1,1,189,0,0.577880," ","integrate(sec(d*x+c)^10*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{64512 i \, a e^{\left(10 i \, d x + 10 i \, c\right)} + 53760 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 30720 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 11520 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 2560 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 256 i \, a}{315 \, {\left(d e^{\left(20 i \, d x + 20 i \, c\right)} + 10 \, d e^{\left(18 i \, d x + 18 i \, c\right)} + 45 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 120 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 210 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 252 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 210 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 120 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 45 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 10 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/315*(64512*I*a*e^(10*I*d*x + 10*I*c) + 53760*I*a*e^(8*I*d*x + 8*I*c) + 30720*I*a*e^(6*I*d*x + 6*I*c) + 11520*I*a*e^(4*I*d*x + 4*I*c) + 2560*I*a*e^(2*I*d*x + 2*I*c) + 256*I*a)/(d*e^(20*I*d*x + 20*I*c) + 10*d*e^(18*I*d*x + 18*I*c) + 45*d*e^(16*I*d*x + 16*I*c) + 120*d*e^(14*I*d*x + 14*I*c) + 210*d*e^(12*I*d*x + 12*I*c) + 252*d*e^(10*I*d*x + 10*I*c) + 210*d*e^(8*I*d*x + 8*I*c) + 120*d*e^(6*I*d*x + 6*I*c) + 45*d*e^(4*I*d*x + 4*I*c) + 10*d*e^(2*I*d*x + 2*I*c) + d)","B",0
2,1,153,0,0.691346," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2240 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 1792 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 896 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 256 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i \, a}{35 \, {\left(d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/35*(2240*I*a*e^(8*I*d*x + 8*I*c) + 1792*I*a*e^(6*I*d*x + 6*I*c) + 896*I*a*e^(4*I*d*x + 4*I*c) + 256*I*a*e^(2*I*d*x + 2*I*c) + 32*I*a)/(d*e^(16*I*d*x + 16*I*c) + 8*d*e^(14*I*d*x + 14*I*c) + 28*d*e^(12*I*d*x + 12*I*c) + 56*d*e^(10*I*d*x + 10*I*c) + 70*d*e^(8*I*d*x + 8*I*c) + 56*d*e^(6*I*d*x + 6*I*c) + 28*d*e^(4*I*d*x + 4*I*c) + 8*d*e^(2*I*d*x + 2*I*c) + d)","B",0
3,1,117,0,0.480415," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{320 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 240 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 96 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, a}{15 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/15*(320*I*a*e^(6*I*d*x + 6*I*c) + 240*I*a*e^(4*I*d*x + 4*I*c) + 96*I*a*e^(2*I*d*x + 2*I*c) + 16*I*a)/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","B",0
4,1,81,0,0.431964," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{24 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(24*I*a*e^(4*I*d*x + 4*I*c) + 16*I*a*e^(2*I*d*x + 2*I*c) + 4*I*a)/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
5,1,44,0,0.396732," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(4*I*a*e^(2*I*d*x + 2*I*c) + 2*I*a)/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
6,1,18,0,0.630713," ","integrate(a+I*a*tan(d*x+c),x, algorithm=""fricas"")","-\frac{i \, a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d}"," ",0,"-I*a*log(e^(2*I*d*x + 2*I*c) + 1)/d","A",0
7,1,23,0,0.673205," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d x - i \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{4 \, d}"," ",0,"1/4*(2*a*d*x - I*a*e^(2*I*d*x + 2*I*c))/d","A",0
8,1,56,0,0.479580," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(12 \, a d x e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 6 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 2 i \, a\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{32 \, d}"," ",0,"1/32*(12*a*d*x*e^(2*I*d*x + 2*I*c) - I*a*e^(6*I*d*x + 6*I*c) - 6*I*a*e^(4*I*d*x + 4*I*c) + 2*I*a)*e^(-2*I*d*x - 2*I*c)/d","A",0
9,1,80,0,0.482398," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(120 \, a d x e^{\left(4 i \, d x + 4 i \, c\right)} - 2 i \, a e^{\left(10 i \, d x + 10 i \, c\right)} - 15 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} - 60 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 30 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, a\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{384 \, d}"," ",0,"1/384*(120*a*d*x*e^(4*I*d*x + 4*I*c) - 2*I*a*e^(10*I*d*x + 10*I*c) - 15*I*a*e^(8*I*d*x + 8*I*c) - 60*I*a*e^(6*I*d*x + 6*I*c) + 30*I*a*e^(2*I*d*x + 2*I*c) + 3*I*a)*e^(-4*I*d*x - 4*I*c)/d","A",0
10,1,104,0,0.538327," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(840 \, a d x e^{\left(6 i \, d x + 6 i \, c\right)} - 3 i \, a e^{\left(14 i \, d x + 14 i \, c\right)} - 28 i \, a e^{\left(12 i \, d x + 12 i \, c\right)} - 126 i \, a e^{\left(10 i \, d x + 10 i \, c\right)} - 420 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 252 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 42 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{3072 \, d}"," ",0,"1/3072*(840*a*d*x*e^(6*I*d*x + 6*I*c) - 3*I*a*e^(14*I*d*x + 14*I*c) - 28*I*a*e^(12*I*d*x + 12*I*c) - 126*I*a*e^(10*I*d*x + 10*I*c) - 420*I*a*e^(8*I*d*x + 8*I*c) + 252*I*a*e^(4*I*d*x + 4*I*c) + 42*I*a*e^(2*I*d*x + 2*I*c) + 4*I*a)*e^(-6*I*d*x - 6*I*c)/d","A",0
11,1,372,0,0.541395," ","integrate(sec(d*x+c)^7*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-210 i \, a e^{\left(13 i \, d x + 13 i \, c\right)} - 1400 i \, a e^{\left(11 i \, d x + 11 i \, c\right)} - 3962 i \, a e^{\left(9 i \, d x + 9 i \, c\right)} + 6144 i \, a e^{\left(7 i \, d x + 7 i \, c\right)} + 3962 i \, a e^{\left(5 i \, d x + 5 i \, c\right)} + 1400 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 210 i \, a e^{\left(i \, d x + i \, c\right)} + 105 \, {\left(a e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, a e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, a e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, {\left(a e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, a e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, a e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{336 \, {\left(d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/336*(-210*I*a*e^(13*I*d*x + 13*I*c) - 1400*I*a*e^(11*I*d*x + 11*I*c) - 3962*I*a*e^(9*I*d*x + 9*I*c) + 6144*I*a*e^(7*I*d*x + 7*I*c) + 3962*I*a*e^(5*I*d*x + 5*I*c) + 1400*I*a*e^(3*I*d*x + 3*I*c) + 210*I*a*e^(I*d*x + I*c) + 105*(a*e^(14*I*d*x + 14*I*c) + 7*a*e^(12*I*d*x + 12*I*c) + 21*a*e^(10*I*d*x + 10*I*c) + 35*a*e^(8*I*d*x + 8*I*c) + 35*a*e^(6*I*d*x + 6*I*c) + 21*a*e^(4*I*d*x + 4*I*c) + 7*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(I*d*x + I*c) + I) - 105*(a*e^(14*I*d*x + 14*I*c) + 7*a*e^(12*I*d*x + 12*I*c) + 21*a*e^(10*I*d*x + 10*I*c) + 35*a*e^(8*I*d*x + 8*I*c) + 35*a*e^(6*I*d*x + 6*I*c) + 21*a*e^(4*I*d*x + 4*I*c) + 7*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(I*d*x + I*c) - I))/(d*e^(14*I*d*x + 14*I*c) + 7*d*e^(12*I*d*x + 12*I*c) + 21*d*e^(10*I*d*x + 10*I*c) + 35*d*e^(8*I*d*x + 8*I*c) + 35*d*e^(6*I*d*x + 6*I*c) + 21*d*e^(4*I*d*x + 4*I*c) + 7*d*e^(2*I*d*x + 2*I*c) + d)","B",0
12,1,276,0,0.449039," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-30 i \, a e^{\left(9 i \, d x + 9 i \, c\right)} - 140 i \, a e^{\left(7 i \, d x + 7 i \, c\right)} + 256 i \, a e^{\left(5 i \, d x + 5 i \, c\right)} + 140 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 30 i \, a e^{\left(i \, d x + i \, c\right)} + 15 \, {\left(a e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(a e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{40 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/40*(-30*I*a*e^(9*I*d*x + 9*I*c) - 140*I*a*e^(7*I*d*x + 7*I*c) + 256*I*a*e^(5*I*d*x + 5*I*c) + 140*I*a*e^(3*I*d*x + 3*I*c) + 30*I*a*e^(I*d*x + I*c) + 15*(a*e^(10*I*d*x + 10*I*c) + 5*a*e^(8*I*d*x + 8*I*c) + 10*a*e^(6*I*d*x + 6*I*c) + 10*a*e^(4*I*d*x + 4*I*c) + 5*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(I*d*x + I*c) + I) - 15*(a*e^(10*I*d*x + 10*I*c) + 5*a*e^(8*I*d*x + 8*I*c) + 10*a*e^(6*I*d*x + 6*I*c) + 10*a*e^(4*I*d*x + 4*I*c) + 5*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(I*d*x + I*c) - I))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
13,1,180,0,0.593143," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-6 i \, a e^{\left(5 i \, d x + 5 i \, c\right)} + 16 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 6 i \, a e^{\left(i \, d x + i \, c\right)} + 3 \, {\left(a e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, {\left(a e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{6 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/6*(-6*I*a*e^(5*I*d*x + 5*I*c) + 16*I*a*e^(3*I*d*x + 3*I*c) + 6*I*a*e^(I*d*x + I*c) + 3*(a*e^(6*I*d*x + 6*I*c) + 3*a*e^(4*I*d*x + 4*I*c) + 3*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(I*d*x + I*c) + I) - 3*(a*e^(6*I*d*x + 6*I*c) + 3*a*e^(4*I*d*x + 4*I*c) + 3*a*e^(2*I*d*x + 2*I*c) + a)*log(e^(I*d*x + I*c) - I))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
14,1,82,0,0.505987," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 i \, a e^{\left(i \, d x + i \, c\right)} + {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(2*I*a*e^(I*d*x + I*c) + (a*e^(2*I*d*x + 2*I*c) + a)*log(e^(I*d*x + I*c) + I) - (a*e^(2*I*d*x + 2*I*c) + a)*log(e^(I*d*x + I*c) - I))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
15,1,15,0,0.708520," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{i \, a e^{\left(i \, d x + i \, c\right)}}{d}"," ",0,"-I*a*e^(I*d*x + I*c)/d","A",0
16,1,42,0,0.406886," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 6 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, a\right)} e^{\left(-i \, d x - i \, c\right)}}{12 \, d}"," ",0,"1/12*(-I*a*e^(4*I*d*x + 4*I*c) - 6*I*a*e^(2*I*d*x + 2*I*c) + 3*I*a)*e^(-I*d*x - I*c)/d","A",0
17,1,66,0,0.473828," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-3 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} - 20 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 90 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 60 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, a\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{240 \, d}"," ",0,"1/240*(-3*I*a*e^(8*I*d*x + 8*I*c) - 20*I*a*e^(6*I*d*x + 6*I*c) - 90*I*a*e^(4*I*d*x + 4*I*c) + 60*I*a*e^(2*I*d*x + 2*I*c) + 5*I*a)*e^(-3*I*d*x - 3*I*c)/d","A",0
18,1,90,0,0.599087," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-5 i \, a e^{\left(12 i \, d x + 12 i \, c\right)} - 42 i \, a e^{\left(10 i \, d x + 10 i \, c\right)} - 175 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} - 700 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 525 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 70 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, a\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{2240 \, d}"," ",0,"1/2240*(-5*I*a*e^(12*I*d*x + 12*I*c) - 42*I*a*e^(10*I*d*x + 10*I*c) - 175*I*a*e^(8*I*d*x + 8*I*c) - 700*I*a*e^(6*I*d*x + 6*I*c) + 525*I*a*e^(4*I*d*x + 4*I*c) + 70*I*a*e^(2*I*d*x + 2*I*c) + 7*I*a)*e^(-5*I*d*x - 5*I*c)/d","A",0
19,1,189,0,0.486417," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{8064 i \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} + 8064 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 5376 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 2304 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 576 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 64 i \, a^{2}}{63 \, {\left(d e^{\left(18 i \, d x + 18 i \, c\right)} + 9 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 36 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 84 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 126 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 126 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 84 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 36 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 9 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/63*(8064*I*a^2*e^(10*I*d*x + 10*I*c) + 8064*I*a^2*e^(8*I*d*x + 8*I*c) + 5376*I*a^2*e^(6*I*d*x + 6*I*c) + 2304*I*a^2*e^(4*I*d*x + 4*I*c) + 576*I*a^2*e^(2*I*d*x + 2*I*c) + 64*I*a^2)/(d*e^(18*I*d*x + 18*I*c) + 9*d*e^(16*I*d*x + 16*I*c) + 36*d*e^(14*I*d*x + 14*I*c) + 84*d*e^(12*I*d*x + 12*I*c) + 126*d*e^(10*I*d*x + 10*I*c) + 126*d*e^(8*I*d*x + 8*I*c) + 84*d*e^(6*I*d*x + 6*I*c) + 36*d*e^(4*I*d*x + 4*I*c) + 9*d*e^(2*I*d*x + 2*I*c) + d)","B",0
20,1,151,0,0.574140," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4480 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 4480 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 2688 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 896 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i \, a^{2}}{105 \, {\left(d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/105*(4480*I*a^2*e^(8*I*d*x + 8*I*c) + 4480*I*a^2*e^(6*I*d*x + 6*I*c) + 2688*I*a^2*e^(4*I*d*x + 4*I*c) + 896*I*a^2*e^(2*I*d*x + 2*I*c) + 128*I*a^2)/(d*e^(14*I*d*x + 14*I*c) + 7*d*e^(12*I*d*x + 12*I*c) + 21*d*e^(10*I*d*x + 10*I*c) + 35*d*e^(8*I*d*x + 8*I*c) + 35*d*e^(6*I*d*x + 6*I*c) + 21*d*e^(4*I*d*x + 4*I*c) + 7*d*e^(2*I*d*x + 2*I*c) + d)","B",0
21,1,113,0,0.513680," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{80 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 80 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 40 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{2}}{5 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/5*(80*I*a^2*e^(6*I*d*x + 6*I*c) + 80*I*a^2*e^(4*I*d*x + 4*I*c) + 40*I*a^2*e^(2*I*d*x + 2*I*c) + 8*I*a^2)/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
22,1,75,0,0.516647," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{24 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 24 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{2}}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(24*I*a^2*e^(4*I*d*x + 4*I*c) + 24*I*a^2*e^(2*I*d*x + 2*I*c) + 8*I*a^2)/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
23,1,55,0,0.640436," ","integrate((a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-2 i \, a^{2} + {\left(-2 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{2}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(-2*I*a^2 + (-2*I*a^2*e^(2*I*d*x + 2*I*c) - 2*I*a^2)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
24,1,17,0,0.618418," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)}}{2 \, d}"," ",0,"-1/2*I*a^2*e^(2*I*d*x + 2*I*c)/d","A",0
25,1,41,0,0.407325," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} d x - i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)}}{16 \, d}"," ",0,"1/16*(4*a^2*d*x - I*a^2*e^(4*I*d*x + 4*I*c) - 4*I*a^2*e^(2*I*d*x + 2*I*c))/d","A",0
26,1,78,0,0.615479," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(24 \, a^{2} d x e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 6 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 18 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, a^{2}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{96 \, d}"," ",0,"1/96*(24*a^2*d*x*e^(2*I*d*x + 2*I*c) - I*a^2*e^(8*I*d*x + 8*I*c) - 6*I*a^2*e^(6*I*d*x + 6*I*c) - 18*I*a^2*e^(4*I*d*x + 4*I*c) + 3*I*a^2)*e^(-2*I*d*x - 2*I*c)/d","A",0
27,1,106,0,0.561172," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(120 \, a^{2} d x e^{\left(4 i \, d x + 4 i \, c\right)} - i \, a^{2} e^{\left(12 i \, d x + 12 i \, c\right)} - 8 i \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} - 30 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 80 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 24 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a^{2}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{512 \, d}"," ",0,"1/512*(120*a^2*d*x*e^(4*I*d*x + 4*I*c) - I*a^2*e^(12*I*d*x + 12*I*c) - 8*I*a^2*e^(10*I*d*x + 10*I*c) - 30*I*a^2*e^(8*I*d*x + 8*I*c) - 80*I*a^2*e^(6*I*d*x + 6*I*c) + 24*I*a^2*e^(2*I*d*x + 2*I*c) + 2*I*a^2)*e^(-4*I*d*x - 4*I*c)/d","A",0
28,1,364,0,0.473573," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-210 i \, a^{2} e^{\left(11 i \, d x + 11 i \, c\right)} - 1190 i \, a^{2} e^{\left(9 i \, d x + 9 i \, c\right)} + 3372 i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + 2772 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 1190 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 210 i \, a^{2} e^{\left(i \, d x + i \, c\right)} + 105 \, {\left(a^{2} e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, {\left(a^{2} e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{240 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/240*(-210*I*a^2*e^(11*I*d*x + 11*I*c) - 1190*I*a^2*e^(9*I*d*x + 9*I*c) + 3372*I*a^2*e^(7*I*d*x + 7*I*c) + 2772*I*a^2*e^(5*I*d*x + 5*I*c) + 1190*I*a^2*e^(3*I*d*x + 3*I*c) + 210*I*a^2*e^(I*d*x + I*c) + 105*(a^2*e^(12*I*d*x + 12*I*c) + 6*a^2*e^(10*I*d*x + 10*I*c) + 15*a^2*e^(8*I*d*x + 8*I*c) + 20*a^2*e^(6*I*d*x + 6*I*c) + 15*a^2*e^(4*I*d*x + 4*I*c) + 6*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(I*d*x + I*c) + I) - 105*(a^2*e^(12*I*d*x + 12*I*c) + 6*a^2*e^(10*I*d*x + 10*I*c) + 15*a^2*e^(8*I*d*x + 8*I*c) + 20*a^2*e^(6*I*d*x + 6*I*c) + 15*a^2*e^(4*I*d*x + 4*I*c) + 6*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(I*d*x + I*c) - I))/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","B",0
29,1,256,0,0.653568," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-30 i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + 146 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 110 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 30 i \, a^{2} e^{\left(i \, d x + i \, c\right)} + 15 \, {\left(a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{24 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/24*(-30*I*a^2*e^(7*I*d*x + 7*I*c) + 146*I*a^2*e^(5*I*d*x + 5*I*c) + 110*I*a^2*e^(3*I*d*x + 3*I*c) + 30*I*a^2*e^(I*d*x + I*c) + 15*(a^2*e^(8*I*d*x + 8*I*c) + 4*a^2*e^(6*I*d*x + 6*I*c) + 6*a^2*e^(4*I*d*x + 4*I*c) + 4*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(I*d*x + I*c) + I) - 15*(a^2*e^(8*I*d*x + 8*I*c) + 4*a^2*e^(6*I*d*x + 6*I*c) + 6*a^2*e^(4*I*d*x + 4*I*c) + 4*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(I*d*x + I*c) - I))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
30,1,148,0,0.444431," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{10 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 6 i \, a^{2} e^{\left(i \, d x + i \, c\right)} + 3 \, {\left(a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, {\left(a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{2 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/2*(10*I*a^2*e^(3*I*d*x + 3*I*c) + 6*I*a^2*e^(I*d*x + I*c) + 3*(a^2*e^(4*I*d*x + 4*I*c) + 2*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(I*d*x + I*c) + I) - 3*(a^2*e^(4*I*d*x + 4*I*c) + 2*a^2*e^(2*I*d*x + 2*I*c) + a^2)*log(e^(I*d*x + I*c) - I))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
31,1,52,0,0.525662," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-2 i \, a^{2} e^{\left(i \, d x + i \, c\right)} - a^{2} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) + a^{2} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{d}"," ",0,"(-2*I*a^2*e^(I*d*x + I*c) - a^2*log(e^(I*d*x + I*c) + I) + a^2*log(e^(I*d*x + I*c) - I))/d","A",0
32,1,34,0,0.476362," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{-i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 3 i \, a^{2} e^{\left(i \, d x + i \, c\right)}}{6 \, d}"," ",0,"1/6*(-I*a^2*e^(3*I*d*x + 3*I*c) - 3*I*a^2*e^(I*d*x + I*c))/d","A",0
33,1,62,0,0.579600," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 5 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 15 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, a^{2}\right)} e^{\left(-i \, d x - i \, c\right)}}{40 \, d}"," ",0,"1/40*(-I*a^2*e^(6*I*d*x + 6*I*c) - 5*I*a^2*e^(4*I*d*x + 4*I*c) - 15*I*a^2*e^(2*I*d*x + 2*I*c) + 5*I*a^2)*e^(-I*d*x - I*c)/d","A",0
