)^{5} + a^{2} \sec\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^6 + 2*a*b*sec(d*x + c)^5 + a^2*sec(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
545,0,0,0,2.675678," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{5} + 2 \, a b \sec\left(d x + c\right)^{4} + a^{2} \sec\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^5 + 2*a*b*sec(d*x + c)^4 + a^2*sec(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
546,0,0,0,0.706889," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
547,0,0,0,0.766086," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{3} + 2 \, a b \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^3 + 2*a*b*sec(d*x + c)^2 + a^2*sec(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
548,0,0,0,0.852041," ","integrate((a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
549,0,0,0,25.398031," ","integrate(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*cos(d*x + c)*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)*sec(d*x + c) + a^2*cos(d*x + c))*sqrt(b*sec(d*x + c) + a), x)","F",0
550,0,0,0,1.238627," ","integrate(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^2*sec(d*x + c) + a^2*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a), x)","F",0
551,0,0,0,28.414678," ","integrate(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^3*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^3*sec(d*x + c) + a^2*cos(d*x + c)^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
552,0,0,0,34.337330," ","integrate(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^4*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^4*sec(d*x + c) + a^2*cos(d*x + c)^4)*sqrt(b*sec(d*x + c) + a), x)","F",0
553,0,0,0,1.025922," ","integrate((a+b*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)*sqrt(b*sec(d*x + c) + a), x)","F",0
554,0,0,0,0.528871," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{5}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^5/sqrt(b*sec(d*x + c) + a), x)","F",0
555,0,0,0,0.495692," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{4}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^4/sqrt(b*sec(d*x + c) + a), x)","F",0
556,0,0,0,0.723382," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{3}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^3/sqrt(b*sec(d*x + c) + a), x)","F",0
557,0,0,0,0.452636," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{2}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^2/sqrt(b*sec(d*x + c) + a), x)","F",0
558,0,0,0,0.906796," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
559,0,0,0,25.968514," ","integrate(1/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(1/sqrt(b*sec(d*x + c) + a), x)","F",0
560,0,0,0,0.811090," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)/sqrt(b*sec(d*x + c) + a), x)","F",0
561,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,0,0,0,0.673115," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{5}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^5/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
563,0,0,0,0.940724," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^4/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
564,0,0,0,0.809100," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
565,0,0,0,0.517615," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
566,0,0,0,0.565179," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
567,0,0,0,25.836692," ","integrate(1/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
568,0,0,0,24.225800," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
569,0,0,0,31.413791," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
570,0,0,0,0.562495," ","integrate(sec(d*x+c)^5/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{5}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^5/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
571,0,0,0,0.535662," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^4/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
572,0,0,0,0.542476," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^3/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
573,0,0,0,0.605372," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{2}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^2/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
574,0,0,0,0.673627," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
575,0,0,0,26.379124," ","integrate(1/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
576,0,0,0,32.015336," ","integrate(cos(d*x+c)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
577,0,0,0,1.286983," ","integrate(cos(d*x+c)^2/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^2/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
578,0,0,0,1.133306," ","integrate(1/(a+b*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/(b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4), x)","F",0
579,0,0,0,0.455469," ","integrate(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b*sec(d*x + c)^3 + a*sec(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
580,0,0,0,0.518325," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b*sec(d*x + c)^2 + a*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
581,0,0,0,0.640054," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)*sqrt(sec(d*x + c)), x)","F",0
582,0,0,0,0.493144," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x + c\right) + a}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
583,0,0,0,0.566405," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
584,0,0,0,0.512364," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
585,0,0,0,1.041850," ","integrate((a+b*sec(d*x+c))/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x + c\right) + a}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
586,0,0,0,1.208762," ","integrate(sec(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2)*sqrt(sec(d*x + c)), x)","F",0
587,0,0,0,0.924315," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{3} + 2 \, a b \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^3 + 2*a*b*sec(d*x + c)^2 + a^2*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
588,0,0,0,0.733473," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(sec(d*x + c)), x)","F",0
589,0,0,0,0.991495," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)/sqrt(sec(d*x + c)), x)","F",0