34,1,90,0,0.691059," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-3 i \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} - 21 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 70 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 210 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 105 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, a^{2}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{672 \, d}"," ",0,"1/672*(-3*I*a^2*e^(10*I*d*x + 10*I*c) - 21*I*a^2*e^(8*I*d*x + 8*I*c) - 70*I*a^2*e^(6*I*d*x + 6*I*c) - 210*I*a^2*e^(4*I*d*x + 4*I*c) + 105*I*a^2*e^(2*I*d*x + 2*I*c) + 7*I*a^2)*e^(-3*I*d*x - 3*I*c)/d","A",0
35,1,118,0,0.604203," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-5 i \, a^{2} e^{\left(14 i \, d x + 14 i \, c\right)} - 45 i \, a^{2} e^{\left(12 i \, d x + 12 i \, c\right)} - 189 i \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} - 525 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 1575 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 945 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 105 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 9 i \, a^{2}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{5760 \, d}"," ",0,"1/5760*(-5*I*a^2*e^(14*I*d*x + 14*I*c) - 45*I*a^2*e^(12*I*d*x + 12*I*c) - 189*I*a^2*e^(10*I*d*x + 10*I*c) - 525*I*a^2*e^(8*I*d*x + 8*I*c) - 1575*I*a^2*e^(6*I*d*x + 6*I*c) + 945*I*a^2*e^(4*I*d*x + 4*I*c) + 105*I*a^2*e^(2*I*d*x + 2*I*c) + 9*I*a^2)*e^(-5*I*d*x - 5*I*c)/d","A",0
36,1,215,0,0.524535," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{26880 i \, a^{3} e^{\left(12 i \, d x + 12 i \, c\right)} + 32256 i \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} + 26880 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 15360 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 5760 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 1280 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i \, a^{3}}{105 \, {\left(d e^{\left(20 i \, d x + 20 i \, c\right)} + 10 \, d e^{\left(18 i \, d x + 18 i \, c\right)} + 45 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 120 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 210 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 252 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 210 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 120 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 45 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 10 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/105*(26880*I*a^3*e^(12*I*d*x + 12*I*c) + 32256*I*a^3*e^(10*I*d*x + 10*I*c) + 26880*I*a^3*e^(8*I*d*x + 8*I*c) + 15360*I*a^3*e^(6*I*d*x + 6*I*c) + 5760*I*a^3*e^(4*I*d*x + 4*I*c) + 1280*I*a^3*e^(2*I*d*x + 2*I*c) + 128*I*a^3)/(d*e^(20*I*d*x + 20*I*c) + 10*d*e^(18*I*d*x + 18*I*c) + 45*d*e^(16*I*d*x + 16*I*c) + 120*d*e^(14*I*d*x + 14*I*c) + 210*d*e^(12*I*d*x + 12*I*c) + 252*d*e^(10*I*d*x + 10*I*c) + 210*d*e^(8*I*d*x + 8*I*c) + 120*d*e^(6*I*d*x + 6*I*c) + 45*d*e^(4*I*d*x + 4*I*c) + 10*d*e^(2*I*d*x + 2*I*c) + d)","B",0
37,1,177,0,0.401520," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{1792 i \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} + 2240 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 1792 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 896 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 256 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i \, a^{3}}{21 \, {\left(d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/21*(1792*I*a^3*e^(10*I*d*x + 10*I*c) + 2240*I*a^3*e^(8*I*d*x + 8*I*c) + 1792*I*a^3*e^(6*I*d*x + 6*I*c) + 896*I*a^3*e^(4*I*d*x + 4*I*c) + 256*I*a^3*e^(2*I*d*x + 2*I*c) + 32*I*a^3)/(d*e^(16*I*d*x + 16*I*c) + 8*d*e^(14*I*d*x + 14*I*c) + 28*d*e^(12*I*d*x + 12*I*c) + 56*d*e^(10*I*d*x + 10*I*c) + 70*d*e^(8*I*d*x + 8*I*c) + 56*d*e^(6*I*d*x + 6*I*c) + 28*d*e^(4*I*d*x + 4*I*c) + 8*d*e^(2*I*d*x + 2*I*c) + d)","B",0
38,1,139,0,0.585727," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{480 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 640 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 480 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 192 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i \, a^{3}}{15 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/15*(480*I*a^3*e^(8*I*d*x + 8*I*c) + 640*I*a^3*e^(6*I*d*x + 6*I*c) + 480*I*a^3*e^(4*I*d*x + 4*I*c) + 192*I*a^3*e^(2*I*d*x + 2*I*c) + 32*I*a^3)/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","B",0
39,1,100,0,0.453158," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{16 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 24 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a^{3}}{d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(16*I*a^3*e^(6*I*d*x + 6*I*c) + 24*I*a^3*e^(4*I*d*x + 4*I*c) + 16*I*a^3*e^(2*I*d*x + 2*I*c) + 4*I*a^3)/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
40,1,95,0,0.536575," ","integrate((a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, a^{3} + {\left(-4 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{3}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(-8*I*a^3*e^(2*I*d*x + 2*I*c) - 6*I*a^3 + (-4*I*a^3*e^(4*I*d*x + 4*I*c) - 8*I*a^3*e^(2*I*d*x + 2*I*c) - 4*I*a^3)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
41,1,36,0,0.628287," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, a^{3} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d}"," ",0,"(-I*a^3*e^(2*I*d*x + 2*I*c) + I*a^3*log(e^(2*I*d*x + 2*I*c) + 1))/d","A",0
42,1,34,0,0.483289," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)}}{8 \, d}"," ",0,"1/8*(-I*a^3*e^(4*I*d*x + 4*I*c) - 2*I*a^3*e^(2*I*d*x + 2*I*c))/d","A",0
43,1,55,0,0.553285," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{12 \, a^{3} d x - 2 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 9 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 18 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)}}{96 \, d}"," ",0,"1/96*(12*a^3*d*x - 2*I*a^3*e^(6*I*d*x + 6*I*c) - 9*I*a^3*e^(4*I*d*x + 4*I*c) - 18*I*a^3*e^(2*I*d*x + 2*I*c))/d","A",0
44,1,92,0,0.588050," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(120 \, a^{3} d x e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} - 20 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 60 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 120 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 12 i \, a^{3}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{768 \, d}"," ",0,"1/768*(120*a^3*d*x*e^(2*I*d*x + 2*I*c) - 3*I*a^3*e^(10*I*d*x + 10*I*c) - 20*I*a^3*e^(8*I*d*x + 8*I*c) - 60*I*a^3*e^(6*I*d*x + 6*I*c) - 120*I*a^3*e^(4*I*d*x + 4*I*c) + 12*I*a^3)*e^(-2*I*d*x - 2*I*c)/d","A",0
45,1,310,0,0.608840," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-210 i \, a^{3} e^{\left(9 i \, d x + 9 i \, c\right)} + 1580 i \, a^{3} e^{\left(7 i \, d x + 7 i \, c\right)} + 1792 i \, a^{3} e^{\left(5 i \, d x + 5 i \, c\right)} + 980 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} + 210 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + 105 \, {\left(a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, {\left(a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{120 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/120*(-210*I*a^3*e^(9*I*d*x + 9*I*c) + 1580*I*a^3*e^(7*I*d*x + 7*I*c) + 1792*I*a^3*e^(5*I*d*x + 5*I*c) + 980*I*a^3*e^(3*I*d*x + 3*I*c) + 210*I*a^3*e^(I*d*x + I*c) + 105*(a^3*e^(10*I*d*x + 10*I*c) + 5*a^3*e^(8*I*d*x + 8*I*c) + 10*a^3*e^(6*I*d*x + 6*I*c) + 10*a^3*e^(4*I*d*x + 4*I*c) + 5*a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(I*d*x + I*c) + I) - 105*(a^3*e^(10*I*d*x + 10*I*c) + 5*a^3*e^(8*I*d*x + 8*I*c) + 10*a^3*e^(6*I*d*x + 6*I*c) + 10*a^3*e^(4*I*d*x + 4*I*c) + 5*a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(I*d*x + I*c) - I))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
46,1,202,0,0.540941," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{66 i \, a^{3} e^{\left(5 i \, d x + 5 i \, c\right)} + 80 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} + 30 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + 15 \, {\left(a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{6 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/6*(66*I*a^3*e^(5*I*d*x + 5*I*c) + 80*I*a^3*e^(3*I*d*x + 3*I*c) + 30*I*a^3*e^(I*d*x + I*c) + 15*(a^3*e^(6*I*d*x + 6*I*c) + 3*a^3*e^(4*I*d*x + 4*I*c) + 3*a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(I*d*x + I*c) + I) - 15*(a^3*e^(6*I*d*x + 6*I*c) + 3*a^3*e^(4*I*d*x + 4*I*c) + 3*a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(I*d*x + I*c) - I))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
47,1,107,0,0.554708," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-4 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 6 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - 3 \, {\left(a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) + 3 \, {\left(a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(-4*I*a^3*e^(3*I*d*x + 3*I*c) - 6*I*a^3*e^(I*d*x + I*c) - 3*(a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(I*d*x + I*c) + I) + 3*(a^3*e^(2*I*d*x + 2*I*c) + a^3)*log(e^(I*d*x + I*c) - I))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
48,1,17,0,0.459995," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)}}{3 \, d}"," ",0,"-1/3*I*a^3*e^(3*I*d*x + 3*I*c)/d","A",0
49,1,48,0,0.435570," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{-3 i \, a^{3} e^{\left(5 i \, d x + 5 i \, c\right)} - 10 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 15 i \, a^{3} e^{\left(i \, d x + i \, c\right)}}{60 \, d}"," ",0,"1/60*(-3*I*a^3*e^(5*I*d*x + 5*I*c) - 10*I*a^3*e^(3*I*d*x + 3*I*c) - 15*I*a^3*e^(I*d*x + I*c))/d","A",0
50,1,76,0,0.789150," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-5 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 28 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 70 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 140 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 35 i \, a^{3}\right)} e^{\left(-i \, d x - i \, c\right)}}{560 \, d}"," ",0,"1/560*(-5*I*a^3*e^(8*I*d*x + 8*I*c) - 28*I*a^3*e^(6*I*d*x + 6*I*c) - 70*I*a^3*e^(4*I*d*x + 4*I*c) - 140*I*a^3*e^(2*I*d*x + 2*I*c) + 35*I*a^3)*e^(-I*d*x - I*c)/d","A",0
51,1,104,0,0.502773," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-7 i \, a^{3} e^{\left(12 i \, d x + 12 i \, c\right)} - 54 i \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} - 189 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 420 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 945 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 378 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 21 i \, a^{3}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{4032 \, d}"," ",0,"1/4032*(-7*I*a^3*e^(12*I*d*x + 12*I*c) - 54*I*a^3*e^(10*I*d*x + 10*I*c) - 189*I*a^3*e^(8*I*d*x + 8*I*c) - 420*I*a^3*e^(6*I*d*x + 6*I*c) - 945*I*a^3*e^(4*I*d*x + 4*I*c) + 378*I*a^3*e^(2*I*d*x + 2*I*c) + 21*I*a^3)*e^(-3*I*d*x - 3*I*c)/d","A",0
52,1,364,0,0.669709," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{-630 i \, a^{4} e^{\left(11 i \, d x + 11 i \, c\right)} + 6670 i \, a^{4} e^{\left(9 i \, d x + 9 i \, c\right)} + 10116 i \, a^{4} e^{\left(7 i \, d x + 7 i \, c\right)} + 8316 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} + 3570 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} + 630 i \, a^{4} e^{\left(i \, d x + i \, c\right)} + 315 \, {\left(a^{4} e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 315 \, {\left(a^{4} e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{240 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/240*(-630*I*a^4*e^(11*I*d*x + 11*I*c) + 6670*I*a^4*e^(9*I*d*x + 9*I*c) + 10116*I*a^4*e^(7*I*d*x + 7*I*c) + 8316*I*a^4*e^(5*I*d*x + 5*I*c) + 3570*I*a^4*e^(3*I*d*x + 3*I*c) + 630*I*a^4*e^(I*d*x + I*c) + 315*(a^4*e^(12*I*d*x + 12*I*c) + 6*a^4*e^(10*I*d*x + 10*I*c) + 15*a^4*e^(8*I*d*x + 8*I*c) + 20*a^4*e^(6*I*d*x + 6*I*c) + 15*a^4*e^(4*I*d*x + 4*I*c) + 6*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(I*d*x + I*c) + I) - 315*(a^4*e^(12*I*d*x + 12*I*c) + 6*a^4*e^(10*I*d*x + 10*I*c) + 15*a^4*e^(8*I*d*x + 8*I*c) + 20*a^4*e^(6*I*d*x + 6*I*c) + 15*a^4*e^(4*I*d*x + 4*I*c) + 6*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(I*d*x + I*c) - I))/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","B",0
53,1,256,0,0.574323," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{558 i \, a^{4} e^{\left(7 i \, d x + 7 i \, c\right)} + 1022 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} + 770 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} + 210 i \, a^{4} e^{\left(i \, d x + i \, c\right)} + 105 \, {\left(a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, {\left(a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{24 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/24*(558*I*a^4*e^(7*I*d*x + 7*I*c) + 1022*I*a^4*e^(5*I*d*x + 5*I*c) + 770*I*a^4*e^(3*I*d*x + 3*I*c) + 210*I*a^4*e^(I*d*x + I*c) + 105*(a^4*e^(8*I*d*x + 8*I*c) + 4*a^4*e^(6*I*d*x + 6*I*c) + 6*a^4*e^(4*I*d*x + 4*I*c) + 4*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(I*d*x + I*c) + I) - 105*(a^4*e^(8*I*d*x + 8*I*c) + 4*a^4*e^(6*I*d*x + 6*I*c) + 6*a^4*e^(4*I*d*x + 4*I*c) + 4*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(I*d*x + I*c) - I))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
54,1,162,0,1.286403," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{-16 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} - 50 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} - 30 i \, a^{4} e^{\left(i \, d x + i \, c\right)} - 15 \, {\left(a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) + 15 \, {\left(a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{2 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/2*(-16*I*a^4*e^(5*I*d*x + 5*I*c) - 50*I*a^4*e^(3*I*d*x + 3*I*c) - 30*I*a^4*e^(I*d*x + I*c) - 15*(a^4*e^(4*I*d*x + 4*I*c) + 2*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(I*d*x + I*c) + I) + 15*(a^4*e^(4*I*d*x + 4*I*c) + 2*a^4*e^(2*I*d*x + 2*I*c) + a^4)*log(e^(I*d*x + I*c) - I))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
55,1,68,0,0.584771," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{-2 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} + 6 i \, a^{4} e^{\left(i \, d x + i \, c\right)} + 3 \, a^{4} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, a^{4} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{3 \, d}"," ",0,"1/3*(-2*I*a^4*e^(3*I*d*x + 3*I*c) + 6*I*a^4*e^(I*d*x + I*c) + 3*a^4*log(e^(I*d*x + I*c) + I) - 3*a^4*log(e^(I*d*x + I*c) - I))/d","A",0
56,1,34,0,0.624602," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{-3 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} - 5 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)}}{30 \, d}"," ",0,"1/30*(-3*I*a^4*e^(5*I*d*x + 5*I*c) - 5*I*a^4*e^(3*I*d*x + 3*I*c))/d","A",0
57,1,62,0,0.718227," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{-5 i \, a^{4} e^{\left(7 i \, d x + 7 i \, c\right)} - 21 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} - 35 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} - 35 i \, a^{4} e^{\left(i \, d x + i \, c\right)}}{280 \, d}"," ",0,"1/280*(-5*I*a^4*e^(7*I*d*x + 7*I*c) - 21*I*a^4*e^(5*I*d*x + 5*I*c) - 35*I*a^4*e^(3*I*d*x + 3*I*c) - 35*I*a^4*e^(I*d*x + I*c))/d","A",0
58,1,90,0,0.579590," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(-7 i \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} - 45 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} - 126 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 210 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 315 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 63 i \, a^{4}\right)} e^{\left(-i \, d x - i \, c\right)}}{2016 \, d}"," ",0,"1/2016*(-7*I*a^4*e^(10*I*d*x + 10*I*c) - 45*I*a^4*e^(8*I*d*x + 8*I*c) - 126*I*a^4*e^(6*I*d*x + 6*I*c) - 210*I*a^4*e^(4*I*d*x + 4*I*c) - 315*I*a^4*e^(2*I*d*x + 2*I*c) + 63*I*a^4)*e^(-I*d*x - I*c)/d","A",0
59,1,267,0,0.884802," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{506880 i \, a^{5} e^{\left(16 i \, d x + 16 i \, c\right)} + 811008 i \, a^{5} e^{\left(14 i \, d x + 14 i \, c\right)} + 946176 i \, a^{5} e^{\left(12 i \, d x + 12 i \, c\right)} + 811008 i \, a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} + 506880 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} + 225280 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} + 67584 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 12288 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 1024 i \, a^{5}}{495 \, {\left(d e^{\left(24 i \, d x + 24 i \, c\right)} + 12 \, d e^{\left(22 i \, d x + 22 i \, c\right)} + 66 \, d e^{\left(20 i \, d x + 20 i \, c\right)} + 220 \, d e^{\left(18 i \, d x + 18 i \, c\right)} + 495 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 792 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 924 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 792 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 495 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 220 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 66 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 12 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/495*(506880*I*a^5*e^(16*I*d*x + 16*I*c) + 811008*I*a^5*e^(14*I*d*x + 14*I*c) + 946176*I*a^5*e^(12*I*d*x + 12*I*c) + 811008*I*a^5*e^(10*I*d*x + 10*I*c) + 506880*I*a^5*e^(8*I*d*x + 8*I*c) + 225280*I*a^5*e^(6*I*d*x + 6*I*c) + 67584*I*a^5*e^(4*I*d*x + 4*I*c) + 12288*I*a^5*e^(2*I*d*x + 2*I*c) + 1024*I*a^5)/(d*e^(24*I*d*x + 24*I*c) + 12*d*e^(22*I*d*x + 22*I*c) + 66*d*e^(20*I*d*x + 20*I*c) + 220*d*e^(18*I*d*x + 18*I*c) + 495*d*e^(16*I*d*x + 16*I*c) + 792*d*e^(14*I*d*x + 14*I*c) + 924*d*e^(12*I*d*x + 12*I*c) + 792*d*e^(10*I*d*x + 10*I*c) + 495*d*e^(8*I*d*x + 8*I*c) + 220*d*e^(6*I*d*x + 6*I*c) + 66*d*e^(4*I*d*x + 4*I*c) + 12*d*e^(2*I*d*x + 2*I*c) + d)","B",0
60,1,229,0,0.554312," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{15360 i \, a^{5} e^{\left(14 i \, d x + 14 i \, c\right)} + 26880 i \, a^{5} e^{\left(12 i \, d x + 12 i \, c\right)} + 32256 i \, a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} + 26880 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} + 15360 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} + 5760 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 1280 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i \, a^{5}}{45 \, {\left(d e^{\left(20 i \, d x + 20 i \, c\right)} + 10 \, d e^{\left(18 i \, d x + 18 i \, c\right)} + 45 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 120 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 210 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 252 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 210 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 120 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 45 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 10 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/45*(15360*I*a^5*e^(14*I*d*x + 14*I*c) + 26880*I*a^5*e^(12*I*d*x + 12*I*c) + 32256*I*a^5*e^(10*I*d*x + 10*I*c) + 26880*I*a^5*e^(8*I*d*x + 8*I*c) + 15360*I*a^5*e^(6*I*d*x + 6*I*c) + 5760*I*a^5*e^(4*I*d*x + 4*I*c) + 1280*I*a^5*e^(2*I*d*x + 2*I*c) + 128*I*a^5)/(d*e^(20*I*d*x + 20*I*c) + 10*d*e^(18*I*d*x + 18*I*c) + 45*d*e^(16*I*d*x + 16*I*c) + 120*d*e^(14*I*d*x + 14*I*c) + 210*d*e^(12*I*d*x + 12*I*c) + 252*d*e^(10*I*d*x + 10*I*c) + 210*d*e^(8*I*d*x + 8*I*c) + 120*d*e^(6*I*d*x + 6*I*c) + 45*d*e^(4*I*d*x + 4*I*c) + 10*d*e^(2*I*d*x + 2*I*c) + d)","B",0
61,1,191,0,0.468836," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{896 i \, a^{5} e^{\left(12 i \, d x + 12 i \, c\right)} + 1792 i \, a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} + 2240 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} + 1792 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} + 896 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 256 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i \, a^{5}}{7 \, {\left(d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/7*(896*I*a^5*e^(12*I*d*x + 12*I*c) + 1792*I*a^5*e^(10*I*d*x + 10*I*c) + 2240*I*a^5*e^(8*I*d*x + 8*I*c) + 1792*I*a^5*e^(6*I*d*x + 6*I*c) + 896*I*a^5*e^(4*I*d*x + 4*I*c) + 256*I*a^5*e^(2*I*d*x + 2*I*c) + 32*I*a^5)/(d*e^(16*I*d*x + 16*I*c) + 8*d*e^(14*I*d*x + 14*I*c) + 28*d*e^(12*I*d*x + 12*I*c) + 56*d*e^(10*I*d*x + 10*I*c) + 70*d*e^(8*I*d*x + 8*I*c) + 56*d*e^(6*I*d*x + 6*I*c) + 28*d*e^(4*I*d*x + 4*I*c) + 8*d*e^(2*I*d*x + 2*I*c) + d)","B",0