590,0,0,0,0.838396," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)/sec(d*x + c)^(3/2), x)","F",0
591,0,0,0,0.655478," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)/sec(d*x + c)^(5/2), x)","F",0
592,0,0,0,1.778864," ","integrate((a+b*sec(d*x+c))^2/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)/sec(d*x + c)^(7/2), x)","F",0
593,0,0,0,1.032612," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \sec\left(d x + c\right)^{4} + 3 \, a b^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{2} b \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^4 + 3*a*b^2*sec(d*x + c)^3 + 3*a^2*b*sec(d*x + c)^2 + a^3*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
594,0,0,0,0.471410," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)*sqrt(sec(d*x + c)), x)","F",0
595,0,0,0,1.186378," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)/sqrt(sec(d*x + c)), x)","F",0
596,0,0,0,0.793245," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)/sec(d*x + c)^(3/2), x)","F",0
597,0,0,0,0.449477," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)/sec(d*x + c)^(5/2), x)","F",0
598,0,0,0,0.484411," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)/sec(d*x + c)^(7/2), x)","F",0
599,0,0,0,0.626646," ","integrate((a+b*sec(d*x+c))^3/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)/sec(d*x + c)^(9/2), x)","F",0
600,0,0,0,1.063876," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{4} \sec\left(d x + c\right)^{5} + 4 \, a b^{3} \sec\left(d x + c\right)^{4} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{3} + 4 \, a^{3} b \sec\left(d x + c\right)^{2} + a^{4} \sec\left(d x + c\right)\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^4*sec(d*x + c)^5 + 4*a*b^3*sec(d*x + c)^4 + 6*a^2*b^2*sec(d*x + c)^3 + 4*a^3*b*sec(d*x + c)^2 + a^4*sec(d*x + c))*sqrt(sec(d*x + c)), x)","F",0
601,0,0,0,0.518779," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}\right)} \sqrt{\sec\left(d x + c\right)}, x\right)"," ",0,"integral((b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4)*sqrt(sec(d*x + c)), x)","F",0
602,0,0,0,0.728841," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4)/sqrt(sec(d*x + c)), x)","F",0
603,0,0,0,0.551055," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4)/sec(d*x + c)^(3/2), x)","F",0
604,0,0,0,0.515351," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4)/sec(d*x + c)^(5/2), x)","F",0
605,0,0,0,0.514767," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4)/sec(d*x + c)^(7/2), x)","F",0
606,0,0,0,0.853652," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4)/sec(d*x + c)^(9/2), x)","F",0
607,0,0,0,0.653096," ","integrate((a+b*sec(d*x+c))^4/sec(d*x+c)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{4} \sec\left(d x + c\right)^{4} + 4 \, a b^{3} \sec\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \sec\left(d x + c\right)^{2} + 4 \, a^{3} b \sec\left(d x + c\right) + a^{4}}{\sec\left(d x + c\right)^{\frac{11}{2}}}, x\right)"," ",0,"integral((b^4*sec(d*x + c)^4 + 4*a*b^3*sec(d*x + c)^3 + 6*a^2*b^2*sec(d*x + c)^2 + 4*a^3*b*sec(d*x + c) + a^4)/sec(d*x + c)^(11/2), x)","F",0
608,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,0,0,0,67.687446," ","integrate(1/(a+b*sec(d*x+c))/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(b*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
613,0,0,0,69.793089," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(b*sec(d*x + c)^3 + a*sec(d*x + c)^2), x)","F",0
614,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,0,0,0,116.577775," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2), x)","F",0
621,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,0,0,0,135.357168," ","integrate(1/(a+b*sec(d*x+c))^3/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{4} + 3 \, a b^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{2} b \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^4 + 3*a*b^2*sec(d*x + c)^3 + 3*a^2*b*sec(d*x + c)^2 + a^3*sec(d*x + c)), x)","F",0
627,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,0,0,0,0.895818," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
631,0,0,0,1.263228," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(3/2), x)","F",0
632,0,0,0,1.034082," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
633,0,0,0,2.508774," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
634,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,0,0,0,5.240039," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sqrt(sec(d*x + c)), x)","F",0
637,0,0,0,2.181377," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(3/2), x)","F",0
638,0,0,0,0.947045," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/2), x)","F",0
639,0,0,0,0.926478," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/2), x)","F",0
640,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,0,0,0,4.103335," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sqrt{\sec\left(d x + c\right)}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sqrt(sec(d*x + c)), x)","F",0
643,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,0,0,0,0.723938," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/2), x)","F",0
645,0,0,0,0.830829," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/2), x)","F",0
646,0,0,0,0.750474," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{9}{2}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(9/2), x)","F",0
647,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
648,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
649,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,0,0,0,0.991259," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
651,0,0,0,1.031207," ","integrate(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
652,0,0,0,1.392696," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^3 + a*sec(d*x + c)^2), x)","F",0
653,0,0,0,0.519742," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b*sec(d*x + c)^4 + a*sec(d*x + c)^3), x)","F",0
654,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
655,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
656,0,0,0,0.772102," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
657,0,0,0,0.876236," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
658,0,0,0,0.959042," ","integrate(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{3} + 2 \, a b \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^3 + 2*a*b*sec(d*x + c)^2 + a^2*sec(d*x + c)), x)","F",0
659,0,0,0,0.530447," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2), x)","F",0
660,0,0,0,1.277576," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{5} + 2 \, a b \sec\left(d x + c\right)^{4} + a^{2} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^2*sec(d*x + c)^5 + 2*a*b*sec(d*x + c)^4 + a^2*sec(d*x + c)^3), x)","F",0
661,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(9/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
662,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
663,0,0,0,1.190490," ","integrate(sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{2}}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/2)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
664,0,0,0,1.331307," ","integrate(sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{3}{2}}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(3/2)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
665,0,0,0,1.860745," ","integrate(sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
666,0,0,0,1.202066," ","integrate(1/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{4} + 3 \, a b^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{2} b \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^4 + 3*a*b^2*sec(d*x + c)^3 + 3*a^2*b*sec(d*x + c)^2 + a^3*sec(d*x + c)), x)","F",0
667,0,0,0,0.744539," ","integrate(1/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{5} + 3 \, a b^{2} \sec\left(d x + c\right)^{4} + 3 \, a^{2} b \sec\left(d x + c\right)^{3} + a^{3} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^5 + 3*a*b^2*sec(d*x + c)^4 + 3*a^2*b*sec(d*x + c)^3 + a^3*sec(d*x + c)^2), x)","F",0
668,0,0,0,0.621558," ","integrate(1/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\sec\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{6} + 3 \, a b^{2} \sec\left(d x + c\right)^{5} + 3 \, a^{2} b \sec\left(d x + c\right)^{4} + a^{3} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(sec(d*x + c))/(b^3*sec(d*x + c)^6 + 3*a*b^2*sec(d*x + c)^5 + 3*a^2*b*sec(d*x + c)^4 + a^3*sec(d*x + c)^3), x)","F",0
669,0,0,0,0.470127," ","integrate(1/sec(d*x+c)^(1/2)/(2+3*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, \sec\left(d x + c\right) + 2} \sqrt{\sec\left(d x + c\right)}}{3 \, \sec\left(d x + c\right)^{2} + 2 \, \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(3*sec(d*x + c) + 2)*sqrt(sec(d*x + c))/(3*sec(d*x + c)^2 + 2*sec(d*x + c)), x)","F",0
670,0,0,0,0.460634," ","integrate(1/sec(d*x+c)^(1/2)/(-2+3*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, \sec\left(d x + c\right) - 2} \sqrt{\sec\left(d x + c\right)}}{3 \, \sec\left(d x + c\right)^{2} - 2 \, \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(3*sec(d*x + c) - 2)*sqrt(sec(d*x + c))/(3*sec(d*x + c)^2 - 2*sec(d*x + c)), x)","F",0
671,0,0,0,0.453775," ","integrate(1/(2-3*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, \sec\left(d x + c\right) + 2} \sqrt{\sec\left(d x + c\right)}}{3 \, \sec\left(d x + c\right)^{2} - 2 \, \sec\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-3*sec(d*x + c) + 2)*sqrt(sec(d*x + c))/(3*sec(d*x + c)^2 - 2*sec(d*x + c)), x)","F",0
672,0,0,0,0.444511," ","integrate(1/(-2-3*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, \sec\left(d x + c\right) - 2} \sqrt{\sec\left(d x + c\right)}}{3 \, \sec\left(d x + c\right)^{2} + 2 \, \sec\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-3*sec(d*x + c) - 2)*sqrt(sec(d*x + c))/(3*sec(d*x + c)^2 + 2*sec(d*x + c)), x)","F",0
673,0,0,0,0.440382," ","integrate(1/sec(d*x+c)^(1/2)/(3+2*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, \sec\left(d x + c\right) + 3} \sqrt{\sec\left(d x + c\right)}}{2 \, \sec\left(d x + c\right)^{2} + 3 \, \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(2*sec(d*x + c) + 3)*sqrt(sec(d*x + c))/(2*sec(d*x + c)^2 + 3*sec(d*x + c)), x)","F",0
674,0,0,0,0.500970," ","integrate(1/(3-2*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, \sec\left(d x + c\right) + 3} \sqrt{\sec\left(d x + c\right)}}{2 \, \sec\left(d x + c\right)^{2} - 3 \, \sec\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-2*sec(d*x + c) + 3)*sqrt(sec(d*x + c))/(2*sec(d*x + c)^2 - 3*sec(d*x + c)), x)","F",0
675,0,0,0,0.504355," ","integrate(1/sec(d*x+c)^(1/2)/(-3+2*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, \sec\left(d x + c\right) - 3} \sqrt{\sec\left(d x + c\right)}}{2 \, \sec\left(d x + c\right)^{2} - 3 \, \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(2*sec(d*x + c) - 3)*sqrt(sec(d*x + c))/(2*sec(d*x + c)^2 - 3*sec(d*x + c)), x)","F",0
676,0,0,0,0.508312," ","integrate(1/(-3-2*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, \sec\left(d x + c\right) - 3} \sqrt{\sec\left(d x + c\right)}}{2 \, \sec\left(d x + c\right)^{2} + 3 \, \sec\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(-2*sec(d*x + c) - 3)*sqrt(sec(d*x + c))/(2*sec(d*x + c)^2 + 3*sec(d*x + c)), x)","F",0
677,0,0,0,0.480988," ","integrate(sec(d*x+c)^(1/2)/(2+3*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{3 \, \sec\left(d x + c\right) + 2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/sqrt(3*sec(d*x + c) + 2), x)","F",0
678,0,0,0,0.492073," ","integrate(sec(d*x+c)^(1/2)/(-2+3*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{3 \, \sec\left(d x + c\right) - 2}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/sqrt(3*sec(d*x + c) - 2), x)","F",0
679,0,0,0,0.542357," ","integrate(sec(d*x+c)^(1/2)/(2-3*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, \sec\left(d x + c\right) + 2} \sqrt{\sec\left(d x + c\right)}}{3 \, \sec\left(d x + c\right) - 2}, x\right)"," ",0,"integral(-sqrt(-3*sec(d*x + c) + 2)*sqrt(sec(d*x + c))/(3*sec(d*x + c) - 2), x)","F",0
680,0,0,0,0.455141," ","integrate(sec(d*x+c)^(1/2)/(-2-3*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-3 \, \sec\left(d x + c\right) - 2} \sqrt{\sec\left(d x + c\right)}}{3 \, \sec\left(d x + c\right) + 2}, x\right)"," ",0,"integral(-sqrt(-3*sec(d*x + c) - 2)*sqrt(sec(d*x + c))/(3*sec(d*x + c) + 2), x)","F",0
681,0,0,0,0.471530," ","integrate(sec(d*x+c)^(1/2)/(3+2*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{2 \, \sec\left(d x + c\right) + 3}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/sqrt(2*sec(d*x + c) + 3), x)","F",0