62,1,153,0,0.581466," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{192 i \, a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} + 480 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} + 640 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} + 480 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 192 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i \, a^{5}}{3 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(192*I*a^5*e^(10*I*d*x + 10*I*c) + 480*I*a^5*e^(8*I*d*x + 8*I*c) + 640*I*a^5*e^(6*I*d*x + 6*I*c) + 480*I*a^5*e^(4*I*d*x + 4*I*c) + 192*I*a^5*e^(2*I*d*x + 2*I*c) + 32*I*a^5)/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","B",0
63,1,176,0,0.620415," ","integrate((a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-192 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} - 432 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} - 352 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} - 100 i \, a^{5} + {\left(-48 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} - 192 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} - 288 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} - 192 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} - 48 i \, a^{5}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(-192*I*a^5*e^(6*I*d*x + 6*I*c) - 432*I*a^5*e^(4*I*d*x + 4*I*c) - 352*I*a^5*e^(2*I*d*x + 2*I*c) - 100*I*a^5 + (-48*I*a^5*e^(8*I*d*x + 8*I*c) - 192*I*a^5*e^(6*I*d*x + 6*I*c) - 288*I*a^5*e^(4*I*d*x + 4*I*c) - 192*I*a^5*e^(2*I*d*x + 2*I*c) - 48*I*a^5)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","A",0
64,1,123,0,0.498939," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-4 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} - 8 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 8 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 10 i \, a^{5} + {\left(12 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 24 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 12 i \, a^{5}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(-4*I*a^5*e^(6*I*d*x + 6*I*c) - 8*I*a^5*e^(4*I*d*x + 4*I*c) + 8*I*a^5*e^(2*I*d*x + 2*I*c) + 10*I*a^5 + (12*I*a^5*e^(4*I*d*x + 4*I*c) + 24*I*a^5*e^(2*I*d*x + 2*I*c) + 12*I*a^5)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
65,1,51,0,0.587989," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{5} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{2 \, d}"," ",0,"1/2*(-I*a^5*e^(4*I*d*x + 4*I*c) + 2*I*a^5*e^(2*I*d*x + 2*I*c) - 2*I*a^5*log(e^(2*I*d*x + 2*I*c) + 1))/d","A",0
66,1,34,0,0.902497," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-2 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} - 3 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)}}{24 \, d}"," ",0,"1/24*(-2*I*a^5*e^(6*I*d*x + 6*I*c) - 3*I*a^5*e^(4*I*d*x + 4*I*c))/d","A",0
67,1,62,0,0.597056," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} - 4 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} - 6 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)}}{64 \, d}"," ",0,"1/64*(-I*a^5*e^(8*I*d*x + 8*I*c) - 4*I*a^5*e^(6*I*d*x + 6*I*c) - 6*I*a^5*e^(4*I*d*x + 4*I*c) - 4*I*a^5*e^(2*I*d*x + 2*I*c))/d","B",0
68,1,83,0,0.742877," ","integrate(cos(d*x+c)^10*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{120 \, a^{5} d x - 12 i \, a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} - 75 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} - 200 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} - 300 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} - 300 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)}}{3840 \, d}"," ",0,"1/3840*(120*a^5*d*x - 12*I*a^5*e^(10*I*d*x + 10*I*c) - 75*I*a^5*e^(8*I*d*x + 8*I*c) - 200*I*a^5*e^(6*I*d*x + 6*I*c) - 300*I*a^5*e^(4*I*d*x + 4*I*c) - 300*I*a^5*e^(2*I*d*x + 2*I*c))/d","A",0
69,1,120,0,0.621230," ","integrate(cos(d*x+c)^12*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{{\left(840 \, a^{5} d x e^{\left(2 i \, d x + 2 i \, c\right)} - 10 i \, a^{5} e^{\left(14 i \, d x + 14 i \, c\right)} - 84 i \, a^{5} e^{\left(12 i \, d x + 12 i \, c\right)} - 315 i \, a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} - 700 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} - 1050 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} - 1260 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 60 i \, a^{5}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{15360 \, d}"," ",0,"1/15360*(840*a^5*d*x*e^(2*I*d*x + 2*I*c) - 10*I*a^5*e^(14*I*d*x + 14*I*c) - 84*I*a^5*e^(12*I*d*x + 12*I*c) - 315*I*a^5*e^(10*I*d*x + 10*I*c) - 700*I*a^5*e^(8*I*d*x + 8*I*c) - 1050*I*a^5*e^(6*I*d*x + 6*I*c) - 1260*I*a^5*e^(4*I*d*x + 4*I*c) + 60*I*a^5)*e^(-2*I*d*x - 2*I*c)/d","A",0
70,1,310,0,0.516270," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{1930 i \, a^{5} e^{\left(9 i \, d x + 9 i \, c\right)} + 4740 i \, a^{5} e^{\left(7 i \, d x + 7 i \, c\right)} + 5376 i \, a^{5} e^{\left(5 i \, d x + 5 i \, c\right)} + 2940 i \, a^{5} e^{\left(3 i \, d x + 3 i \, c\right)} + 630 i \, a^{5} e^{\left(i \, d x + i \, c\right)} + 315 \, {\left(a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{5}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 315 \, {\left(a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{5}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{40 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/40*(1930*I*a^5*e^(9*I*d*x + 9*I*c) + 4740*I*a^5*e^(7*I*d*x + 7*I*c) + 5376*I*a^5*e^(5*I*d*x + 5*I*c) + 2940*I*a^5*e^(3*I*d*x + 3*I*c) + 630*I*a^5*e^(I*d*x + I*c) + 315*(a^5*e^(10*I*d*x + 10*I*c) + 5*a^5*e^(8*I*d*x + 8*I*c) + 10*a^5*e^(6*I*d*x + 6*I*c) + 10*a^5*e^(4*I*d*x + 4*I*c) + 5*a^5*e^(2*I*d*x + 2*I*c) + a^5)*log(e^(I*d*x + I*c) + I) - 315*(a^5*e^(10*I*d*x + 10*I*c) + 5*a^5*e^(8*I*d*x + 8*I*c) + 10*a^5*e^(6*I*d*x + 6*I*c) + 10*a^5*e^(4*I*d*x + 4*I*c) + 5*a^5*e^(2*I*d*x + 2*I*c) + a^5)*log(e^(I*d*x + I*c) - I))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
71,1,216,0,0.626436," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-96 i \, a^{5} e^{\left(7 i \, d x + 7 i \, c\right)} - 462 i \, a^{5} e^{\left(5 i \, d x + 5 i \, c\right)} - 560 i \, a^{5} e^{\left(3 i \, d x + 3 i \, c\right)} - 210 i \, a^{5} e^{\left(i \, d x + i \, c\right)} - 105 \, {\left(a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{5}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) + 105 \, {\left(a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{5}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{6 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/6*(-96*I*a^5*e^(7*I*d*x + 7*I*c) - 462*I*a^5*e^(5*I*d*x + 5*I*c) - 560*I*a^5*e^(3*I*d*x + 3*I*c) - 210*I*a^5*e^(I*d*x + I*c) - 105*(a^5*e^(6*I*d*x + 6*I*c) + 3*a^5*e^(4*I*d*x + 4*I*c) + 3*a^5*e^(2*I*d*x + 2*I*c) + a^5)*log(e^(I*d*x + I*c) + I) + 105*(a^5*e^(6*I*d*x + 6*I*c) + 3*a^5*e^(4*I*d*x + 4*I*c) + 3*a^5*e^(2*I*d*x + 2*I*c) + a^5)*log(e^(I*d*x + I*c) - I))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","A",0
72,1,122,0,0.493201," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-4 i \, a^{5} e^{\left(5 i \, d x + 5 i \, c\right)} + 20 i \, a^{5} e^{\left(3 i \, d x + 3 i \, c\right)} + 30 i \, a^{5} e^{\left(i \, d x + i \, c\right)} + 15 \, {\left(a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{5}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{5}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(-4*I*a^5*e^(5*I*d*x + 5*I*c) + 20*I*a^5*e^(3*I*d*x + 3*I*c) + 30*I*a^5*e^(I*d*x + I*c) + 15*(a^5*e^(2*I*d*x + 2*I*c) + a^5)*log(e^(I*d*x + I*c) + I) - 15*(a^5*e^(2*I*d*x + 2*I*c) + a^5)*log(e^(I*d*x + I*c) - I))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
73,1,17,0,0.421866," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","-\frac{i \, a^{5} e^{\left(5 i \, d x + 5 i \, c\right)}}{5 \, d}"," ",0,"-1/5*I*a^5*e^(5*I*d*x + 5*I*c)/d","A",0
74,1,48,0,0.537505," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-15 i \, a^{5} e^{\left(7 i \, d x + 7 i \, c\right)} - 42 i \, a^{5} e^{\left(5 i \, d x + 5 i \, c\right)} - 35 i \, a^{5} e^{\left(3 i \, d x + 3 i \, c\right)}}{420 \, d}"," ",0,"1/420*(-15*I*a^5*e^(7*I*d*x + 7*I*c) - 42*I*a^5*e^(5*I*d*x + 5*I*c) - 35*I*a^5*e^(3*I*d*x + 3*I*c))/d","A",0
75,1,76,0,0.570521," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{-35 i \, a^{5} e^{\left(9 i \, d x + 9 i \, c\right)} - 180 i \, a^{5} e^{\left(7 i \, d x + 7 i \, c\right)} - 378 i \, a^{5} e^{\left(5 i \, d x + 5 i \, c\right)} - 420 i \, a^{5} e^{\left(3 i \, d x + 3 i \, c\right)} - 315 i \, a^{5} e^{\left(i \, d x + i \, c\right)}}{5040 \, d}"," ",0,"1/5040*(-35*I*a^5*e^(9*I*d*x + 9*I*c) - 180*I*a^5*e^(7*I*d*x + 7*I*c) - 378*I*a^5*e^(5*I*d*x + 5*I*c) - 420*I*a^5*e^(3*I*d*x + 3*I*c) - 315*I*a^5*e^(I*d*x + I*c))/d","A",0
76,1,104,0,0.480979," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","\frac{{\left(-21 i \, a^{5} e^{\left(12 i \, d x + 12 i \, c\right)} - 154 i \, a^{5} e^{\left(10 i \, d x + 10 i \, c\right)} - 495 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} - 924 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} - 1155 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} - 1386 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 231 i \, a^{5}\right)} e^{\left(-i \, d x - i \, c\right)}}{14784 \, d}"," ",0,"1/14784*(-21*I*a^5*e^(12*I*d*x + 12*I*c) - 154*I*a^5*e^(10*I*d*x + 10*I*c) - 495*I*a^5*e^(8*I*d*x + 8*I*c) - 924*I*a^5*e^(6*I*d*x + 6*I*c) - 1155*I*a^5*e^(4*I*d*x + 4*I*c) - 1386*I*a^5*e^(2*I*d*x + 2*I*c) + 231*I*a^5)*e^(-I*d*x - I*c)/d","A",0
77,1,345,0,0.661326," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{11182080 i \, a^{8} e^{\left(22 i \, d x + 22 i \, c\right)} + 24600576 i \, a^{8} e^{\left(20 i \, d x + 20 i \, c\right)} + 41000960 i \, a^{8} e^{\left(18 i \, d x + 18 i \, c\right)} + 52715520 i \, a^{8} e^{\left(16 i \, d x + 16 i \, c\right)} + 52715520 i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} + 41000960 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} + 24600576 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 11182080 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 3727360 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 860160 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 122880 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + 8192 i \, a^{8}}{1365 \, {\left(d e^{\left(30 i \, d x + 30 i \, c\right)} + 15 \, d e^{\left(28 i \, d x + 28 i \, c\right)} + 105 \, d e^{\left(26 i \, d x + 26 i \, c\right)} + 455 \, d e^{\left(24 i \, d x + 24 i \, c\right)} + 1365 \, d e^{\left(22 i \, d x + 22 i \, c\right)} + 3003 \, d e^{\left(20 i \, d x + 20 i \, c\right)} + 5005 \, d e^{\left(18 i \, d x + 18 i \, c\right)} + 6435 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 6435 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 5005 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 3003 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 1365 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 455 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 105 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 15 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/1365*(11182080*I*a^8*e^(22*I*d*x + 22*I*c) + 24600576*I*a^8*e^(20*I*d*x + 20*I*c) + 41000960*I*a^8*e^(18*I*d*x + 18*I*c) + 52715520*I*a^8*e^(16*I*d*x + 16*I*c) + 52715520*I*a^8*e^(14*I*d*x + 14*I*c) + 41000960*I*a^8*e^(12*I*d*x + 12*I*c) + 24600576*I*a^8*e^(10*I*d*x + 10*I*c) + 11182080*I*a^8*e^(8*I*d*x + 8*I*c) + 3727360*I*a^8*e^(6*I*d*x + 6*I*c) + 860160*I*a^8*e^(4*I*d*x + 4*I*c) + 122880*I*a^8*e^(2*I*d*x + 2*I*c) + 8192*I*a^8)/(d*e^(30*I*d*x + 30*I*c) + 15*d*e^(28*I*d*x + 28*I*c) + 105*d*e^(26*I*d*x + 26*I*c) + 455*d*e^(24*I*d*x + 24*I*c) + 1365*d*e^(22*I*d*x + 22*I*c) + 3003*d*e^(20*I*d*x + 20*I*c) + 5005*d*e^(18*I*d*x + 18*I*c) + 6435*d*e^(16*I*d*x + 16*I*c) + 6435*d*e^(14*I*d*x + 14*I*c) + 5005*d*e^(12*I*d*x + 12*I*c) + 3003*d*e^(10*I*d*x + 10*I*c) + 1365*d*e^(8*I*d*x + 8*I*c) + 455*d*e^(6*I*d*x + 6*I*c) + 105*d*e^(4*I*d*x + 4*I*c) + 15*d*e^(2*I*d*x + 2*I*c) + d)","B",0
78,1,307,0,0.469009," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{1171456 i \, a^{8} e^{\left(20 i \, d x + 20 i \, c\right)} + 2928640 i \, a^{8} e^{\left(18 i \, d x + 18 i \, c\right)} + 5271552 i \, a^{8} e^{\left(16 i \, d x + 16 i \, c\right)} + 7028736 i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} + 7028736 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} + 5271552 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 2928640 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 1171456 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 319488 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 53248 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + 4096 i \, a^{8}}{429 \, {\left(d e^{\left(26 i \, d x + 26 i \, c\right)} + 13 \, d e^{\left(24 i \, d x + 24 i \, c\right)} + 78 \, d e^{\left(22 i \, d x + 22 i \, c\right)} + 286 \, d e^{\left(20 i \, d x + 20 i \, c\right)} + 715 \, d e^{\left(18 i \, d x + 18 i \, c\right)} + 1287 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 1716 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 1716 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 1287 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 715 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 286 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 78 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 13 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/429*(1171456*I*a^8*e^(20*I*d*x + 20*I*c) + 2928640*I*a^8*e^(18*I*d*x + 18*I*c) + 5271552*I*a^8*e^(16*I*d*x + 16*I*c) + 7028736*I*a^8*e^(14*I*d*x + 14*I*c) + 7028736*I*a^8*e^(12*I*d*x + 12*I*c) + 5271552*I*a^8*e^(10*I*d*x + 10*I*c) + 2928640*I*a^8*e^(8*I*d*x + 8*I*c) + 1171456*I*a^8*e^(6*I*d*x + 6*I*c) + 319488*I*a^8*e^(4*I*d*x + 4*I*c) + 53248*I*a^8*e^(2*I*d*x + 2*I*c) + 4096*I*a^8)/(d*e^(26*I*d*x + 26*I*c) + 13*d*e^(24*I*d*x + 24*I*c) + 78*d*e^(22*I*d*x + 22*I*c) + 286*d*e^(20*I*d*x + 20*I*c) + 715*d*e^(18*I*d*x + 18*I*c) + 1287*d*e^(16*I*d*x + 16*I*c) + 1716*d*e^(14*I*d*x + 14*I*c) + 1716*d*e^(12*I*d*x + 12*I*c) + 1287*d*e^(10*I*d*x + 10*I*c) + 715*d*e^(8*I*d*x + 8*I*c) + 286*d*e^(6*I*d*x + 6*I*c) + 78*d*e^(4*I*d*x + 4*I*c) + 13*d*e^(2*I*d*x + 2*I*c) + d)","B",0
79,1,269,0,0.443028," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{56320 i \, a^{8} e^{\left(18 i \, d x + 18 i \, c\right)} + 168960 i \, a^{8} e^{\left(16 i \, d x + 16 i \, c\right)} + 337920 i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} + 473088 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} + 473088 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 337920 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 168960 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 56320 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 11264 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + 1024 i \, a^{8}}{55 \, {\left(d e^{\left(22 i \, d x + 22 i \, c\right)} + 11 \, d e^{\left(20 i \, d x + 20 i \, c\right)} + 55 \, d e^{\left(18 i \, d x + 18 i \, c\right)} + 165 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 330 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 462 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 462 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 330 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 165 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 55 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 11 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/55*(56320*I*a^8*e^(18*I*d*x + 18*I*c) + 168960*I*a^8*e^(16*I*d*x + 16*I*c) + 337920*I*a^8*e^(14*I*d*x + 14*I*c) + 473088*I*a^8*e^(12*I*d*x + 12*I*c) + 473088*I*a^8*e^(10*I*d*x + 10*I*c) + 337920*I*a^8*e^(8*I*d*x + 8*I*c) + 168960*I*a^8*e^(6*I*d*x + 6*I*c) + 56320*I*a^8*e^(4*I*d*x + 4*I*c) + 11264*I*a^8*e^(2*I*d*x + 2*I*c) + 1024*I*a^8)/(d*e^(22*I*d*x + 22*I*c) + 11*d*e^(20*I*d*x + 20*I*c) + 55*d*e^(18*I*d*x + 18*I*c) + 165*d*e^(16*I*d*x + 16*I*c) + 330*d*e^(14*I*d*x + 14*I*c) + 462*d*e^(12*I*d*x + 12*I*c) + 462*d*e^(10*I*d*x + 10*I*c) + 330*d*e^(8*I*d*x + 8*I*c) + 165*d*e^(6*I*d*x + 6*I*c) + 55*d*e^(4*I*d*x + 4*I*c) + 11*d*e^(2*I*d*x + 2*I*c) + d)","B",0
80,1,231,0,0.497858," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{4608 i \, a^{8} e^{\left(16 i \, d x + 16 i \, c\right)} + 18432 i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} + 43008 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} + 64512 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 64512 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 43008 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 18432 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 4608 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + 512 i \, a^{8}}{9 \, {\left(d e^{\left(18 i \, d x + 18 i \, c\right)} + 9 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 36 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 84 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 126 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 126 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 84 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 36 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 9 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/9*(4608*I*a^8*e^(16*I*d*x + 16*I*c) + 18432*I*a^8*e^(14*I*d*x + 14*I*c) + 43008*I*a^8*e^(12*I*d*x + 12*I*c) + 64512*I*a^8*e^(10*I*d*x + 10*I*c) + 64512*I*a^8*e^(8*I*d*x + 8*I*c) + 43008*I*a^8*e^(6*I*d*x + 6*I*c) + 18432*I*a^8*e^(4*I*d*x + 4*I*c) + 4608*I*a^8*e^(2*I*d*x + 2*I*c) + 512*I*a^8)/(d*e^(18*I*d*x + 18*I*c) + 9*d*e^(16*I*d*x + 16*I*c) + 36*d*e^(14*I*d*x + 14*I*c) + 84*d*e^(12*I*d*x + 12*I*c) + 126*d*e^(10*I*d*x + 10*I*c) + 126*d*e^(8*I*d*x + 8*I*c) + 84*d*e^(6*I*d*x + 6*I*c) + 36*d*e^(4*I*d*x + 4*I*c) + 9*d*e^(2*I*d*x + 2*I*c) + d)","B",0
81,1,296,0,0.563681," ","integrate((a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-94080 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} - 423360 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} - 862400 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} - 980000 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} - 644448 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} - 230496 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} - 34848 i \, a^{8} + {\left(-13440 i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} - 94080 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} - 282240 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} - 470400 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} - 470400 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} - 282240 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} - 94080 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} - 13440 i \, a^{8}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{105 \, {\left(d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/105*(-94080*I*a^8*e^(12*I*d*x + 12*I*c) - 423360*I*a^8*e^(10*I*d*x + 10*I*c) - 862400*I*a^8*e^(8*I*d*x + 8*I*c) - 980000*I*a^8*e^(6*I*d*x + 6*I*c) - 644448*I*a^8*e^(4*I*d*x + 4*I*c) - 230496*I*a^8*e^(2*I*d*x + 2*I*c) - 34848*I*a^8 + (-13440*I*a^8*e^(14*I*d*x + 14*I*c) - 94080*I*a^8*e^(12*I*d*x + 12*I*c) - 282240*I*a^8*e^(10*I*d*x + 10*I*c) - 470400*I*a^8*e^(8*I*d*x + 8*I*c) - 470400*I*a^8*e^(6*I*d*x + 6*I*c) - 282240*I*a^8*e^(4*I*d*x + 4*I*c) - 94080*I*a^8*e^(2*I*d*x + 2*I*c) - 13440*I*a^8)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(14*I*d*x + 14*I*c) + 7*d*e^(12*I*d*x + 12*I*c) + 21*d*e^(10*I*d*x + 10*I*c) + 35*d*e^(8*I*d*x + 8*I*c) + 35*d*e^(6*I*d*x + 6*I*c) + 21*d*e^(4*I*d*x + 4*I*c) + 7*d*e^(2*I*d*x + 2*I*c) + d)","A",0