682,0,0,0,0.519831," ","integrate(sec(d*x+c)^(1/2)/(3-2*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, \sec\left(d x + c\right) + 3} \sqrt{\sec\left(d x + c\right)}}{2 \, \sec\left(d x + c\right) - 3}, x\right)"," ",0,"integral(-sqrt(-2*sec(d*x + c) + 3)*sqrt(sec(d*x + c))/(2*sec(d*x + c) - 3), x)","F",0
683,0,0,0,0.518961," ","integrate(sec(d*x+c)^(1/2)/(-3+2*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\sec\left(d x + c\right)}}{\sqrt{2 \, \sec\left(d x + c\right) - 3}}, x\right)"," ",0,"integral(sqrt(sec(d*x + c))/sqrt(2*sec(d*x + c) - 3), x)","F",0
684,0,0,0,0.565283," ","integrate(sec(d*x+c)^(1/2)/(-3-2*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-2 \, \sec\left(d x + c\right) - 3} \sqrt{\sec\left(d x + c\right)}}{2 \, \sec\left(d x + c\right) + 3}, x\right)"," ",0,"integral(-sqrt(-2*sec(d*x + c) - 3)*sqrt(sec(d*x + c))/(2*sec(d*x + c) + 3), x)","F",0
685,0,0,0,0.505585," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right), x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(1/3)*sec(d*x + c), x)","F",0
686,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
687,0,0,0,0.701949," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^4, x)","F",0
688,0,0,0,0.656485," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^3, x)","F",0
689,0,0,0,0.750687," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)^2, x)","F",0
690,0,0,0,0.481572," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right), x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c), x)","F",0
691,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,0,0,0,1.014189," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c)^2 + a*sec(d*x + c))*(b*sec(d*x + c) + a)^(1/3), x)","F",0
693,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,0,0,0,1.164726," ","integrate(sec(d*x+c)^4*(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{5} + a \sec\left(d x + c\right)^{4}\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c)^5 + a*sec(d*x + c)^4)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
695,0,0,0,1.272079," ","integrate(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c)^4 + a*sec(d*x + c)^3)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
696,0,0,0,0.856171," ","integrate(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c)^3 + a*sec(d*x + c)^2)*(b*sec(d*x + c) + a)^(2/3), x)","F",0
697,0,0,0,1.114017," ","integrate(sec(d*x+c)*(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c)^2 + a*sec(d*x + c))*(b*sec(d*x + c) + a)^(2/3), x)","F",0
698,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,0,0,0,1.105702," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{4}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)^4/(b*sec(d*x + c) + a)^(1/3), x)","F",0
700,0,0,0,0.512080," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{3}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)^3/(b*sec(d*x + c) + a)^(1/3), x)","F",0
701,0,0,0,1.141632," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{2}}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)^2/(b*sec(d*x + c) + a)^(1/3), x)","F",0
702,0,0,0,0.580430," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)/(b*sec(d*x + c) + a)^(1/3), x)","F",0
703,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
704,0,0,0,0.509526," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)}{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral(sec(d*x + c)/(b*sec(d*x + c) + a)^(2/3), x)","F",0
705,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,0,0,0,1.016354," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{2}{3}} \sec\left(d x + c\right)}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(2/3)*sec(d*x + c)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
707,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,0,0,0,0.617618," ","integrate(sec(d*x+c)^4/(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{4}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^4/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
709,0,0,0,0.932505," ","integrate(sec(d*x+c)^3/(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{3}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^3/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
710,0,0,0,0.579741," ","integrate(sec(d*x+c)^2/(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)^{2}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(1/3)*sec(d*x + c)^2/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
711,0,0,0,0.524190," ","integrate(sec(d*x+c)/(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{1}{3}} \sec\left(d x + c\right)}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(1/3)*sec(d*x + c)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
712,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,-1,0,0,0.000000," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(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)^(1/3)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
715,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
716,-1,0,0,0.000000," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
717,0,0,0,0.914756," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(7/3), x)","F",0
718,0,0,0,2.474068," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/3), x)","F",0
719,0,0,0,0.959088," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{4}{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(4/3), x)","F",0
720,0,0,0,3.627475," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3), x)","F",0
721,0,0,0,1.445674," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3), x)","F",0
722,0,0,0,4.670045," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{1}{3}}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(1/3), x)","F",0
723,0,0,0,1.512576," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{2}{3}}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(2/3), x)","F",0
724,0,0,0,2.102794," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{4}{3}}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(4/3), x)","F",0
725,0,0,0,1.612559," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{3}}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/3), x)","F",0
726,0,0,0,1.956829," ","integrate((a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{3}}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/3), x)","F",0
727,0,0,0,0.771378," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c)^3 + a*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3), x)","F",0
728,0,0,0,0.776600," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c)^2 + a*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3), x)","F",0
729,0,0,0,0.727490," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c)^2 + a*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3), x)","F",0
730,0,0,0,2.147398," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(2/3), x)","F",0
731,0,0,0,1.606480," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)*sec(d*x + c)^(1/3), x)","F",0
732,0,0,0,2.676229," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{1}{3}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(1/3), x)","F",0
733,0,0,0,2.455868," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{2}{3}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(2/3), x)","F",0
734,0,0,0,3.210698," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{4}{3}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(4/3), x)","F",0
735,0,0,0,1.378649," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{5}{3}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(5/3), x)","F",0
736,0,0,0,2.262272," ","integrate((a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sec\left(d x + c\right)^{\frac{7}{3}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)/sec(d*x + c)^(7/3), x)","F",0
737,0,0,0,0.848237," ","integrate(sec(d*x+c)^(7/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3), x)","F",0
738,0,0,0,0.807855," ","integrate(sec(d*x+c)^(5/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{3} + 2 \, a b \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^3 + 2*a*b*sec(d*x + c)^2 + a^2*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3), x)","F",0
739,0,0,0,0.775809," ","integrate(sec(d*x+c)^(4/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{3} + 2 \, a b \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^3 + 2*a*b*sec(d*x + c)^2 + a^2*sec(d*x + c))*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3), x)","F",0
740,0,0,0,2.321571," ","integrate(sec(d*x+c)^(2/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3), x)","F",0
741,0,0,0,1.700879," ","integrate(sec(d*x+c)^(1/3)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3), x)","F",0
742,0,0,0,2.039935," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{1}{3}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(1/3), x)","F",0
743,0,0,0,1.757694," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{2}{3}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(2/3), x)","F",0
744,0,0,0,2.175961," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{4}{3}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(4/3), x)","F",0
745,0,0,0,1.283124," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{5}{3}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(5/3), x)","F",0
746,0,0,0,2.346697," ","integrate((a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a}}{\sec\left(d x + c\right)^{\frac{7}{3}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)/sec(d*x + c)^(7/3), x)","F",0
747,0,0,0,0.624731," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{7}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^(7/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
748,0,0,0,0.692134," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{5}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^(5/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
749,0,0,0,0.554609," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{4}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^(4/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
750,0,0,0,2.636211," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{2}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^(2/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
751,0,0,0,1.056592," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{\frac{1}{3}}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sec(d*x + c)^(1/3)/sqrt(b*sec(d*x + c) + a), x)","F",0
752,0,0,0,3.761304," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
753,0,0,0,2.595511," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}{b \sec\left(d x + c\right)^{2} + a \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)/(b*sec(d*x + c)^2 + a*sec(d*x + c)), x)","F",0
754,0,0,0,2.337567," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b*sec(d*x + c)^3 + a*sec(d*x + c)^2), x)","F",0
755,0,0,0,1.439035," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}{b \sec\left(d x + c\right)^{3} + a \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)/(b*sec(d*x + c)^3 + a*sec(d*x + c)^2), x)","F",0
756,0,0,0,2.077065," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b \sec\left(d x + c\right)^{4} + a \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b*sec(d*x + c)^4 + a*sec(d*x + c)^3), x)","F",0
757,0,0,0,0.725767," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{3}}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(7/3)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
758,0,0,0,1.217845," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{3}}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/3)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
759,0,0,0,0.717109," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{4}{3}}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(4/3)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
760,0,0,0,2.290003," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
761,0,0,0,1.986066," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
762,0,0,0,2.537791," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)^{3} + 2 \, a b \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b^2*sec(d*x + c)^3 + 2*a*b*sec(d*x + c)^2 + a^2*sec(d*x + c)), x)","F",0
763,0,0,0,1.561453," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}{b^{2} \sec\left(d x + c\right)^{3} + 2 \, a b \sec\left(d x + c\right)^{2} + a^{2} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)/(b^2*sec(d*x + c)^3 + 2*a*b*sec(d*x + c)^2 + a^2*sec(d*x + c)), x)","F",0
764,0,0,0,1.930505," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2), x)","F",0
765,0,0,0,1.824446," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}{b^{2} \sec\left(d x + c\right)^{4} + 2 \, a b \sec\left(d x + c\right)^{3} + a^{2} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)/(b^2*sec(d*x + c)^4 + 2*a*b*sec(d*x + c)^3 + a^2*sec(d*x + c)^2), x)","F",0