82,1,244,0,0.583045," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-160 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} - 800 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 800 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 6400 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 9600 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 6000 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + 1392 i \, a^{8} + {\left(960 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 4800 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 9600 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 9600 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 4800 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + 960 i \, a^{8}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{5 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/5*(-160*I*a^8*e^(12*I*d*x + 12*I*c) - 800*I*a^8*e^(10*I*d*x + 10*I*c) + 800*I*a^8*e^(8*I*d*x + 8*I*c) + 6400*I*a^8*e^(6*I*d*x + 6*I*c) + 9600*I*a^8*e^(4*I*d*x + 4*I*c) + 6000*I*a^8*e^(2*I*d*x + 2*I*c) + 1392*I*a^8 + (960*I*a^8*e^(10*I*d*x + 10*I*c) + 4800*I*a^8*e^(8*I*d*x + 8*I*c) + 9600*I*a^8*e^(6*I*d*x + 6*I*c) + 9600*I*a^8*e^(4*I*d*x + 4*I*c) + 4800*I*a^8*e^(2*I*d*x + 2*I*c) + 960*I*a^8)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
83,1,178,0,0.616107," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-12 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 60 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 252 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 36 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} - 324 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} - 188 i \, a^{8} + {\left(-240 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} - 720 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} - 720 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} - 240 i \, a^{8}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(-12*I*a^8*e^(10*I*d*x + 10*I*c) + 60*I*a^8*e^(8*I*d*x + 8*I*c) + 252*I*a^8*e^(6*I*d*x + 6*I*c) + 36*I*a^8*e^(4*I*d*x + 4*I*c) - 324*I*a^8*e^(2*I*d*x + 2*I*c) - 188*I*a^8 + (-240*I*a^8*e^(6*I*d*x + 6*I*c) - 720*I*a^8*e^(4*I*d*x + 4*I*c) - 720*I*a^8*e^(2*I*d*x + 2*I*c) - 240*I*a^8)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","A",0
84,1,112,0,0.620677," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-2 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} - 12 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} - 18 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, a^{8} + {\left(24 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + 24 i \, a^{8}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(-2*I*a^8*e^(8*I*d*x + 8*I*c) + 4*I*a^8*e^(6*I*d*x + 6*I*c) - 12*I*a^8*e^(4*I*d*x + 4*I*c) - 18*I*a^8*e^(2*I*d*x + 2*I*c) + 6*I*a^8 + (24*I*a^8*e^(2*I*d*x + 2*I*c) + 24*I*a^8)*log(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
85,1,17,0,0.559623," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","-\frac{i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)}}{8 \, d}"," ",0,"-1/8*I*a^8*e^(8*I*d*x + 8*I*c)/d","A",0
86,1,48,0,0.678117," ","integrate(cos(d*x+c)^10*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-6 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} - 15 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} - 10 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)}}{240 \, d}"," ",0,"1/240*(-6*I*a^8*e^(10*I*d*x + 10*I*c) - 15*I*a^8*e^(8*I*d*x + 8*I*c) - 10*I*a^8*e^(6*I*d*x + 6*I*c))/d","A",0
87,1,76,0,0.702125," ","integrate(cos(d*x+c)^12*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-5 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} - 24 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} - 45 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} - 40 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} - 15 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)}}{960 \, d}"," ",0,"1/960*(-5*I*a^8*e^(12*I*d*x + 12*I*c) - 24*I*a^8*e^(10*I*d*x + 10*I*c) - 45*I*a^8*e^(8*I*d*x + 8*I*c) - 40*I*a^8*e^(6*I*d*x + 6*I*c) - 15*I*a^8*e^(4*I*d*x + 4*I*c))/d","A",0
88,1,104,0,0.636591," ","integrate(cos(d*x+c)^14*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} - 7 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} - 21 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} - 35 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} - 35 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} - 21 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} - 7 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)}}{896 \, d}"," ",0,"1/896*(-I*a^8*e^(14*I*d*x + 14*I*c) - 7*I*a^8*e^(12*I*d*x + 12*I*c) - 21*I*a^8*e^(10*I*d*x + 10*I*c) - 35*I*a^8*e^(8*I*d*x + 8*I*c) - 35*I*a^8*e^(6*I*d*x + 6*I*c) - 21*I*a^8*e^(4*I*d*x + 4*I*c) - 7*I*a^8*e^(2*I*d*x + 2*I*c))/d","B",0
89,1,125,0,0.643670," ","integrate(cos(d*x+c)^16*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{1680 \, a^{8} d x - 105 i \, a^{8} e^{\left(16 i \, d x + 16 i \, c\right)} - 960 i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} - 3920 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} - 9408 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} - 14700 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} - 15680 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} - 11760 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} - 6720 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)}}{430080 \, d}"," ",0,"1/430080*(1680*a^8*d*x - 105*I*a^8*e^(16*I*d*x + 16*I*c) - 960*I*a^8*e^(14*I*d*x + 14*I*c) - 3920*I*a^8*e^(12*I*d*x + 12*I*c) - 9408*I*a^8*e^(10*I*d*x + 10*I*c) - 14700*I*a^8*e^(8*I*d*x + 8*I*c) - 15680*I*a^8*e^(6*I*d*x + 6*I*c) - 11760*I*a^8*e^(4*I*d*x + 4*I*c) - 6720*I*a^8*e^(2*I*d*x + 2*I*c))/d","A",0
90,1,162,0,0.707539," ","integrate(cos(d*x+c)^18*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(5040 \, a^{8} d x e^{\left(2 i \, d x + 2 i \, c\right)} - 28 i \, a^{8} e^{\left(20 i \, d x + 20 i \, c\right)} - 315 i \, a^{8} e^{\left(18 i \, d x + 18 i \, c\right)} - 1620 i \, a^{8} e^{\left(16 i \, d x + 16 i \, c\right)} - 5040 i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} - 10584 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} - 15876 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} - 17640 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} - 15120 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} - 11340 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 252 i \, a^{8}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{516096 \, d}"," ",0,"1/516096*(5040*a^8*d*x*e^(2*I*d*x + 2*I*c) - 28*I*a^8*e^(20*I*d*x + 20*I*c) - 315*I*a^8*e^(18*I*d*x + 18*I*c) - 1620*I*a^8*e^(16*I*d*x + 16*I*c) - 5040*I*a^8*e^(14*I*d*x + 14*I*c) - 10584*I*a^8*e^(12*I*d*x + 12*I*c) - 15876*I*a^8*e^(10*I*d*x + 10*I*c) - 17640*I*a^8*e^(8*I*d*x + 8*I*c) - 15120*I*a^8*e^(6*I*d*x + 6*I*c) - 11340*I*a^8*e^(4*I*d*x + 4*I*c) + 252*I*a^8)*e^(-2*I*d*x - 2*I*c)/d","A",0
91,1,378,0,0.678854," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-30720 i \, a^{8} e^{\left(13 i \, d x + 13 i \, c\right)} - 309270 i \, a^{8} e^{\left(11 i \, d x + 11 i \, c\right)} - 953810 i \, a^{8} e^{\left(9 i \, d x + 9 i \, c\right)} - 1446588 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)} - 1189188 i \, a^{8} e^{\left(5 i \, d x + 5 i \, c\right)} - 510510 i \, a^{8} e^{\left(3 i \, d x + 3 i \, c\right)} - 90090 i \, a^{8} e^{\left(i \, d x + i \, c\right)} - 45045 \, {\left(a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{8}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) + 45045 \, {\left(a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{8}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{240 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/240*(-30720*I*a^8*e^(13*I*d*x + 13*I*c) - 309270*I*a^8*e^(11*I*d*x + 11*I*c) - 953810*I*a^8*e^(9*I*d*x + 9*I*c) - 1446588*I*a^8*e^(7*I*d*x + 7*I*c) - 1189188*I*a^8*e^(5*I*d*x + 5*I*c) - 510510*I*a^8*e^(3*I*d*x + 3*I*c) - 90090*I*a^8*e^(I*d*x + I*c) - 45045*(a^8*e^(12*I*d*x + 12*I*c) + 6*a^8*e^(10*I*d*x + 10*I*c) + 15*a^8*e^(8*I*d*x + 8*I*c) + 20*a^8*e^(6*I*d*x + 6*I*c) + 15*a^8*e^(4*I*d*x + 4*I*c) + 6*a^8*e^(2*I*d*x + 2*I*c) + a^8)*log(e^(I*d*x + I*c) + I) + 45045*(a^8*e^(12*I*d*x + 12*I*c) + 6*a^8*e^(10*I*d*x + 10*I*c) + 15*a^8*e^(8*I*d*x + 8*I*c) + 20*a^8*e^(6*I*d*x + 6*I*c) + 15*a^8*e^(4*I*d*x + 4*I*c) + 6*a^8*e^(2*I*d*x + 2*I*c) + a^8)*log(e^(I*d*x + I*c) - I))/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","A",0
92,1,284,0,0.684406," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-256 i \, a^{8} e^{\left(11 i \, d x + 11 i \, c\right)} + 2816 i \, a^{8} e^{\left(9 i \, d x + 9 i \, c\right)} + 18414 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)} + 33726 i \, a^{8} e^{\left(5 i \, d x + 5 i \, c\right)} + 25410 i \, a^{8} e^{\left(3 i \, d x + 3 i \, c\right)} + 6930 i \, a^{8} e^{\left(i \, d x + i \, c\right)} + 3465 \, {\left(a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{8}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3465 \, {\left(a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{8}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{24 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/24*(-256*I*a^8*e^(11*I*d*x + 11*I*c) + 2816*I*a^8*e^(9*I*d*x + 9*I*c) + 18414*I*a^8*e^(7*I*d*x + 7*I*c) + 33726*I*a^8*e^(5*I*d*x + 5*I*c) + 25410*I*a^8*e^(3*I*d*x + 3*I*c) + 6930*I*a^8*e^(I*d*x + I*c) + 3465*(a^8*e^(8*I*d*x + 8*I*c) + 4*a^8*e^(6*I*d*x + 6*I*c) + 6*a^8*e^(4*I*d*x + 4*I*c) + 4*a^8*e^(2*I*d*x + 2*I*c) + a^8)*log(e^(I*d*x + I*c) + I) - 3465*(a^8*e^(8*I*d*x + 8*I*c) + 4*a^8*e^(6*I*d*x + 6*I*c) + 6*a^8*e^(4*I*d*x + 4*I*c) + 4*a^8*e^(2*I*d*x + 2*I*c) + a^8)*log(e^(I*d*x + I*c) - I))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","A",0
93,1,190,0,0.703027," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-16 i \, a^{8} e^{\left(9 i \, d x + 9 i \, c\right)} + 48 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)} - 336 i \, a^{8} e^{\left(5 i \, d x + 5 i \, c\right)} - 1050 i \, a^{8} e^{\left(3 i \, d x + 3 i \, c\right)} - 630 i \, a^{8} e^{\left(i \, d x + i \, c\right)} - 315 \, {\left(a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{8}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) + 315 \, {\left(a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{8}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{10 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/10*(-16*I*a^8*e^(9*I*d*x + 9*I*c) + 48*I*a^8*e^(7*I*d*x + 7*I*c) - 336*I*a^8*e^(5*I*d*x + 5*I*c) - 1050*I*a^8*e^(3*I*d*x + 3*I*c) - 630*I*a^8*e^(I*d*x + I*c) - 315*(a^8*e^(4*I*d*x + 4*I*c) + 2*a^8*e^(2*I*d*x + 2*I*c) + a^8)*log(e^(I*d*x + I*c) + I) + 315*(a^8*e^(4*I*d*x + 4*I*c) + 2*a^8*e^(2*I*d*x + 2*I*c) + a^8)*log(e^(I*d*x + I*c) - I))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
94,1,96,0,0.676093," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-30 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)} + 42 i \, a^{8} e^{\left(5 i \, d x + 5 i \, c\right)} - 70 i \, a^{8} e^{\left(3 i \, d x + 3 i \, c\right)} + 210 i \, a^{8} e^{\left(i \, d x + i \, c\right)} + 105 \, a^{8} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, a^{8} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right)}{105 \, d}"," ",0,"1/105*(-30*I*a^8*e^(7*I*d*x + 7*I*c) + 42*I*a^8*e^(5*I*d*x + 5*I*c) - 70*I*a^8*e^(3*I*d*x + 3*I*c) + 210*I*a^8*e^(I*d*x + I*c) + 105*a^8*log(e^(I*d*x + I*c) + I) - 105*a^8*log(e^(I*d*x + I*c) - I))/d","A",0
95,1,34,0,0.504348," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-7 i \, a^{8} e^{\left(9 i \, d x + 9 i \, c\right)} - 9 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)}}{126 \, d}"," ",0,"1/126*(-7*I*a^8*e^(9*I*d*x + 9*I*c) - 9*I*a^8*e^(7*I*d*x + 7*I*c))/d","A",0
96,1,62,0,0.565987," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-105 i \, a^{8} e^{\left(11 i \, d x + 11 i \, c\right)} - 385 i \, a^{8} e^{\left(9 i \, d x + 9 i \, c\right)} - 495 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)} - 231 i \, a^{8} e^{\left(5 i \, d x + 5 i \, c\right)}}{9240 \, d}"," ",0,"1/9240*(-105*I*a^8*e^(11*I*d*x + 11*I*c) - 385*I*a^8*e^(9*I*d*x + 9*I*c) - 495*I*a^8*e^(7*I*d*x + 7*I*c) - 231*I*a^8*e^(5*I*d*x + 5*I*c))/d","A",0
97,1,90,0,0.567640," ","integrate(cos(d*x+c)^13*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-693 i \, a^{8} e^{\left(13 i \, d x + 13 i \, c\right)} - 4095 i \, a^{8} e^{\left(11 i \, d x + 11 i \, c\right)} - 10010 i \, a^{8} e^{\left(9 i \, d x + 9 i \, c\right)} - 12870 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)} - 9009 i \, a^{8} e^{\left(5 i \, d x + 5 i \, c\right)} - 3003 i \, a^{8} e^{\left(3 i \, d x + 3 i \, c\right)}}{288288 \, d}"," ",0,"1/288288*(-693*I*a^8*e^(13*I*d*x + 13*I*c) - 4095*I*a^8*e^(11*I*d*x + 11*I*c) - 10010*I*a^8*e^(9*I*d*x + 9*I*c) - 12870*I*a^8*e^(7*I*d*x + 7*I*c) - 9009*I*a^8*e^(5*I*d*x + 5*I*c) - 3003*I*a^8*e^(3*I*d*x + 3*I*c))/d","A",0
98,1,118,0,0.546941," ","integrate(cos(d*x+c)^15*(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{-429 i \, a^{8} e^{\left(15 i \, d x + 15 i \, c\right)} - 3465 i \, a^{8} e^{\left(13 i \, d x + 13 i \, c\right)} - 12285 i \, a^{8} e^{\left(11 i \, d x + 11 i \, c\right)} - 25025 i \, a^{8} e^{\left(9 i \, d x + 9 i \, c\right)} - 32175 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)} - 27027 i \, a^{8} e^{\left(5 i \, d x + 5 i \, c\right)} - 15015 i \, a^{8} e^{\left(3 i \, d x + 3 i \, c\right)} - 6435 i \, a^{8} e^{\left(i \, d x + i \, c\right)}}{823680 \, d}"," ",0,"1/823680*(-429*I*a^8*e^(15*I*d*x + 15*I*c) - 3465*I*a^8*e^(13*I*d*x + 13*I*c) - 12285*I*a^8*e^(11*I*d*x + 11*I*c) - 25025*I*a^8*e^(9*I*d*x + 9*I*c) - 32175*I*a^8*e^(7*I*d*x + 7*I*c) - 27027*I*a^8*e^(5*I*d*x + 5*I*c) - 15015*I*a^8*e^(3*I*d*x + 3*I*c) - 6435*I*a^8*e^(I*d*x + I*c))/d","A",0
99,1,146,0,0.631868," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{1792 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 896 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 256 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i}{35 \, {\left(a d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, a d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, a d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, a d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/35*(1792*I*e^(6*I*d*x + 6*I*c) + 896*I*e^(4*I*d*x + 4*I*c) + 256*I*e^(2*I*d*x + 2*I*c) + 32*I)/(a*d*e^(16*I*d*x + 16*I*c) + 8*a*d*e^(14*I*d*x + 14*I*c) + 28*a*d*e^(12*I*d*x + 12*I*c) + 56*a*d*e^(10*I*d*x + 10*I*c) + 70*a*d*e^(8*I*d*x + 8*I*c) + 56*a*d*e^(6*I*d*x + 6*I*c) + 28*a*d*e^(4*I*d*x + 4*I*c) + 8*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
100,1,109,0,0.448677," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{240 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 96 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i}{15 \, {\left(a d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/15*(240*I*e^(4*I*d*x + 4*I*c) + 96*I*e^(2*I*d*x + 2*I*c) + 16*I)/(a*d*e^(12*I*d*x + 12*I*c) + 6*a*d*e^(10*I*d*x + 10*I*c) + 15*a*d*e^(8*I*d*x + 8*I*c) + 20*a*d*e^(6*I*d*x + 6*I*c) + 15*a*d*e^(4*I*d*x + 4*I*c) + 6*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
101,1,72,0,0.586502," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i}{3 \, {\left(a d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/3*(16*I*e^(2*I*d*x + 2*I*c) + 4*I)/(a*d*e^(8*I*d*x + 8*I*c) + 4*a*d*e^(6*I*d*x + 6*I*c) + 6*a*d*e^(4*I*d*x + 4*I*c) + 4*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
102,1,33,0,0.542636," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 i}{a d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d}"," ",0,"2*I/(a*d*e^(4*I*d*x + 4*I*c) + 2*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
103,1,26,0,0.443374," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d x + i \, \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)}{a d}"," ",0,"(2*d*x + I*log(e^(2*I*d*x + 2*I*c) + 1))/(a*d)","A",0
104,1,32,0,0.563055," ","integrate(1/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a d}"," ",0,"1/4*(2*d*x*e^(2*I*d*x + 2*I*c) + I)*e^(-2*I*d*x - 2*I*c)/(a*d)","A",0
105,1,54,0,0.440144," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(12 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} - 2 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{32 \, a d}"," ",0,"1/32*(12*d*x*e^(4*I*d*x + 4*I*c) - 2*I*e^(6*I*d*x + 6*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + I)*e^(-4*I*d*x - 4*I*c)/(a*d)","A",0
106,1,76,0,0.543914," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(120 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} - 3 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 30 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 60 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 15 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{384 \, a d}"," ",0,"1/384*(120*d*x*e^(6*I*d*x + 6*I*c) - 3*I*e^(10*I*d*x + 10*I*c) - 30*I*e^(8*I*d*x + 8*I*c) + 60*I*e^(4*I*d*x + 4*I*c) + 15*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-6*I*d*x - 6*I*c)/(a*d)","A",0
107,1,266,0,0.640915," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 30 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 140 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 256 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 140 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 30 i \, e^{\left(i \, d x + i \, c\right)}}{40 \, {\left(a d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/40*(15*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 15*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 30*I*e^(9*I*d*x + 9*I*c) - 140*I*e^(7*I*d*x + 7*I*c) - 256*I*e^(5*I*d*x + 5*I*c) + 140*I*e^(3*I*d*x + 3*I*c) + 30*I*e^(I*d*x + I*c))/(a*d*e^(10*I*d*x + 10*I*c) + 5*a*d*e^(8*I*d*x + 8*I*c) + 10*a*d*e^(6*I*d*x + 6*I*c) + 10*a*d*e^(4*I*d*x + 4*I*c) + 5*a*d*e^(2*I*d*x + 2*I*c) + a*d)","B",0
108,1,174,0,0.447519," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 6 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 16 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 6 i \, e^{\left(i \, d x + i \, c\right)}}{6 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/6*(3*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 3*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 6*I*e^(5*I*d*x + 5*I*c) - 16*I*e^(3*I*d*x + 3*I*c) + 6*I*e^(I*d*x + I*c))/(a*d*e^(6*I*d*x + 6*I*c) + 3*a*d*e^(4*I*d*x + 4*I*c) + 3*a*d*e^(2*I*d*x + 2*I*c) + a*d)","B",0
109,1,80,0,0.530626," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 2 i \, e^{\left(i \, d x + i \, c\right)}}{a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d}"," ",0,"((e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - (e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 2*I*e^(I*d*x + I*c))/(a*d*e^(2*I*d*x + 2*I*c) + a*d)","B",0
110,1,17,0,0.571175," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{i \, e^{\left(-i \, d x - i \, c\right)}}{a d}"," ",0,"I*e^(-I*d*x - I*c)/(a*d)","A",0
111,1,41,0,0.522702," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{12 \, a d}"," ",0,"1/12*(-3*I*e^(4*I*d*x + 4*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + I)*e^(-3*I*d*x - 3*I*c)/(a*d)","A",0
112,1,63,0,0.469199," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-5 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 60 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 90 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 20 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{240 \, a d}"," ",0,"1/240*(-5*I*e^(8*I*d*x + 8*I*c) - 60*I*e^(6*I*d*x + 6*I*c) + 90*I*e^(4*I*d*x + 4*I*c) + 20*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-5*I*d*x - 5*I*c)/(a*d)","A",0