766,0,0,0,2.161980," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b^{2} \sec\left(d x + c\right)^{5} + 2 \, a b \sec\left(d x + c\right)^{4} + a^{2} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b^2*sec(d*x + c)^5 + 2*a*b*sec(d*x + c)^4 + a^2*sec(d*x + c)^3), x)","F",0
767,0,0,0,1.120604," ","integrate(sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{7}{3}}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(7/3)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
768,0,0,0,0.984246," ","integrate(sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{5}{3}}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(5/3)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
769,0,0,0,0.900682," ","integrate(sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{4}{3}}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(4/3)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
770,0,0,0,4.000497," ","integrate(sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
771,0,0,0,3.186087," ","integrate(sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
772,0,0,0,2.632766," ","integrate(1/sec(d*x+c)^(1/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b^{3} \sec\left(d x + c\right)^{4} + 3 \, a b^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{2} b \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b^3*sec(d*x + c)^4 + 3*a*b^2*sec(d*x + c)^3 + 3*a^2*b*sec(d*x + c)^2 + a^3*sec(d*x + c)), x)","F",0
773,0,0,0,2.887546," ","integrate(1/sec(d*x+c)^(2/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}{b^{3} \sec\left(d x + c\right)^{4} + 3 \, a b^{2} \sec\left(d x + c\right)^{3} + 3 \, a^{2} b \sec\left(d x + c\right)^{2} + a^{3} \sec\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)/(b^3*sec(d*x + c)^4 + 3*a*b^2*sec(d*x + c)^3 + 3*a^2*b*sec(d*x + c)^2 + a^3*sec(d*x + c)), x)","F",0
774,0,0,0,2.491648," ","integrate(1/sec(d*x+c)^(4/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b^{3} \sec\left(d x + c\right)^{5} + 3 \, a b^{2} \sec\left(d x + c\right)^{4} + 3 \, a^{2} b \sec\left(d x + c\right)^{3} + a^{3} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b^3*sec(d*x + c)^5 + 3*a*b^2*sec(d*x + c)^4 + 3*a^2*b*sec(d*x + c)^3 + a^3*sec(d*x + c)^2), x)","F",0
775,0,0,0,4.987290," ","integrate(1/sec(d*x+c)^(5/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{1}{3}}}{b^{3} \sec\left(d x + c\right)^{5} + 3 \, a b^{2} \sec\left(d x + c\right)^{4} + 3 \, a^{2} b \sec\left(d x + c\right)^{3} + a^{3} \sec\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(1/3)/(b^3*sec(d*x + c)^5 + 3*a*b^2*sec(d*x + c)^4 + 3*a^2*b*sec(d*x + c)^3 + a^3*sec(d*x + c)^2), x)","F",0
776,0,0,0,2.256028," ","integrate(1/sec(d*x+c)^(7/3)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sec\left(d x + c\right)^{\frac{2}{3}}}{b^{3} \sec\left(d x + c\right)^{6} + 3 \, a b^{2} \sec\left(d x + c\right)^{5} + 3 \, a^{2} b \sec\left(d x + c\right)^{4} + a^{3} \sec\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sec(d*x + c)^(2/3)/(b^3*sec(d*x + c)^6 + 3*a*b^2*sec(d*x + c)^5 + 3*a^2*b*sec(d*x + c)^4 + a^3*sec(d*x + c)^3), x)","F",0
777,0,0,0,0.661776," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \sec\left(f x + e\right)^{3} + 3 \, a b^{2} \sec\left(f x + e\right)^{2} + 3 \, a^{2} b \sec\left(f x + e\right) + a^{3}\right)} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^3*sec(f*x + e)^3 + 3*a*b^2*sec(f*x + e)^2 + 3*a^2*b*sec(f*x + e) + a^3)*(d*sec(f*x + e))^n, x)","F",0
778,0,0,0,0.497545," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}\right)} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2)*(d*sec(f*x + e))^n, x)","F",0
779,0,0,0,0.640568," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
780,0,0,0,0.714162," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{n}}{b \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*sec(f*x + e))^n/(b*sec(f*x + e) + a), x)","F",0
781,0,0,0,0.521901," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{n}}{b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*sec(f*x + e))^n/(b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2), x)","F",0
782,0,0,0,0.568101," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^(3/2)*(d*sec(f*x + e))^n, x)","F",0
783,0,0,0,0.588901," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e))^n, x)","F",0
784,0,0,0,0.820214," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{n}}{\sqrt{b \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((d*sec(f*x + e))^n/sqrt(b*sec(f*x + e) + a), x)","F",0
785,0,0,0,0.699813," ","integrate((d*sec(f*x+e))^n/(a+b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} \left(d \sec\left(f x + e\right)\right)^{n}}{b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e))^n/(b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2), x)","F",0
786,0,0,0,0.594927," ","integrate(sec(f*x+e)^n*(a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{n}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^m*sec(f*x + e)^n, x)","F",0
787,0,0,0,0.516710," ","integrate((d*sec(f*x+e))^n*(a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{m} \left(d \sec\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^m*(d*sec(f*x + e))^n, x)","F",0
788,0,0,0,0.667392," ","integrate(sec(f*x+e)^3*(a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^m*sec(f*x + e)^3, x)","F",0
789,0,0,0,0.687222," ","integrate(sec(f*x+e)^2*(a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^m*sec(f*x + e)^2, x)","F",0
790,0,0,0,0.576522," ","integrate(sec(f*x+e)*(a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right), x\right)"," ",0,"integral((b*sec(f*x + e) + a)^m*sec(f*x + e), x)","F",0
791,0,0,0,0.470846," ","integrate((a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^m, x)","F",0
792,0,0,0,0.569445," ","integrate(cos(f*x+e)*(a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right), x\right)"," ",0,"integral((b*sec(f*x + e) + a)^m*cos(f*x + e), x)","F",0
793,0,0,0,0.544491," ","integrate(cos(f*x+e)^2*(a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
794,0,0,0,0.504951," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c)^4*sec(d*x + c) + a*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
795,0,0,0,0.562239," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c)^3*sec(d*x + c) + a*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
796,0,0,0,0.530967," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + 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)^2*sec(d*x + c) + a*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
797,0,0,0,0.570419," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) \sec\left(d x + c\right) + a \cos\left(d x + c\right)\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c)*sec(d*x + c) + a*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
798,0,0,0,0.852104," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
799,0,0,0,0.447276," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x + c\right) + a}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)/sqrt(cos(d*x + c)), x)","F",0
800,0,0,0,0.477887," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)/cos(d*x + c)^(3/2), x)","F",0
801,0,0,0,0.565842," ","integrate((a+b*sec(d*x+c))/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sec\left(d x + c\right) + a}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)/cos(d*x + c)^(5/2), x)","F",0
802,0,0,0,0.522459," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^4*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^4*sec(d*x + c) + a^2*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
803,0,0,0,0.500482," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^3*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^3*sec(d*x + c) + a^2*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
804,0,0,0,0.499478," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + 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)^2*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^2*sec(d*x + c) + a^2*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
805,0,0,0,0.570489," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) \sec\left(d x + c\right) + 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)*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)*sec(d*x + c) + a^2*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
806,0,0,0,0.690901," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(cos(d*x + c)), x)","F",0
807,0,0,0,0.553655," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)/sqrt(cos(d*x + c)), x)","F",0
808,0,0,0,1.009246," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)/cos(d*x + c)^(3/2), x)","F",0
809,0,0,0,0.598775," ","integrate((a+b*sec(d*x+c))^2/cos(d*x+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}{\cos\left(d x + c\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)/cos(d*x + c)^(5/2), x)","F",0
810,0,0,0,0.967851," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{4}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^4*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^4*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)^4*sec(d*x + c) + a^3*cos(d*x + c)^4)*sqrt(cos(d*x + c)), x)","F",0
811,0,0,0,0.910064," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^3*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^3*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)^3*sec(d*x + c) + a^3*cos(d*x + c)^3)*sqrt(cos(d*x + c)), x)","F",0
812,0,0,0,0.484135," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{2}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*cos(d*x + c)^2*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)^2*sec(d*x + c) + a^3*cos(d*x + c)^2)*sqrt(cos(d*x + c)), x)","F",0
813,0,0,0,0.627147," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) \sec\left(d x + c\right) + 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)*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)*sec(d*x + c) + a^3*cos(d*x + c))*sqrt(cos(d*x + c)), x)","F",0
814,0,0,0,0.712008," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}\right)} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)*sqrt(cos(d*x + c)), x)","F",0
815,0,0,0,0.986211," ","integrate((a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}{\sqrt{\cos\left(d x + c\right)}}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)/sqrt(cos(d*x + c)), x)","F",0
816,0,0,0,0.460704," ","integrate((a+b*sec(d*x+c))^3/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}{\cos\left(d x + c\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral((b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3)/cos(d*x + c)^(3/2), x)","F",0
817,0,0,0,43.627233," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(cos(d*x + c)^(5/2)/(b*sec(d*x + c) + a), x)","F",0
818,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,0,0,0,83.106789," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{b \sec\left(d x + c\right) + a}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(b*sec(d*x + c) + a), x)","F",0
820,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
824,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
825,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
826,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
827,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
828,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,0,0,0,136.712727," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
832,-1,0,0,0.000000," ","integrate(1/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
833,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
834,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
835,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
836,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,0,0,0,1.454219," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2), x)","F",0
838,0,0,0,1.050767," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2), x)","F",0
839,0,0,0,0.777660," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
840,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,0,0,0,1.894476," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c)^3*sec(d*x + c) + a*cos(d*x + c)^3)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
843,0,0,0,2.346367," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c)^2*sec(d*x + c) + a*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
844,0,0,0,0.606076," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right) \sec\left(d x + c\right) + a \cos\left(d x + c\right)\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*cos(d*x + c)*sec(d*x + c) + a*cos(d*x + c))*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