113,1,85,0,0.563370," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-7 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 70 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 525 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 700 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 175 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 42 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{2240 \, a d}"," ",0,"1/2240*(-7*I*e^(12*I*d*x + 12*I*c) - 70*I*e^(10*I*d*x + 10*I*c) - 525*I*e^(8*I*d*x + 8*I*c) + 700*I*e^(6*I*d*x + 6*I*c) + 175*I*e^(4*I*d*x + 4*I*c) + 42*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-7*I*d*x - 7*I*c)/(a*d)","A",0
114,1,138,0,0.501994," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2688 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 896 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i}{105 \, {\left(a^{2} d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, a^{2} d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, a^{2} d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/105*(2688*I*e^(4*I*d*x + 4*I*c) + 896*I*e^(2*I*d*x + 2*I*c) + 128*I)/(a^2*d*e^(14*I*d*x + 14*I*c) + 7*a^2*d*e^(12*I*d*x + 12*I*c) + 21*a^2*d*e^(10*I*d*x + 10*I*c) + 35*a^2*d*e^(8*I*d*x + 8*I*c) + 35*a^2*d*e^(6*I*d*x + 6*I*c) + 21*a^2*d*e^(4*I*d*x + 4*I*c) + 7*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
115,1,97,0,0.410847," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{40 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i}{5 \, {\left(a^{2} d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/5*(40*I*e^(2*I*d*x + 2*I*c) + 8*I)/(a^2*d*e^(10*I*d*x + 10*I*c) + 5*a^2*d*e^(8*I*d*x + 8*I*c) + 10*a^2*d*e^(6*I*d*x + 6*I*c) + 10*a^2*d*e^(4*I*d*x + 4*I*c) + 5*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
116,1,54,0,0.446942," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{8 i}{3 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"8/3*I/(a^2*d*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^(4*I*d*x + 4*I*c) + 3*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
117,1,68,0,0.499543," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + 4 \, d x + {\left(2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 2 i}{a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d}"," ",0,"(4*d*x*e^(2*I*d*x + 2*I*c) + 4*d*x + (2*I*e^(2*I*d*x + 2*I*c) + 2*I)*log(e^(2*I*d*x + 2*I*c) + 1) - 2*I)/(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
118,1,17,0,0.497209," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{i \, e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{2} d}"," ",0,"1/2*I*e^(-2*I*d*x - 2*I*c)/(a^2*d)","A",0
119,1,43,0,0.532002," ","integrate(1/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{2} d}"," ",0,"1/16*(4*d*x*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c) + I)*e^(-4*I*d*x - 4*I*c)/(a^2*d)","A",0
120,1,65,0,0.496093," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(24 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} - 3 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{2} d}"," ",0,"1/96*(24*d*x*e^(6*I*d*x + 6*I*c) - 3*I*e^(8*I*d*x + 8*I*c) + 18*I*e^(4*I*d*x + 4*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + I)*e^(-6*I*d*x - 6*I*c)/(a^2*d)","A",0
121,1,87,0,0.536062," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(120 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 2 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 24 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 80 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 30 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 8 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{512 \, a^{2} d}"," ",0,"1/512*(120*d*x*e^(8*I*d*x + 8*I*c) - 2*I*e^(12*I*d*x + 12*I*c) - 24*I*e^(10*I*d*x + 10*I*c) + 80*I*e^(6*I*d*x + 6*I*c) + 30*I*e^(4*I*d*x + 4*I*c) + 8*I*e^(2*I*d*x + 2*I*c) + I)*e^(-8*I*d*x - 8*I*c)/(a^2*d)","A",0
122,1,326,0,0.672419," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{105 \, {\left(e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, {\left(e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 210 i \, e^{\left(11 i \, d x + 11 i \, c\right)} - 1190 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 2772 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 3372 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 1190 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 210 i \, e^{\left(i \, d x + i \, c\right)}}{240 \, {\left(a^{2} d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{2} d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/240*(105*(e^(12*I*d*x + 12*I*c) + 6*e^(10*I*d*x + 10*I*c) + 15*e^(8*I*d*x + 8*I*c) + 20*e^(6*I*d*x + 6*I*c) + 15*e^(4*I*d*x + 4*I*c) + 6*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 105*(e^(12*I*d*x + 12*I*c) + 6*e^(10*I*d*x + 10*I*c) + 15*e^(8*I*d*x + 8*I*c) + 20*e^(6*I*d*x + 6*I*c) + 15*e^(4*I*d*x + 4*I*c) + 6*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 210*I*e^(11*I*d*x + 11*I*c) - 1190*I*e^(9*I*d*x + 9*I*c) - 2772*I*e^(7*I*d*x + 7*I*c) - 3372*I*e^(5*I*d*x + 5*I*c) + 1190*I*e^(3*I*d*x + 3*I*c) + 210*I*e^(I*d*x + I*c))/(a^2*d*e^(12*I*d*x + 12*I*c) + 6*a^2*d*e^(10*I*d*x + 10*I*c) + 15*a^2*d*e^(8*I*d*x + 8*I*c) + 20*a^2*d*e^(6*I*d*x + 6*I*c) + 15*a^2*d*e^(4*I*d*x + 4*I*c) + 6*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
123,1,230,0,0.545004," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 30 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 110 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 146 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 30 i \, e^{\left(i \, d x + i \, c\right)}}{24 \, {\left(a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/24*(15*(e^(8*I*d*x + 8*I*c) + 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 15*(e^(8*I*d*x + 8*I*c) + 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 30*I*e^(7*I*d*x + 7*I*c) - 110*I*e^(5*I*d*x + 5*I*c) - 146*I*e^(3*I*d*x + 3*I*c) + 30*I*e^(I*d*x + I*c))/(a^2*d*e^(8*I*d*x + 8*I*c) + 4*a^2*d*e^(6*I*d*x + 6*I*c) + 6*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
124,1,134,0,0.570075," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 6 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 10 i \, e^{\left(i \, d x + i \, c\right)}}{2 \, {\left(a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/2*(3*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 3*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 6*I*e^(3*I*d*x + 3*I*c) - 10*I*e^(I*d*x + I*c))/(a^2*d*e^(4*I*d*x + 4*I*c) + 2*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
125,1,64,0,0.584863," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(e^{\left(i \, d x + i \, c\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - e^{\left(i \, d x + i \, c\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 2 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2} d}"," ",0,"-(e^(I*d*x + I*c)*log(e^(I*d*x + I*c) + I) - e^(I*d*x + I*c)*log(e^(I*d*x + I*c) - I) - 2*I)*e^(-I*d*x - I*c)/(a^2*d)","A",0
126,1,30,0,0.544905," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{6 \, a^{2} d}"," ",0,"1/6*(3*I*e^(2*I*d*x + 2*I*c) + I)*e^(-3*I*d*x - 3*I*c)/(a^2*d)","A",0
127,1,52,0,0.677594," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-5 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 15 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{40 \, a^{2} d}"," ",0,"1/40*(-5*I*e^(6*I*d*x + 6*I*c) + 15*I*e^(4*I*d*x + 4*I*c) + 5*I*e^(2*I*d*x + 2*I*c) + I)*e^(-5*I*d*x - 5*I*c)/(a^2*d)","A",0
128,1,74,0,0.604508," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-7 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 105 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 210 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 70 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 21 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{672 \, a^{2} d}"," ",0,"1/672*(-7*I*e^(10*I*d*x + 10*I*c) - 105*I*e^(8*I*d*x + 8*I*c) + 210*I*e^(6*I*d*x + 6*I*c) + 70*I*e^(4*I*d*x + 4*I*c) + 21*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-7*I*d*x - 7*I*c)/(a^2*d)","A",0
129,1,96,0,0.577770," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-9 i \, e^{\left(14 i \, d x + 14 i \, c\right)} - 105 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 945 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 1575 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 525 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 189 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 45 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-9 i \, d x - 9 i \, c\right)}}{5760 \, a^{2} d}"," ",0,"1/5760*(-9*I*e^(14*I*d*x + 14*I*c) - 105*I*e^(12*I*d*x + 12*I*c) - 945*I*e^(10*I*d*x + 10*I*c) + 1575*I*e^(8*I*d*x + 8*I*c) + 525*I*e^(6*I*d*x + 6*I*c) + 189*I*e^(4*I*d*x + 4*I*c) + 45*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-9*I*d*x - 9*I*c)/(a^2*d)","A",0
130,1,194,0,0.561595," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{15360 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 5760 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 1280 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i}{105 \, {\left(a^{3} d e^{\left(20 i \, d x + 20 i \, c\right)} + 10 \, a^{3} d e^{\left(18 i \, d x + 18 i \, c\right)} + 45 \, a^{3} d e^{\left(16 i \, d x + 16 i \, c\right)} + 120 \, a^{3} d e^{\left(14 i \, d x + 14 i \, c\right)} + 210 \, a^{3} d e^{\left(12 i \, d x + 12 i \, c\right)} + 252 \, a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 210 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 120 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 45 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 10 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/105*(15360*I*e^(6*I*d*x + 6*I*c) + 5760*I*e^(4*I*d*x + 4*I*c) + 1280*I*e^(2*I*d*x + 2*I*c) + 128*I)/(a^3*d*e^(20*I*d*x + 20*I*c) + 10*a^3*d*e^(18*I*d*x + 18*I*c) + 45*a^3*d*e^(16*I*d*x + 16*I*c) + 120*a^3*d*e^(14*I*d*x + 14*I*c) + 210*a^3*d*e^(12*I*d*x + 12*I*c) + 252*a^3*d*e^(10*I*d*x + 10*I*c) + 210*a^3*d*e^(8*I*d*x + 8*I*c) + 120*a^3*d*e^(6*I*d*x + 6*I*c) + 45*a^3*d*e^(4*I*d*x + 4*I*c) + 10*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
131,1,153,0,0.576442," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{896 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 256 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i}{21 \, {\left(a^{3} d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, a^{3} d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, a^{3} d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/21*(896*I*e^(4*I*d*x + 4*I*c) + 256*I*e^(2*I*d*x + 2*I*c) + 32*I)/(a^3*d*e^(16*I*d*x + 16*I*c) + 8*a^3*d*e^(14*I*d*x + 14*I*c) + 28*a^3*d*e^(12*I*d*x + 12*I*c) + 56*a^3*d*e^(10*I*d*x + 10*I*c) + 70*a^3*d*e^(8*I*d*x + 8*I*c) + 56*a^3*d*e^(6*I*d*x + 6*I*c) + 28*a^3*d*e^(4*I*d*x + 4*I*c) + 8*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
132,1,112,0,0.597149," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{192 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i}{15 \, {\left(a^{3} d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/15*(192*I*e^(2*I*d*x + 2*I*c) + 32*I)/(a^3*d*e^(12*I*d*x + 12*I*c) + 6*a^3*d*e^(10*I*d*x + 10*I*c) + 15*a^3*d*e^(8*I*d*x + 8*I*c) + 20*a^3*d*e^(6*I*d*x + 6*I*c) + 15*a^3*d*e^(4*I*d*x + 4*I*c) + 6*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
133,1,69,0,0.575722," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 i}{a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d}"," ",0,"4*I/(a^3*d*e^(8*I*d*x + 8*I*c) + 4*a^3*d*e^(6*I*d*x + 6*I*c) + 6*a^3*d*e^(4*I*d*x + 4*I*c) + 4*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
134,1,110,0,0.731094," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, d x + {\left(16 \, d x - 4 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 8 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 6 i}{a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d}"," ",0,"(8*d*x*e^(4*I*d*x + 4*I*c) + 8*d*x + (16*d*x - 4*I)*e^(2*I*d*x + 2*I*c) + (4*I*e^(4*I*d*x + 4*I*c) + 8*I*e^(2*I*d*x + 2*I*c) + 4*I)*log(e^(2*I*d*x + 2*I*c) + 1) - 6*I)/(a^3*d*e^(4*I*d*x + 4*I*c) + 2*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
135,1,55,0,0.521454," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, d x e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - i\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{a^{3} d}"," ",0,"-(2*d*x*e^(2*I*d*x + 2*I*c) + I*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - I)*e^(-2*I*d*x - 2*I*c)/(a^3*d)","A",0
136,1,30,0,0.579476," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{8 \, a^{3} d}"," ",0,"1/8*(2*I*e^(2*I*d*x + 2*I*c) + I)*e^(-4*I*d*x - 4*I*c)/(a^3*d)","A",0
137,1,54,0,0.434945," ","integrate(1/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(12 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + 18 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 9 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{96 \, a^{3} d}"," ",0,"1/96*(12*d*x*e^(6*I*d*x + 6*I*c) + 18*I*e^(4*I*d*x + 4*I*c) + 9*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
138,1,76,0,0.548820," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(120 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} - 12 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 120 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 60 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 20 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{768 \, a^{3} d}"," ",0,"1/768*(120*d*x*e^(8*I*d*x + 8*I*c) - 12*I*e^(10*I*d*x + 10*I*c) + 120*I*e^(6*I*d*x + 6*I*c) + 60*I*e^(4*I*d*x + 4*I*c) + 20*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-8*I*d*x - 8*I*c)/(a^3*d)","A",0
139,1,98,0,0.542350," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(840 \, d x e^{\left(10 i \, d x + 10 i \, c\right)} - 10 i \, e^{\left(14 i \, d x + 14 i \, c\right)} - 140 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 700 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 350 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 140 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 35 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i\right)} e^{\left(-10 i \, d x - 10 i \, c\right)}}{5120 \, a^{3} d}"," ",0,"1/5120*(840*d*x*e^(10*I*d*x + 10*I*c) - 10*I*e^(14*I*d*x + 14*I*c) - 140*I*e^(12*I*d*x + 12*I*c) + 700*I*e^(8*I*d*x + 8*I*c) + 350*I*e^(6*I*d*x + 6*I*c) + 140*I*e^(4*I*d*x + 4*I*c) + 35*I*e^(2*I*d*x + 2*I*c) + 4*I)*e^(-10*I*d*x - 10*I*c)/(a^3*d)","A",0
140,1,278,0,0.521278," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{105 \, {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 210 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 980 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 1792 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 1580 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 210 i \, e^{\left(i \, d x + i \, c\right)}}{120 \, {\left(a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/120*(105*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 105*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 210*I*e^(9*I*d*x + 9*I*c) - 980*I*e^(7*I*d*x + 7*I*c) - 1792*I*e^(5*I*d*x + 5*I*c) - 1580*I*e^(3*I*d*x + 3*I*c) + 210*I*e^(I*d*x + I*c))/(a^3*d*e^(10*I*d*x + 10*I*c) + 5*a^3*d*e^(8*I*d*x + 8*I*c) + 10*a^3*d*e^(6*I*d*x + 6*I*c) + 10*a^3*d*e^(4*I*d*x + 4*I*c) + 5*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
141,1,182,0,0.748480," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 30 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 80 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 66 i \, e^{\left(i \, d x + i \, c\right)}}{6 \, {\left(a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/6*(15*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 15*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 30*I*e^(5*I*d*x + 5*I*c) - 80*I*e^(3*I*d*x + 3*I*c) - 66*I*e^(I*d*x + I*c))/(a^3*d*e^(6*I*d*x + 6*I*c) + 3*a^3*d*e^(4*I*d*x + 4*I*c) + 3*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
142,1,112,0,0.537959," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, {\left(e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i}{a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}}"," ",0,"-(3*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c))*log(e^(I*d*x + I*c) + I) - 3*(e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c))*log(e^(I*d*x + I*c) - I) - 6*I*e^(2*I*d*x + 2*I*c) - 4*I)/(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))","A",0
143,1,17,0,0.507677," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{i \, e^{\left(-3 i \, d x - 3 i \, c\right)}}{3 \, a^{3} d}"," ",0,"1/3*I*e^(-3*I*d*x - 3*I*c)/(a^3*d)","A",0
144,1,41,0,0.488830," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(15 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 10 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{60 \, a^{3} d}"," ",0,"1/60*(15*I*e^(4*I*d*x + 4*I*c) + 10*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-5*I*d*x - 5*I*c)/(a^3*d)","A",0
145,1,63,0,0.598277," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-35 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 140 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 70 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 28 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{560 \, a^{3} d}"," ",0,"1/560*(-35*I*e^(8*I*d*x + 8*I*c) + 140*I*e^(6*I*d*x + 6*I*c) + 70*I*e^(4*I*d*x + 4*I*c) + 28*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-7*I*d*x - 7*I*c)/(a^3*d)","A",0
146,1,85,0,0.659052," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-21 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 378 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 945 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 420 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 189 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 54 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i\right)} e^{\left(-9 i \, d x - 9 i \, c\right)}}{4032 \, a^{3} d}"," ",0,"1/4032*(-21*I*e^(12*I*d*x + 12*I*c) - 378*I*e^(10*I*d*x + 10*I*c) + 945*I*e^(8*I*d*x + 8*I*c) + 420*I*e^(6*I*d*x + 6*I*c) + 189*I*e^(4*I*d*x + 4*I*c) + 54*I*e^(2*I*d*x + 2*I*c) + 7*I)*e^(-9*I*d*x - 9*I*c)/(a^3*d)","A",0
147,1,107,0,0.418198," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-99 i \, e^{\left(16 i \, d x + 16 i \, c\right)} - 1320 i \, e^{\left(14 i \, d x + 14 i \, c\right)} - 13860 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 27720 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 11550 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 5544 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 1980 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 440 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 45 i\right)} e^{\left(-11 i \, d x - 11 i \, c\right)}}{126720 \, a^{3} d}"," ",0,"1/126720*(-99*I*e^(16*I*d*x + 16*I*c) - 1320*I*e^(14*I*d*x + 14*I*c) - 13860*I*e^(12*I*d*x + 12*I*c) + 27720*I*e^(10*I*d*x + 10*I*c) + 11550*I*e^(8*I*d*x + 8*I*c) + 5544*I*e^(6*I*d*x + 6*I*c) + 1980*I*e^(4*I*d*x + 4*I*c) + 440*I*e^(2*I*d*x + 2*I*c) + 45*I)*e^(-11*I*d*x - 11*I*c)/(a^3*d)","A",0
148,1,168,0,0.542465," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{4608 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 1152 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i}{63 \, {\left(a^{4} d e^{\left(18 i \, d x + 18 i \, c\right)} + 9 \, a^{4} d e^{\left(16 i \, d x + 16 i \, c\right)} + 36 \, a^{4} d e^{\left(14 i \, d x + 14 i \, c\right)} + 84 \, a^{4} d e^{\left(12 i \, d x + 12 i \, c\right)} + 126 \, a^{4} d e^{\left(10 i \, d x + 10 i \, c\right)} + 126 \, a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} + 84 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 36 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 9 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/63*(4608*I*e^(4*I*d*x + 4*I*c) + 1152*I*e^(2*I*d*x + 2*I*c) + 128*I)/(a^4*d*e^(18*I*d*x + 18*I*c) + 9*a^4*d*e^(16*I*d*x + 16*I*c) + 36*a^4*d*e^(14*I*d*x + 14*I*c) + 84*a^4*d*e^(12*I*d*x + 12*I*c) + 126*a^4*d*e^(10*I*d*x + 10*I*c) + 126*a^4*d*e^(8*I*d*x + 8*I*c) + 84*a^4*d*e^(6*I*d*x + 6*I*c) + 36*a^4*d*e^(4*I*d*x + 4*I*c) + 9*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","B",0
149,1,127,0,0.659540," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{448 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 64 i}{21 \, {\left(a^{4} d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, a^{4} d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, a^{4} d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/21*(448*I*e^(2*I*d*x + 2*I*c) + 64*I)/(a^4*d*e^(14*I*d*x + 14*I*c) + 7*a^4*d*e^(12*I*d*x + 12*I*c) + 21*a^4*d*e^(10*I*d*x + 10*I*c) + 35*a^4*d*e^(8*I*d*x + 8*I*c) + 35*a^4*d*e^(6*I*d*x + 6*I*c) + 21*a^4*d*e^(4*I*d*x + 4*I*c) + 7*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","B",0
150,1,84,0,0.595507," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{32 i}{5 \, {\left(a^{4} d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"32/5*I/(a^4*d*e^(10*I*d*x + 10*I*c) + 5*a^4*d*e^(8*I*d*x + 8*I*c) + 10*a^4*d*e^(6*I*d*x + 6*I*c) + 10*a^4*d*e^(4*I*d*x + 4*I*c) + 5*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","B",0
151,1,153,0,0.497941," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{48 \, d x e^{\left(6 i \, d x + 6 i \, c\right)} + 48 \, d x + {\left(144 \, d x - 24 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(144 \, d x - 60 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + {\left(24 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 72 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 72 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 24 i\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 44 i}{3 \, {\left(a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/3*(48*d*x*e^(6*I*d*x + 6*I*c) + 48*d*x + (144*d*x - 24*I)*e^(4*I*d*x + 4*I*c) + (144*d*x - 60*I)*e^(2*I*d*x + 2*I*c) + (24*I*e^(6*I*d*x + 6*I*c) + 72*I*e^(4*I*d*x + 4*I*c) + 72*I*e^(2*I*d*x + 2*I*c) + 24*I)*log(e^(2*I*d*x + 2*I*c) + 1) - 44*I)/(a^4*d*e^(6*I*d*x + 6*I*c) + 3*a^4*d*e^(4*I*d*x + 4*I*c) + 3*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","A",0
152,1,101,0,0.618729," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{8 \, d x e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(8 \, d x - 4 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(-4 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 2 i}{a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)}}"," ",0,"-(8*d*x*e^(4*I*d*x + 4*I*c) + (8*d*x - 4*I)*e^(2*I*d*x + 2*I*c) - (-4*I*e^(4*I*d*x + 4*I*c) - 4*I*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 2*I)/(a^4*d*e^(4*I*d*x + 4*I*c) + a^4*d*e^(2*I*d*x + 2*I*c))","A",0
153,1,17,0,0.662246," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{i \, e^{\left(-4 i \, d x - 4 i \, c\right)}}{4 \, a^{4} d}"," ",0,"1/4*I*e^(-4*I*d*x - 4*I*c)/(a^4*d)","A",0
154,1,41,0,0.579829," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{24 \, a^{4} d}"," ",0,"1/24*(3*I*e^(4*I*d*x + 4*I*c) + 3*I*e^(2*I*d*x + 2*I*c) + I)*e^(-6*I*d*x - 6*I*c)/(a^4*d)","A",0
155,1,65,0,0.397823," ","integrate(1/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(24 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} + 48 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 36 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*(24*d*x*e^(8*I*d*x + 8*I*c) + 48*I*e^(6*I*d*x + 6*I*c) + 36*I*e^(4*I*d*x + 4*I*c) + 16*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
156,1,87,0,0.642857," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(120 \, d x e^{\left(10 i \, d x + 10 i \, c\right)} - 10 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 150 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 100 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 50 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 15 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-10 i \, d x - 10 i \, c\right)}}{1280 \, a^{4} d}"," ",0,"1/1280*(120*d*x*e^(10*I*d*x + 10*I*c) - 10*I*e^(12*I*d*x + 12*I*c) + 150*I*e^(8*I*d*x + 8*I*c) + 100*I*e^(6*I*d*x + 6*I*c) + 50*I*e^(4*I*d*x + 4*I*c) + 15*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-10*I*d*x - 10*I*c)/(a^4*d)","A",0
157,1,109,0,0.561232," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(1680 \, d x e^{\left(12 i \, d x + 12 i \, c\right)} - 15 i \, e^{\left(16 i \, d x + 16 i \, c\right)} - 240 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 1680 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 1050 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 560 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 210 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 48 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-12 i \, d x - 12 i \, c\right)}}{15360 \, a^{4} d}"," ",0,"1/15360*(1680*d*x*e^(12*I*d*x + 12*I*c) - 15*I*e^(16*I*d*x + 16*I*c) - 240*I*e^(14*I*d*x + 14*I*c) + 1680*I*e^(10*I*d*x + 10*I*c) + 1050*I*e^(8*I*d*x + 8*I*c) + 560*I*e^(6*I*d*x + 6*I*c) + 210*I*e^(4*I*d*x + 4*I*c) + 48*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-12*I*d*x - 12*I*c)/(a^4*d)","A",0
158,1,230,0,0.511517," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{105 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 210 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 770 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 1022 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 558 i \, e^{\left(i \, d x + i \, c\right)}}{24 \, {\left(a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/24*(105*(e^(8*I*d*x + 8*I*c) + 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) + I) - 105*(e^(8*I*d*x + 8*I*c) + 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) + 1)*log(e^(I*d*x + I*c) - I) - 210*I*e^(7*I*d*x + 7*I*c) - 770*I*e^(5*I*d*x + 5*I*c) - 1022*I*e^(3*I*d*x + 3*I*c) - 558*I*e^(I*d*x + I*c))/(a^4*d*e^(8*I*d*x + 8*I*c) + 4*a^4*d*e^(6*I*d*x + 6*I*c) + 6*a^4*d*e^(4*I*d*x + 4*I*c) + 4*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","A",0
159,1,160,0,0.456910," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","-\frac{15 \, {\left(e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 15 \, {\left(e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, e^{\left(3 i \, d x + 3 i \, c\right)} + e^{\left(i \, d x + i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 30 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 50 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 16 i}{2 \, {\left(a^{4} d e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{4} d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"-1/2*(15*(e^(5*I*d*x + 5*I*c) + 2*e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c))*log(e^(I*d*x + I*c) + I) - 15*(e^(5*I*d*x + 5*I*c) + 2*e^(3*I*d*x + 3*I*c) + e^(I*d*x + I*c))*log(e^(I*d*x + I*c) - I) - 30*I*e^(4*I*d*x + 4*I*c) - 50*I*e^(2*I*d*x + 2*I*c) - 16*I)/(a^4*d*e^(5*I*d*x + 5*I*c) + 2*a^4*d*e^(3*I*d*x + 3*I*c) + a^4*d*e^(I*d*x + I*c))","A",0
160,1,76,0,0.520044," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(3 \, e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3 \, e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{3 \, a^{4} d}"," ",0,"1/3*(3*e^(3*I*d*x + 3*I*c)*log(e^(I*d*x + I*c) + I) - 3*e^(3*I*d*x + 3*I*c)*log(e^(I*d*x + I*c) - I) - 6*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-3*I*d*x - 3*I*c)/(a^4*d)","A",0
161,1,30,0,0.556459," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{30 \, a^{4} d}"," ",0,"1/30*(5*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-5*I*d*x - 5*I*c)/(a^4*d)","A",0
162,1,52,0,0.537705," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(35 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 35 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 21 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{280 \, a^{4} d}"," ",0,"1/280*(35*I*e^(6*I*d*x + 6*I*c) + 35*I*e^(4*I*d*x + 4*I*c) + 21*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-7*I*d*x - 7*I*c)/(a^4*d)","A",0
163,1,74,0,0.525289," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(-63 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 315 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 210 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 126 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 45 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i\right)} e^{\left(-9 i \, d x - 9 i \, c\right)}}{2016 \, a^{4} d}"," ",0,"1/2016*(-63*I*e^(10*I*d*x + 10*I*c) + 315*I*e^(8*I*d*x + 8*I*c) + 210*I*e^(6*I*d*x + 6*I*c) + 126*I*e^(4*I*d*x + 4*I*c) + 45*I*e^(2*I*d*x + 2*I*c) + 7*I)*e^(-9*I*d*x - 9*I*c)/(a^4*d)","A",0
164,1,96,0,0.446033," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(-33 i \, e^{\left(14 i \, d x + 14 i \, c\right)} - 693 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 2079 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 1155 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 693 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 297 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 77 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 9 i\right)} e^{\left(-11 i \, d x - 11 i \, c\right)}}{12672 \, a^{4} d}"," ",0,"1/12672*(-33*I*e^(14*I*d*x + 14*I*c) - 693*I*e^(12*I*d*x + 12*I*c) + 2079*I*e^(10*I*d*x + 10*I*c) + 1155*I*e^(8*I*d*x + 8*I*c) + 693*I*e^(6*I*d*x + 6*I*c) + 297*I*e^(4*I*d*x + 4*I*c) + 77*I*e^(2*I*d*x + 2*I*c) + 9*I)*e^(-11*I*d*x - 11*I*c)/(a^4*d)","A",0
165,1,118,0,0.552363," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(-143 i \, e^{\left(18 i \, d x + 18 i \, c\right)} - 2145 i \, e^{\left(16 i \, d x + 16 i \, c\right)} - 25740 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 60060 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 30030 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 18018 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 8580 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 2860 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 585 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 55 i\right)} e^{\left(-13 i \, d x - 13 i \, c\right)}}{366080 \, a^{4} d}"," ",0,"1/366080*(-143*I*e^(18*I*d*x + 18*I*c) - 2145*I*e^(16*I*d*x + 16*I*c) - 25740*I*e^(14*I*d*x + 14*I*c) + 60060*I*e^(12*I*d*x + 12*I*c) + 30030*I*e^(10*I*d*x + 10*I*c) + 18018*I*e^(8*I*d*x + 8*I*c) + 8580*I*e^(6*I*d*x + 6*I*c) + 2860*I*e^(4*I*d*x + 4*I*c) + 585*I*e^(2*I*d*x + 2*I*c) + 55*I)*e^(-13*I*d*x - 13*I*c)/(a^4*d)","A",0
166,1,269,0,0.638778," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","-\frac{1920 \, d x e^{\left(12 i \, d x + 12 i \, c\right)} + {\left(9600 \, d x - 960 i\right)} e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(19200 \, d x - 4320 i\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(19200 \, d x - 7520 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(9600 \, d x - 6160 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(1920 \, d x - 2192 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - {\left(-960 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 4800 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 9600 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 9600 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 4800 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 960 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 160 i}{5 \, {\left(a^{8} d e^{\left(12 i \, d x + 12 i \, c\right)} + 5 \, a^{8} d e^{\left(10 i \, d x + 10 i \, c\right)} + 10 \, a^{8} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{8} d e^{\left(6 i \, d x + 6 i \, c\right)} + 5 \, a^{8} d e^{\left(4 i \, d x + 4 i \, c\right)} + a^{8} d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"-1/5*(1920*d*x*e^(12*I*d*x + 12*I*c) + (9600*d*x - 960*I)*e^(10*I*d*x + 10*I*c) + (19200*d*x - 4320*I)*e^(8*I*d*x + 8*I*c) + (19200*d*x - 7520*I)*e^(6*I*d*x + 6*I*c) + (9600*d*x - 6160*I)*e^(4*I*d*x + 4*I*c) + (1920*d*x - 2192*I)*e^(2*I*d*x + 2*I*c) - (-960*I*e^(12*I*d*x + 12*I*c) - 4800*I*e^(10*I*d*x + 10*I*c) - 9600*I*e^(8*I*d*x + 8*I*c) - 9600*I*e^(6*I*d*x + 6*I*c) - 4800*I*e^(4*I*d*x + 4*I*c) - 960*I*e^(2*I*d*x + 2*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 160*I)/(a^8*d*e^(12*I*d*x + 12*I*c) + 5*a^8*d*e^(10*I*d*x + 10*I*c) + 10*a^8*d*e^(8*I*d*x + 8*I*c) + 10*a^8*d*e^(6*I*d*x + 6*I*c) + 5*a^8*d*e^(4*I*d*x + 4*I*c) + a^8*d*e^(2*I*d*x + 2*I*c))","B",0
167,1,195,0,0.657448," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{480 \, d x e^{\left(10 i \, d x + 10 i \, c\right)} + {\left(1440 \, d x - 240 i\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(1440 \, d x - 600 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(480 \, d x - 440 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(240 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 720 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 720 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 240 i \, e^{\left(4 i \, d x + 4 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 60 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 12 i}{3 \, {\left(a^{8} d e^{\left(10 i \, d x + 10 i \, c\right)} + 3 \, a^{8} d e^{\left(8 i \, d x + 8 i \, c\right)} + 3 \, a^{8} d e^{\left(6 i \, d x + 6 i \, c\right)} + a^{8} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/3*(480*d*x*e^(10*I*d*x + 10*I*c) + (1440*d*x - 240*I)*e^(8*I*d*x + 8*I*c) + (1440*d*x - 600*I)*e^(6*I*d*x + 6*I*c) + (480*d*x - 440*I)*e^(4*I*d*x + 4*I*c) + (240*I*e^(10*I*d*x + 10*I*c) + 720*I*e^(8*I*d*x + 8*I*c) + 720*I*e^(6*I*d*x + 6*I*c) + 240*I*e^(4*I*d*x + 4*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 60*I*e^(2*I*d*x + 2*I*c) + 12*I)/(a^8*d*e^(10*I*d*x + 10*I*c) + 3*a^8*d*e^(8*I*d*x + 8*I*c) + 3*a^8*d*e^(6*I*d*x + 6*I*c) + a^8*d*e^(4*I*d*x + 4*I*c))","A",0
168,1,123,0,0.606810," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","-\frac{48 \, d x e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(48 \, d x - 24 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - {\left(-24 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 24 i \, e^{\left(6 i \, d x + 6 i \, c\right)}\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 12 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i}{3 \, {\left(a^{8} d e^{\left(8 i \, d x + 8 i \, c\right)} + a^{8} d e^{\left(6 i \, d x + 6 i \, c\right)}\right)}}"," ",0,"-1/3*(48*d*x*e^(8*I*d*x + 8*I*c) + (48*d*x - 24*I)*e^(6*I*d*x + 6*I*c) - (-24*I*e^(8*I*d*x + 8*I*c) - 24*I*e^(6*I*d*x + 6*I*c))*log(e^(2*I*d*x + 2*I*c) + 1) - 12*I*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c) - 2*I)/(a^8*d*e^(8*I*d*x + 8*I*c) + a^8*d*e^(6*I*d*x + 6*I*c))","A",0
169,1,17,0,0.555500," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{i \, e^{\left(-8 i \, d x - 8 i \, c\right)}}{8 \, a^{8} d}"," ",0,"1/8*I*e^(-8*I*d*x - 8*I*c)/(a^8*d)","A",0
170,1,41,0,0.663455," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(10 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 15 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i\right)} e^{\left(-10 i \, d x - 10 i \, c\right)}}{240 \, a^{8} d}"," ",0,"1/240*(10*I*e^(4*I*d*x + 4*I*c) + 15*I*e^(2*I*d*x + 2*I*c) + 6*I)*e^(-10*I*d*x - 10*I*c)/(a^8*d)","A",0
171,1,63,0,0.699287," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(15 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 40 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 45 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 24 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-12 i \, d x - 12 i \, c\right)}}{960 \, a^{8} d}"," ",0,"1/960*(15*I*e^(8*I*d*x + 8*I*c) + 40*I*e^(6*I*d*x + 6*I*c) + 45*I*e^(4*I*d*x + 4*I*c) + 24*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-12*I*d*x - 12*I*c)/(a^8*d)","A",0
172,1,85,0,0.801327," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(7 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 21 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 35 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 35 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 21 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 7 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-14 i \, d x - 14 i \, c\right)}}{896 \, a^{8} d}"," ",0,"1/896*(7*I*e^(12*I*d*x + 12*I*c) + 21*I*e^(10*I*d*x + 10*I*c) + 35*I*e^(8*I*d*x + 8*I*c) + 35*I*e^(6*I*d*x + 6*I*c) + 21*I*e^(4*I*d*x + 4*I*c) + 7*I*e^(2*I*d*x + 2*I*c) + I)*e^(-14*I*d*x - 14*I*c)/(a^8*d)","B",0
173,1,109,0,0.689146," ","integrate(1/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(1680 \, d x e^{\left(16 i \, d x + 16 i \, c\right)} + 6720 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 11760 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 15680 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 14700 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 9408 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 3920 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 960 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 105 i\right)} e^{\left(-16 i \, d x - 16 i \, c\right)}}{430080 \, a^{8} d}"," ",0,"1/430080*(1680*d*x*e^(16*I*d*x + 16*I*c) + 6720*I*e^(14*I*d*x + 14*I*c) + 11760*I*e^(12*I*d*x + 12*I*c) + 15680*I*e^(10*I*d*x + 10*I*c) + 14700*I*e^(8*I*d*x + 8*I*c) + 9408*I*e^(6*I*d*x + 6*I*c) + 3920*I*e^(4*I*d*x + 4*I*c) + 960*I*e^(2*I*d*x + 2*I*c) + 105*I)*e^(-16*I*d*x - 16*I*c)/(a^8*d)","A",0
174,1,131,0,0.674658," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(5040 \, d x e^{\left(18 i \, d x + 18 i \, c\right)} - 252 i \, e^{\left(20 i \, d x + 20 i \, c\right)} + 11340 i \, e^{\left(16 i \, d x + 16 i \, c\right)} + 15120 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 17640 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 15876 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 10584 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 5040 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 1620 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 315 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 28 i\right)} e^{\left(-18 i \, d x - 18 i \, c\right)}}{516096 \, a^{8} d}"," ",0,"1/516096*(5040*d*x*e^(18*I*d*x + 18*I*c) - 252*I*e^(20*I*d*x + 20*I*c) + 11340*I*e^(16*I*d*x + 16*I*c) + 15120*I*e^(14*I*d*x + 14*I*c) + 17640*I*e^(12*I*d*x + 12*I*c) + 15876*I*e^(10*I*d*x + 10*I*c) + 10584*I*e^(8*I*d*x + 8*I*c) + 5040*I*e^(6*I*d*x + 6*I*c) + 1620*I*e^(4*I*d*x + 4*I*c) + 315*I*e^(2*I*d*x + 2*I*c) + 28*I)*e^(-18*I*d*x - 18*I*c)/(a^8*d)","A",0
175,1,153,0,0.612348," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(55440 \, d x e^{\left(20 i \, d x + 20 i \, c\right)} - 210 i \, e^{\left(24 i \, d x + 24 i \, c\right)} - 5040 i \, e^{\left(22 i \, d x + 22 i \, c\right)} + 92400 i \, e^{\left(18 i \, d x + 18 i \, c\right)} + 103950 i \, e^{\left(16 i \, d x + 16 i \, c\right)} + 110880 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 97020 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 66528 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 34650 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 13200 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 3465 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 560 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 42 i\right)} e^{\left(-20 i \, d x - 20 i \, c\right)}}{3440640 \, a^{8} d}"," ",0,"1/3440640*(55440*d*x*e^(20*I*d*x + 20*I*c) - 210*I*e^(24*I*d*x + 24*I*c) - 5040*I*e^(22*I*d*x + 22*I*c) + 92400*I*e^(18*I*d*x + 18*I*c) + 103950*I*e^(16*I*d*x + 16*I*c) + 110880*I*e^(14*I*d*x + 14*I*c) + 97020*I*e^(12*I*d*x + 12*I*c) + 66528*I*e^(10*I*d*x + 10*I*c) + 34650*I*e^(8*I*d*x + 8*I*c) + 13200*I*e^(6*I*d*x + 6*I*c) + 3465*I*e^(4*I*d*x + 4*I*c) + 560*I*e^(2*I*d*x + 2*I*c) + 42*I)*e^(-20*I*d*x - 20*I*c)/(a^8*d)","A",0