845,0,0,0,2.608124," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b*sec(d*x + c) + a)^(3/2)*sqrt(cos(d*x + c)), x)","F",0
846,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,0,0,0,1.235153," ","integrate(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{4} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{4} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^4*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^4*sec(d*x + c) + a^2*cos(d*x + c)^4)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
849,0,0,0,1.561449," ","integrate(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{3}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^3*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^3*sec(d*x + c) + a^2*cos(d*x + c)^3)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
850,0,0,0,0.952779," ","integrate(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*cos(d*x + c)^2*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^2*sec(d*x + c) + a^2*cos(d*x + c)^2)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
851,-1,0,0,0.000000," ","integrate(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,0,0,0,2.867349," ","integrate(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}\right)} \sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}, x\right)"," ",0,"integral((b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2)*sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c)), x)","F",0
853,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,0,0,0,0.926272," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^(5/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
856,0,0,0,0.874921," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^(3/2)/sqrt(b*sec(d*x + c) + a), x)","F",0
857,0,0,0,1.234010," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{\cos\left(d x + c\right)}}{\sqrt{b \sec\left(d x + c\right) + a}}, x\right)"," ",0,"integral(sqrt(cos(d*x + c))/sqrt(b*sec(d*x + c) + a), x)","F",0
858,0,0,0,0.700448," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b \cos\left(d x + c\right) \sec\left(d x + c\right) + a \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b*cos(d*x + c)*sec(d*x + c) + a*cos(d*x + c)), x)","F",0
859,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,0,0,0,1.384168," ","integrate(cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{5}{2}}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(5/2)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
863,0,0,0,1.073663," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
864,0,0,0,1.015279," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \sec\left(d x + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*sec(d*x + c)^2 + 2*a*b*sec(d*x + c) + a^2), x)","F",0
865,0,0,0,0.927527," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)*sec(d*x + c) + a^2*cos(d*x + c)), x)","F",0
866,0,0,0,0.983930," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 2 \, a b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{2} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^2*cos(d*x + c)^2*sec(d*x + c)^2 + 2*a*b*cos(d*x + c)^2*sec(d*x + c) + a^2*cos(d*x + c)^2), x)","F",0
867,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
869,0,0,0,1.221374," ","integrate(cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \cos\left(d x + c\right)^{\frac{3}{2}}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*cos(d*x + c)^(3/2)/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
870,0,0,0,1.161482," ","integrate(cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \sec\left(d x + c\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*sec(d*x + c)^3 + 3*a*b^2*sec(d*x + c)^2 + 3*a^2*b*sec(d*x + c) + a^3), x)","F",0
871,0,0,0,1.346187," ","integrate(1/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right) \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right) \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right) \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)*sec(d*x + c) + a^3*cos(d*x + c)), x)","F",0
872,0,0,0,1.220891," ","integrate(1/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{2} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right)^{2} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{2}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^2*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^2*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)^2*sec(d*x + c) + a^3*cos(d*x + c)^2), x)","F",0
873,0,0,0,1.389910," ","integrate(1/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(d x + c\right) + a} \sqrt{\cos\left(d x + c\right)}}{b^{3} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right)^{3} \sec\left(d x + c\right)^{2} + 3 \, a^{2} b \cos\left(d x + c\right)^{3} \sec\left(d x + c\right) + a^{3} \cos\left(d x + c\right)^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(d*x + c) + a)*sqrt(cos(d*x + c))/(b^3*cos(d*x + c)^3*sec(d*x + c)^3 + 3*a*b^2*cos(d*x + c)^3*sec(d*x + c)^2 + 3*a^2*b*cos(d*x + c)^3*sec(d*x + c) + a^3*cos(d*x + c)^3), x)","F",0
874,-1,0,0,0.000000," ","integrate(1/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
875,0,0,0,0.449256," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \sec\left(f x + e\right)^{3} + 3 \, a b^{2} \sec\left(f x + e\right)^{2} + 3 \, a^{2} b \sec\left(f x + e\right) + a^{3}\right)} \left(d \cos\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^3*sec(f*x + e)^3 + 3*a*b^2*sec(f*x + e)^2 + 3*a^2*b*sec(f*x + e) + a^3)*(d*cos(f*x + e))^n, x)","F",0
876,0,0,0,2.007951," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}\right)} \left(d \cos\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2)*(d*cos(f*x + e))^n, x)","F",0
877,0,0,0,1.113384," ","integrate((d*cos(f*x+e))^n*(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)*(d*cos(f*x + e))^n, x)","F",0
878,0,0,0,0.436671," ","integrate((d*cos(f*x+e))^n/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \cos\left(f x + e\right)\right)^{n}}{b \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*cos(f*x + e))^n/(b*sec(f*x + e) + a), x)","F",0
879,0,0,0,0.681476," ","integrate((d*cos(f*x+e))^n/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \cos\left(f x + e\right)\right)^{n}}{b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*cos(f*x + e))^n/(b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2), x)","F",0