176,1,267,0,0.817974," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{3465 \, {\left(e^{\left(11 i \, d x + 11 i \, c\right)} + 4 \, e^{\left(9 i \, d x + 9 i \, c\right)} + 6 \, e^{\left(7 i \, d x + 7 i \, c\right)} + 4 \, e^{\left(5 i \, d x + 5 i \, c\right)} + e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 3465 \, {\left(e^{\left(11 i \, d x + 11 i \, c\right)} + 4 \, e^{\left(9 i \, d x + 9 i \, c\right)} + 6 \, e^{\left(7 i \, d x + 7 i \, c\right)} + 4 \, e^{\left(5 i \, d x + 5 i \, c\right)} + e^{\left(3 i \, d x + 3 i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 6930 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 25410 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 33726 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 18414 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 2816 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 256 i}{24 \, {\left(a^{8} d e^{\left(11 i \, d x + 11 i \, c\right)} + 4 \, a^{8} d e^{\left(9 i \, d x + 9 i \, c\right)} + 6 \, a^{8} d e^{\left(7 i \, d x + 7 i \, c\right)} + 4 \, a^{8} d e^{\left(5 i \, d x + 5 i \, c\right)} + a^{8} d e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/24*(3465*(e^(11*I*d*x + 11*I*c) + 4*e^(9*I*d*x + 9*I*c) + 6*e^(7*I*d*x + 7*I*c) + 4*e^(5*I*d*x + 5*I*c) + e^(3*I*d*x + 3*I*c))*log(e^(I*d*x + I*c) + I) - 3465*(e^(11*I*d*x + 11*I*c) + 4*e^(9*I*d*x + 9*I*c) + 6*e^(7*I*d*x + 7*I*c) + 4*e^(5*I*d*x + 5*I*c) + e^(3*I*d*x + 3*I*c))*log(e^(I*d*x + I*c) - I) - 6930*I*e^(10*I*d*x + 10*I*c) - 25410*I*e^(8*I*d*x + 8*I*c) - 33726*I*e^(6*I*d*x + 6*I*c) - 18414*I*e^(4*I*d*x + 4*I*c) - 2816*I*e^(2*I*d*x + 2*I*c) + 256*I)/(a^8*d*e^(11*I*d*x + 11*I*c) + 4*a^8*d*e^(9*I*d*x + 9*I*c) + 6*a^8*d*e^(7*I*d*x + 7*I*c) + 4*a^8*d*e^(5*I*d*x + 5*I*c) + a^8*d*e^(3*I*d*x + 3*I*c))","A",0
177,1,182,0,0.753772," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","-\frac{315 \, {\left(e^{\left(9 i \, d x + 9 i \, c\right)} + 2 \, e^{\left(7 i \, d x + 7 i \, c\right)} + e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 315 \, {\left(e^{\left(9 i \, d x + 9 i \, c\right)} + 2 \, e^{\left(7 i \, d x + 7 i \, c\right)} + e^{\left(5 i \, d x + 5 i \, c\right)}\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 630 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 1050 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 336 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 48 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 16 i}{10 \, {\left(a^{8} d e^{\left(9 i \, d x + 9 i \, c\right)} + 2 \, a^{8} d e^{\left(7 i \, d x + 7 i \, c\right)} + a^{8} d e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}"," ",0,"-1/10*(315*(e^(9*I*d*x + 9*I*c) + 2*e^(7*I*d*x + 7*I*c) + e^(5*I*d*x + 5*I*c))*log(e^(I*d*x + I*c) + I) - 315*(e^(9*I*d*x + 9*I*c) + 2*e^(7*I*d*x + 7*I*c) + e^(5*I*d*x + 5*I*c))*log(e^(I*d*x + I*c) - I) - 630*I*e^(8*I*d*x + 8*I*c) - 1050*I*e^(6*I*d*x + 6*I*c) - 336*I*e^(4*I*d*x + 4*I*c) + 48*I*e^(2*I*d*x + 2*I*c) - 16*I)/(a^8*d*e^(9*I*d*x + 9*I*c) + 2*a^8*d*e^(7*I*d*x + 7*I*c) + a^8*d*e^(5*I*d*x + 5*I*c))","A",0
178,1,98,0,0.526955," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(105 \, e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(e^{\left(i \, d x + i \, c\right)} + i\right) - 105 \, e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(e^{\left(i \, d x + i \, c\right)} - i\right) - 210 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 70 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 42 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 30 i\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{105 \, a^{8} d}"," ",0,"1/105*(105*e^(7*I*d*x + 7*I*c)*log(e^(I*d*x + I*c) + I) - 105*e^(7*I*d*x + 7*I*c)*log(e^(I*d*x + I*c) - I) - 210*I*e^(6*I*d*x + 6*I*c) + 70*I*e^(4*I*d*x + 4*I*c) - 42*I*e^(2*I*d*x + 2*I*c) + 30*I)*e^(-7*I*d*x - 7*I*c)/(a^8*d)","A",0
179,1,30,0,0.471821," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(9 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i\right)} e^{\left(-9 i \, d x - 9 i \, c\right)}}{126 \, a^{8} d}"," ",0,"1/126*(9*I*e^(2*I*d*x + 2*I*c) + 7*I)*e^(-9*I*d*x - 9*I*c)/(a^8*d)","A",0
180,1,52,0,0.464009," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(231 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 495 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 385 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 105 i\right)} e^{\left(-11 i \, d x - 11 i \, c\right)}}{9240 \, a^{8} d}"," ",0,"1/9240*(231*I*e^(6*I*d*x + 6*I*c) + 495*I*e^(4*I*d*x + 4*I*c) + 385*I*e^(2*I*d*x + 2*I*c) + 105*I)*e^(-11*I*d*x - 11*I*c)/(a^8*d)","A",0
181,1,74,0,0.578403," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(3003 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 9009 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 12870 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10010 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4095 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 693 i\right)} e^{\left(-13 i \, d x - 13 i \, c\right)}}{288288 \, a^{8} d}"," ",0,"1/288288*(3003*I*e^(10*I*d*x + 10*I*c) + 9009*I*e^(8*I*d*x + 8*I*c) + 12870*I*e^(6*I*d*x + 6*I*c) + 10010*I*e^(4*I*d*x + 4*I*c) + 4095*I*e^(2*I*d*x + 2*I*c) + 693*I)*e^(-13*I*d*x - 13*I*c)/(a^8*d)","A",0
182,1,96,0,0.591067," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(6435 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 15015 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 27027 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 32175 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 25025 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 12285 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3465 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 429 i\right)} e^{\left(-15 i \, d x - 15 i \, c\right)}}{823680 \, a^{8} d}"," ",0,"1/823680*(6435*I*e^(14*I*d*x + 14*I*c) + 15015*I*e^(12*I*d*x + 12*I*c) + 27027*I*e^(10*I*d*x + 10*I*c) + 32175*I*e^(8*I*d*x + 8*I*c) + 25025*I*e^(6*I*d*x + 6*I*c) + 12285*I*e^(4*I*d*x + 4*I*c) + 3465*I*e^(2*I*d*x + 2*I*c) + 429*I)*e^(-15*I*d*x - 15*I*c)/(a^8*d)","A",0
183,1,118,0,0.548068," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(-12155 i \, e^{\left(18 i \, d x + 18 i \, c\right)} + 109395 i \, e^{\left(16 i \, d x + 16 i \, c\right)} + 145860 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 204204 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 218790 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 170170 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 92820 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 33660 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 7293 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 715 i\right)} e^{\left(-17 i \, d x - 17 i \, c\right)}}{6223360 \, a^{8} d}"," ",0,"1/6223360*(-12155*I*e^(18*I*d*x + 18*I*c) + 109395*I*e^(16*I*d*x + 16*I*c) + 145860*I*e^(14*I*d*x + 14*I*c) + 204204*I*e^(12*I*d*x + 12*I*c) + 218790*I*e^(10*I*d*x + 10*I*c) + 170170*I*e^(8*I*d*x + 8*I*c) + 92820*I*e^(6*I*d*x + 6*I*c) + 33660*I*e^(4*I*d*x + 4*I*c) + 7293*I*e^(2*I*d*x + 2*I*c) + 715*I)*e^(-17*I*d*x - 17*I*c)/(a^8*d)","A",0
184,1,140,0,0.568637," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^8,x, algorithm=""fricas"")","\frac{{\left(-4199 i \, e^{\left(22 i \, d x + 22 i \, c\right)} - 138567 i \, e^{\left(20 i \, d x + 20 i \, c\right)} + 692835 i \, e^{\left(18 i \, d x + 18 i \, c\right)} + 692835 i \, e^{\left(16 i \, d x + 16 i \, c\right)} + 831402 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 831402 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 646646 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 377910 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 159885 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 46189 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 8151 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 663 i\right)} e^{\left(-19 i \, d x - 19 i \, c\right)}}{25798656 \, a^{8} d}"," ",0,"1/25798656*(-4199*I*e^(22*I*d*x + 22*I*c) - 138567*I*e^(20*I*d*x + 20*I*c) + 692835*I*e^(18*I*d*x + 18*I*c) + 692835*I*e^(16*I*d*x + 16*I*c) + 831402*I*e^(14*I*d*x + 14*I*c) + 831402*I*e^(12*I*d*x + 12*I*c) + 646646*I*e^(10*I*d*x + 10*I*c) + 377910*I*e^(8*I*d*x + 8*I*c) + 159885*I*e^(6*I*d*x + 6*I*c) + 46189*I*e^(4*I*d*x + 4*I*c) + 8151*I*e^(2*I*d*x + 2*I*c) + 663*I)*e^(-19*I*d*x - 19*I*c)/(a^8*d)","A",0
185,0,0,0,0.411873," ","integrate((e*sec(d*x+c))^(7/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-42 i \, a e^{3} e^{\left(7 i \, d x + 7 i \, c\right)} - 154 i \, a e^{3} e^{\left(5 i \, d x + 5 i \, c\right)} - 46 i \, a e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 14 i \, a e^{3} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 35 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(\frac{3 i \, \sqrt{2} a e^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, d}, x\right)}{35 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/35*(sqrt(2)*(-42*I*a*e^3*e^(7*I*d*x + 7*I*c) - 154*I*a*e^3*e^(5*I*d*x + 5*I*c) - 46*I*a*e^3*e^(3*I*d*x + 3*I*c) - 14*I*a*e^3*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 35*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*integral(3/5*I*sqrt(2)*a*e^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/d, x))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","F",0
186,0,0,0,0.787670," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-10 i \, a e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 24 i \, a e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 10 i \, a e^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} a e^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, d}, x\right)}{15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/15*(sqrt(2)*(-10*I*a*e^2*e^(4*I*d*x + 4*I*c) + 24*I*a*e^2*e^(2*I*d*x + 2*I*c) + 10*I*a*e^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 15*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*integral(-1/3*I*sqrt(2)*a*e^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/d, x))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","F",0
187,0,0,0,0.443216," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-6 i \, a e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 i \, a e e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(\frac{i \, \sqrt{2} a e \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d}, x\right)}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(sqrt(2)*(-6*I*a*e*e^(3*I*d*x + 3*I*c) - 2*I*a*e*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 3*(d*e^(2*I*d*x + 2*I*c) + d)*integral(I*sqrt(2)*a*e*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/d, x))/(d*e^(2*I*d*x + 2*I*c) + d)","F",0
188,0,0,0,0.858901," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 i \, \sqrt{2} a \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + d {\rm integral}\left(-\frac{i \, \sqrt{2} a \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{d}, x\right)}{d}"," ",0,"(2*I*sqrt(2)*a*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + d*integral(-I*sqrt(2)*a*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/d, x))/d","F",0
189,0,0,0,0.679930," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + {\left(d e e^{\left(i \, d x + i \, c\right)} - d e\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a e^{\left(i \, d x + i \, c\right)} - i \, a\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e e^{\left(i \, d x + i \, c\right)}}, x\right)}{d e e^{\left(i \, d x + i \, c\right)} - d e}"," ",0,"(sqrt(2)*(-2*I*a*e^(2*I*d*x + 2*I*c) - 2*I*a)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + (d*e*e^(I*d*x + I*c) - d*e)*integral(sqrt(2)*(-I*a*e^(2*I*d*x + 2*I*c) - 2*I*a*e^(I*d*x + I*c) - I*a)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e*e^(3*I*d*x + 3*I*c) - 2*d*e*e^(2*I*d*x + 2*I*c) + d*e*e^(I*d*x + I*c)), x))/(d*e*e^(I*d*x + I*c) - d*e)","F",0
190,0,0,0,0.480474," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, d e^{2} {\rm integral}\left(-\frac{i \, \sqrt{2} a \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, d e^{2}}, x\right) + \sqrt{2} {\left(-i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, d e^{2}}"," ",0,"1/3*(3*d*e^2*integral(-1/3*I*sqrt(2)*a*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^2), x) + sqrt(2)*(-I*a*e^(2*I*d*x + 2*I*c) - I*a)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^2)","F",0
191,0,0,0,0.532970," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a e^{\left(5 i \, d x + 5 i \, c\right)} + i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 7 i \, a e^{\left(i \, d x + i \, c\right)} - 5 i \, a\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 10 \, {\left(d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - d e^{3} e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-3 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, a e^{\left(i \, d x + i \, c\right)} - 3 i \, a\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(d e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{10 \, {\left(d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - d e^{3} e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/10*(sqrt(2)*(-I*a*e^(5*I*d*x + 5*I*c) + I*a*e^(4*I*d*x + 4*I*c) - 8*I*a*e^(3*I*d*x + 3*I*c) - 4*I*a*e^(2*I*d*x + 2*I*c) - 7*I*a*e^(I*d*x + I*c) - 5*I*a)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 10*(d*e^3*e^(2*I*d*x + 2*I*c) - d*e^3*e^(I*d*x + I*c))*integral(1/5*sqrt(2)*(-3*I*a*e^(2*I*d*x + 2*I*c) - 6*I*a*e^(I*d*x + I*c) - 3*I*a)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^3*e^(3*I*d*x + 3*I*c) - 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3*e^(I*d*x + I*c)), x))/(d*e^3*e^(2*I*d*x + 2*I*c) - d*e^3*e^(I*d*x + I*c))","F",0
192,0,0,0,0.739840," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(84 \, d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(-\frac{5 i \, \sqrt{2} a \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{21 \, d e^{4}}, x\right) + \sqrt{2} {\left(-3 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 19 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 9 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, a\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{84 \, d e^{4}}"," ",0,"1/84*(84*d*e^4*e^(2*I*d*x + 2*I*c)*integral(-5/21*I*sqrt(2)*a*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^4), x) + sqrt(2)*(-3*I*a*e^(6*I*d*x + 6*I*c) - 19*I*a*e^(4*I*d*x + 4*I*c) - 9*I*a*e^(2*I*d*x + 2*I*c) + 7*I*a)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-2*I*d*x - 2*I*c)/(d*e^4)","F",0
193,0,0,0,0.581820," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-42 i \, a^{2} e e^{\left(5 i \, d x + 5 i \, c\right)} - 32 i \, a^{2} e e^{\left(3 i \, d x + 3 i \, c\right)} - 14 i \, a^{2} e e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(\frac{7 i \, \sqrt{2} a^{2} e \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, d}, x\right)}{15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/15*(sqrt(2)*(-42*I*a^2*e*e^(5*I*d*x + 5*I*c) - 32*I*a^2*e*e^(3*I*d*x + 3*I*c) - 14*I*a^2*e*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 15*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*integral(7/5*I*sqrt(2)*a^2*e*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/d, x))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","F",0
194,0,0,0,0.536945," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(14 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 10 i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(-\frac{5 i \, \sqrt{2} a^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, d}, x\right)}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(sqrt(2)*(14*I*a^2*e^(2*I*d*x + 2*I*c) + 10*I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 3*(d*e^(2*I*d*x + 2*I*c) + d)*integral(-5/3*I*sqrt(2)*a^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/d, x))/(d*e^(2*I*d*x + 2*I*c) + d)","F",0
195,0,0,0,0.599460," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{2} e^{\left(i \, d x + i \, c\right)} - 6 i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + {\left(d e e^{\left(i \, d x + i \, c\right)} - d e\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-3 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, a^{2} e^{\left(i \, d x + i \, c\right)} - 3 i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e e^{\left(i \, d x + i \, c\right)}}, x\right)}{d e e^{\left(i \, d x + i \, c\right)} - d e}"," ",0,"(sqrt(2)*(-4*I*a^2*e^(2*I*d*x + 2*I*c) - 2*I*a^2*e^(I*d*x + I*c) - 6*I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + (d*e*e^(I*d*x + I*c) - d*e)*integral(sqrt(2)*(-3*I*a^2*e^(2*I*d*x + 2*I*c) - 6*I*a^2*e^(I*d*x + I*c) - 3*I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e*e^(3*I*d*x + 3*I*c) - 2*d*e*e^(2*I*d*x + 2*I*c) + d*e*e^(I*d*x + I*c)), x))/(d*e*e^(I*d*x + I*c) - d*e)","F",0
196,0,0,0,0.629854," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, d e^{2} {\rm integral}\left(\frac{i \, \sqrt{2} a^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, d e^{2}}, x\right) + \sqrt{2} {\left(-2 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, d e^{2}}"," ",0,"1/3*(3*d*e^2*integral(1/3*I*sqrt(2)*a^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^2), x) + sqrt(2)*(-2*I*a^2*e^(2*I*d*x + 2*I*c) - 2*I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^2)","F",0
197,0,0,0,0.523818," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 3 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, a^{2} e^{\left(i \, d x + i \, c\right)} - 2 i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 5 \, {\left(d e^{3} e^{\left(i \, d x + i \, c\right)} - d e^{3}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{2} e^{\left(i \, d x + i \, c\right)} - i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(d e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{5 \, {\left(d e^{3} e^{\left(i \, d x + i \, c\right)} - d e^{3}\right)}}"," ",0,"1/5*(sqrt(2)*(-I*a^2*e^(4*I*d*x + 4*I*c) + I*a^2*e^(3*I*d*x + 3*I*c) - 3*I*a^2*e^(2*I*d*x + 2*I*c) + I*a^2*e^(I*d*x + I*c) - 2*I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 5*(d*e^3*e^(I*d*x + I*c) - d*e^3)*integral(1/5*sqrt(2)*(-I*a^2*e^(2*I*d*x + 2*I*c) - 2*I*a^2*e^(I*d*x + I*c) - I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^3*e^(3*I*d*x + 3*I*c) - 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3*e^(I*d*x + I*c)), x))/(d*e^3*e^(I*d*x + I*c) - d*e^3)","F",0
198,0,0,0,0.629331," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{14 \, d e^{4} {\rm integral}\left(-\frac{i \, \sqrt{2} a^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{7 \, d e^{4}}, x\right) + \sqrt{2} {\left(-i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{14 \, d e^{4}}"," ",0,"1/14*(14*d*e^4*integral(-1/7*I*sqrt(2)*a^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^4), x) + sqrt(2)*(-I*a^2*e^(4*I*d*x + 4*I*c) - 4*I*a^2*e^(2*I*d*x + 2*I*c) - 3*I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^4)","F",0
199,0,0,0,0.679438," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(9/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a^{2} e^{\left(7 i \, d x + 7 i \, c\right)} + i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 5 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 5 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 19 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 5 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 15 i \, a^{2} e^{\left(i \, d x + i \, c\right)} - 9 i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 36 \, {\left(d e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} - d e^{5} e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{2} e^{\left(i \, d x + i \, c\right)} - i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, {\left(d e^{5} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{5} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{36 \, {\left(d e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} - d e^{5} e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/36*(sqrt(2)*(-I*a^2*e^(7*I*d*x + 7*I*c) + I*a^2*e^(6*I*d*x + 6*I*c) - 5*I*a^2*e^(5*I*d*x + 5*I*c) + 5*I*a^2*e^(4*I*d*x + 4*I*c) - 19*I*a^2*e^(3*I*d*x + 3*I*c) - 5*I*a^2*e^(2*I*d*x + 2*I*c) - 15*I*a^2*e^(I*d*x + I*c) - 9*I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 36*(d*e^5*e^(2*I*d*x + 2*I*c) - d*e^5*e^(I*d*x + I*c))*integral(1/3*sqrt(2)*(-I*a^2*e^(2*I*d*x + 2*I*c) - 2*I*a^2*e^(I*d*x + I*c) - I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^5*e^(3*I*d*x + 3*I*c) - 2*d*e^5*e^(2*I*d*x + 2*I*c) + d*e^5*e^(I*d*x + I*c)), x))/(d*e^5*e^(2*I*d*x + 2*I*c) - d*e^5*e^(I*d*x + I*c))","F",0
200,0,0,0,0.664033," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(11/2),x, algorithm=""fricas"")","\frac{{\left(264 \, d e^{6} e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(-\frac{5 i \, \sqrt{2} a^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{33 \, d e^{6}}, x\right) + \sqrt{2} {\left(-3 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 18 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 56 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 30 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 11 i \, a^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{264 \, d e^{6}}"," ",0,"1/264*(264*d*e^6*e^(2*I*d*x + 2*I*c)*integral(-5/33*I*sqrt(2)*a^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^6), x) + sqrt(2)*(-3*I*a^2*e^(8*I*d*x + 8*I*c) - 18*I*a^2*e^(6*I*d*x + 6*I*c) - 56*I*a^2*e^(4*I*d*x + 4*I*c) - 30*I*a^2*e^(2*I*d*x + 2*I*c) + 11*I*a^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-2*I*d*x - 2*I*c)/(d*e^6)","F",0
201,0,0,0,0.518542," ","integrate((e*sec(d*x+c))^(7/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-462 i \, a^{3} e^{3} e^{\left(11 i \, d x + 11 i \, c\right)} - 2618 i \, a^{3} e^{3} e^{\left(9 i \, d x + 9 i \, c\right)} - 1892 i \, a^{3} e^{3} e^{\left(7 i \, d x + 7 i \, c\right)} - 1740 i \, a^{3} e^{3} e^{\left(5 i \, d x + 5 i \, c\right)} - 814 i \, a^{3} e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 154 i \, a^{3} e^{3} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 231 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(\frac{i \, \sqrt{2} a^{3} e^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d}, x\right)}{231 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/231*(sqrt(2)*(-462*I*a^3*e^3*e^(11*I*d*x + 11*I*c) - 2618*I*a^3*e^3*e^(9*I*d*x + 9*I*c) - 1892*I*a^3*e^3*e^(7*I*d*x + 7*I*c) - 1740*I*a^3*e^3*e^(5*I*d*x + 5*I*c) - 814*I*a^3*e^3*e^(3*I*d*x + 3*I*c) - 154*I*a^3*e^3*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 231*(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)*integral(I*sqrt(2)*a^3*e^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/d, x))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","F",0
202,0,0,0,0.685345," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-390 i \, a^{3} e^{2} e^{\left(8 i \, d x + 8 i \, c\right)} + 2316 i \, a^{3} e^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 2912 i \, a^{3} e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 1716 i \, a^{3} e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 390 i \, a^{3} e^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 315 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(-\frac{13 i \, \sqrt{2} a^{3} e^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{21 \, d}, x\right)}{315 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/315*(sqrt(2)*(-390*I*a^3*e^2*e^(8*I*d*x + 8*I*c) + 2316*I*a^3*e^2*e^(6*I*d*x + 6*I*c) + 2912*I*a^3*e^2*e^(4*I*d*x + 4*I*c) + 1716*I*a^3*e^2*e^(2*I*d*x + 2*I*c) + 390*I*a^3*e^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 315*(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)*integral(-13/21*I*sqrt(2)*a^3*e^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/d, x))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","F",0
203,0,0,0,0.493677," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-462 i \, a^{3} e e^{\left(7 i \, d x + 7 i \, c\right)} - 574 i \, a^{3} e e^{\left(5 i \, d x + 5 i \, c\right)} - 506 i \, a^{3} e e^{\left(3 i \, d x + 3 i \, c\right)} - 154 i \, a^{3} e e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 105 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(\frac{11 i \, \sqrt{2} a^{3} e \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, d}, x\right)}{105 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/105*(sqrt(2)*(-462*I*a^3*e*e^(7*I*d*x + 7*I*c) - 574*I*a^3*e*e^(5*I*d*x + 5*I*c) - 506*I*a^3*e*e^(3*I*d*x + 3*I*c) - 154*I*a^3*e*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 105*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*integral(11/5*I*sqrt(2)*a^3*e*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/d, x))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","F",0
204,0,0,0,0.543606," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(50 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 72 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 30 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 5 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(-\frac{3 i \, \sqrt{2} a^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{d}, x\right)}{5 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/5*(sqrt(2)*(50*I*a^3*e^(4*I*d*x + 4*I*c) + 72*I*a^3*e^(2*I*d*x + 2*I*c) + 30*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 5*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*integral(-3*I*sqrt(2)*a^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/d, x))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","F",0
205,0,0,0,0.823170," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-24 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 18 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 70 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 14 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - 42 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, {\left(d e e^{\left(3 i \, d x + 3 i \, c\right)} - d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e e^{\left(i \, d x + i \, c\right)} - d e\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-7 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 14 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - 7 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e e^{\left(i \, d x + i \, c\right)}}, x\right)}{3 \, {\left(d e e^{\left(3 i \, d x + 3 i \, c\right)} - d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e e^{\left(i \, d x + i \, c\right)} - d e\right)}}"," ",0,"1/3*(sqrt(2)*(-24*I*a^3*e^(4*I*d*x + 4*I*c) - 18*I*a^3*e^(3*I*d*x + 3*I*c) - 70*I*a^3*e^(2*I*d*x + 2*I*c) - 14*I*a^3*e^(I*d*x + I*c) - 42*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 3*(d*e*e^(3*I*d*x + 3*I*c) - d*e*e^(2*I*d*x + 2*I*c) + d*e*e^(I*d*x + I*c) - d*e)*integral(sqrt(2)*(-7*I*a^3*e^(2*I*d*x + 2*I*c) - 14*I*a^3*e^(I*d*x + I*c) - 7*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e*e^(3*I*d*x + 3*I*c) - 2*d*e*e^(2*I*d*x + 2*I*c) + d*e*e^(I*d*x + I*c)), x))/(d*e*e^(3*I*d*x + 3*I*c) - d*e*e^(2*I*d*x + 2*I*c) + d*e*e^(I*d*x + I*c) - d*e)","F",0
206,0,0,0,0.520743," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, d e^{2} {\rm integral}\left(\frac{5 i \, \sqrt{2} a^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, d e^{2}}, x\right) + \sqrt{2} {\left(-4 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 10 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, d e^{2}}"," ",0,"1/3*(3*d*e^2*integral(5/3*I*sqrt(2)*a^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^2), x) + sqrt(2)*(-4*I*a^3*e^(2*I*d*x + 2*I*c) - 10*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^2)","F",0
207,0,0,0,0.667607," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-2 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} + 4 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + 6 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 5 \, {\left(d e^{3} e^{\left(i \, d x + i \, c\right)} - d e^{3}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(3 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + 3 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(d e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{5 \, {\left(d e^{3} e^{\left(i \, d x + i \, c\right)} - d e^{3}\right)}}"," ",0,"1/5*(sqrt(2)*(-2*I*a^3*e^(4*I*d*x + 4*I*c) + 2*I*a^3*e^(3*I*d*x + 3*I*c) + 4*I*a^3*e^(2*I*d*x + 2*I*c) + 2*I*a^3*e^(I*d*x + I*c) + 6*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 5*(d*e^3*e^(I*d*x + I*c) - d*e^3)*integral(1/5*sqrt(2)*(3*I*a^3*e^(2*I*d*x + 2*I*c) + 6*I*a^3*e^(I*d*x + I*c) + 3*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^3*e^(3*I*d*x + 3*I*c) - 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3*e^(I*d*x + I*c)), x))/(d*e^3*e^(I*d*x + I*c) - d*e^3)","F",0
208,0,0,0,0.554248," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{21 \, d e^{4} {\rm integral}\left(\frac{i \, \sqrt{2} a^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{21 \, d e^{4}}, x\right) + \sqrt{2} {\left(-3 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 5 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{21 \, d e^{4}}"," ",0,"1/21*(21*d*e^4*integral(1/21*I*sqrt(2)*a^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^4), x) + sqrt(2)*(-3*I*a^3*e^(4*I*d*x + 4*I*c) - 5*I*a^3*e^(2*I*d*x + 2*I*c) - 2*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^4)","F",0
209,0,0,0,0.524760," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(9/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-5 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 5 i \, a^{3} e^{\left(5 i \, d x + 5 i \, c\right)} - 16 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 23 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 11 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - 12 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 90 \, {\left(d e^{5} e^{\left(i \, d x + i \, c\right)} - d e^{5}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{15 \, {\left(d e^{5} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{5} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{90 \, {\left(d e^{5} e^{\left(i \, d x + i \, c\right)} - d e^{5}\right)}}"," ",0,"1/90*(sqrt(2)*(-5*I*a^3*e^(6*I*d*x + 6*I*c) + 5*I*a^3*e^(5*I*d*x + 5*I*c) - 16*I*a^3*e^(4*I*d*x + 4*I*c) + 16*I*a^3*e^(3*I*d*x + 3*I*c) - 23*I*a^3*e^(2*I*d*x + 2*I*c) + 11*I*a^3*e^(I*d*x + I*c) - 12*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 90*(d*e^5*e^(I*d*x + I*c) - d*e^5)*integral(1/15*sqrt(2)*(-I*a^3*e^(2*I*d*x + 2*I*c) - 2*I*a^3*e^(I*d*x + I*c) - I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^5*e^(3*I*d*x + 3*I*c) - 2*d*e^5*e^(2*I*d*x + 2*I*c) + d*e^5*e^(I*d*x + I*c)), x))/(d*e^5*e^(I*d*x + I*c) - d*e^5)","F",0
210,0,0,0,0.546784," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(11/2),x, algorithm=""fricas"")","\frac{308 \, d e^{6} {\rm integral}\left(-\frac{5 i \, \sqrt{2} a^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{77 \, d e^{6}}, x\right) + \sqrt{2} {\left(-7 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 31 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 61 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 37 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{308 \, d e^{6}}"," ",0,"1/308*(308*d*e^6*integral(-5/77*I*sqrt(2)*a^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^6), x) + sqrt(2)*(-7*I*a^3*e^(6*I*d*x + 6*I*c) - 31*I*a^3*e^(4*I*d*x + 4*I*c) - 61*I*a^3*e^(2*I*d*x + 2*I*c) - 37*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^6)","F",0
211,0,0,0,0.654432," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(13/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-9 i \, a^{3} e^{\left(9 i \, d x + 9 i \, c\right)} + 9 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 50 i \, a^{3} e^{\left(7 i \, d x + 7 i \, c\right)} + 50 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 124 i \, a^{3} e^{\left(5 i \, d x + 5 i \, c\right)} + 124 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 302 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 34 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 219 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - 117 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 936 \, {\left(d e^{7} e^{\left(2 i \, d x + 2 i \, c\right)} - d e^{7} e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-7 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 14 i \, a^{3} e^{\left(i \, d x + i \, c\right)} - 7 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{39 \, {\left(d e^{7} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{7} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{7} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{936 \, {\left(d e^{7} e^{\left(2 i \, d x + 2 i \, c\right)} - d e^{7} e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/936*(sqrt(2)*(-9*I*a^3*e^(9*I*d*x + 9*I*c) + 9*I*a^3*e^(8*I*d*x + 8*I*c) - 50*I*a^3*e^(7*I*d*x + 7*I*c) + 50*I*a^3*e^(6*I*d*x + 6*I*c) - 124*I*a^3*e^(5*I*d*x + 5*I*c) + 124*I*a^3*e^(4*I*d*x + 4*I*c) - 302*I*a^3*e^(3*I*d*x + 3*I*c) - 34*I*a^3*e^(2*I*d*x + 2*I*c) - 219*I*a^3*e^(I*d*x + I*c) - 117*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 936*(d*e^7*e^(2*I*d*x + 2*I*c) - d*e^7*e^(I*d*x + I*c))*integral(1/39*sqrt(2)*(-7*I*a^3*e^(2*I*d*x + 2*I*c) - 14*I*a^3*e^(I*d*x + I*c) - 7*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^7*e^(3*I*d*x + 3*I*c) - 2*d*e^7*e^(2*I*d*x + 2*I*c) + d*e^7*e^(I*d*x + I*c)), x))/(d*e^7*e^(2*I*d*x + 2*I*c) - d*e^7*e^(I*d*x + I*c))","F",0
212,0,0,0,0.469381," ","integrate((a+I*a*tan(d*x+c))^3/(e*sec(d*x+c))^(15/2),x, algorithm=""fricas"")","\frac{{\left(2640 \, d e^{8} e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} a^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{11 \, d e^{8}}, x\right) + \sqrt{2} {\left(-11 i \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} - 73 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 218 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 446 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 235 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 55 i \, a^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2640 \, d e^{8}}"," ",0,"1/2640*(2640*d*e^8*e^(2*I*d*x + 2*I*c)*integral(-1/11*I*sqrt(2)*a^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^8), x) + sqrt(2)*(-11*I*a^3*e^(10*I*d*x + 10*I*c) - 73*I*a^3*e^(8*I*d*x + 8*I*c) - 218*I*a^3*e^(6*I*d*x + 6*I*c) - 446*I*a^3*e^(4*I*d*x + 4*I*c) - 235*I*a^3*e^(2*I*d*x + 2*I*c) + 55*I*a^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-2*I*d*x - 2*I*c)/(d*e^8)","F",0
213,0,0,0,0.663673," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-462 i \, a^{4} e e^{\left(9 i \, d x + 9 i \, c\right)} - 812 i \, a^{4} e e^{\left(7 i \, d x + 7 i \, c\right)} - 1080 i \, a^{4} e e^{\left(5 i \, d x + 5 i \, c\right)} - 660 i \, a^{4} e e^{\left(3 i \, d x + 3 i \, c\right)} - 154 i \, a^{4} e e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 63 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(\frac{11 i \, \sqrt{2} a^{4} e \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, d}, x\right)}{63 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/63*(sqrt(2)*(-462*I*a^4*e*e^(9*I*d*x + 9*I*c) - 812*I*a^4*e*e^(7*I*d*x + 7*I*c) - 1080*I*a^4*e*e^(5*I*d*x + 5*I*c) - 660*I*a^4*e*e^(3*I*d*x + 3*I*c) - 154*I*a^4*e*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 63*(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)*integral(11/3*I*sqrt(2)*a^4*e*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/d, x))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","F",0
214,0,0,0,0.526906," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(730 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 1586 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 1326 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 390 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 35 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} {\rm integral}\left(-\frac{39 i \, \sqrt{2} a^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{7 \, d}, x\right)}{35 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/35*(sqrt(2)*(730*I*a^4*e^(6*I*d*x + 6*I*c) + 1586*I*a^4*e^(4*I*d*x + 4*I*c) + 1326*I*a^4*e^(2*I*d*x + 2*I*c) + 390*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 35*(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)*integral(-39/7*I*sqrt(2)*a^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/d, x))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","F",0
215,0,0,0,0.634552," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-240 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 222 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} - 1034 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 352 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} - 1232 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 154 i \, a^{4} e^{\left(i \, d x + i \, c\right)} - 462 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 15 \, {\left(d e e^{\left(5 i \, d x + 5 i \, c\right)} - d e e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e e^{\left(i \, d x + i \, c\right)} - d e\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-77 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 154 i \, a^{4} e^{\left(i \, d x + i \, c\right)} - 77 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{15 \, {\left(d e e^{\left(5 i \, d x + 5 i \, c\right)} - d e e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e e^{\left(i \, d x + i \, c\right)} - d e\right)}}"," ",0,"1/15*(sqrt(2)*(-240*I*a^4*e^(6*I*d*x + 6*I*c) - 222*I*a^4*e^(5*I*d*x + 5*I*c) - 1034*I*a^4*e^(4*I*d*x + 4*I*c) - 352*I*a^4*e^(3*I*d*x + 3*I*c) - 1232*I*a^4*e^(2*I*d*x + 2*I*c) - 154*I*a^4*e^(I*d*x + I*c) - 462*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 15*(d*e*e^(5*I*d*x + 5*I*c) - d*e*e^(4*I*d*x + 4*I*c) + 2*d*e*e^(3*I*d*x + 3*I*c) - 2*d*e*e^(2*I*d*x + 2*I*c) + d*e*e^(I*d*x + I*c) - d*e)*integral(1/5*sqrt(2)*(-77*I*a^4*e^(2*I*d*x + 2*I*c) - 154*I*a^4*e^(I*d*x + I*c) - 77*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e*e^(3*I*d*x + 3*I*c) - 2*d*e*e^(2*I*d*x + 2*I*c) + d*e*e^(I*d*x + I*c)), x))/(d*e*e^(5*I*d*x + 5*I*c) - d*e*e^(4*I*d*x + 4*I*c) + 2*d*e*e^(3*I*d*x + 3*I*c) - 2*d*e*e^(2*I*d*x + 2*I*c) + d*e*e^(I*d*x + I*c) - d*e)","F",0
216,0,0,0,0.698140," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-8 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 42 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 30 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, {\left(d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)} {\rm integral}\left(\frac{5 i \, \sqrt{2} a^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{d e^{2}}, x\right)}{3 \, {\left(d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)}}"," ",0,"1/3*(sqrt(2)*(-8*I*a^4*e^(4*I*d*x + 4*I*c) - 42*I*a^4*e^(2*I*d*x + 2*I*c) - 30*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 3*(d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)*integral(5*I*sqrt(2)*a^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^2), x))/(d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)","F",0
217,0,0,0,0.548177," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-4 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} + 28 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 14 i \, a^{4} e^{\left(i \, d x + i \, c\right)} + 42 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 5 \, {\left(d e^{3} e^{\left(i \, d x + i \, c\right)} - d e^{3}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(21 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 42 i \, a^{4} e^{\left(i \, d x + i \, c\right)} + 21 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(d e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{5 \, {\left(d e^{3} e^{\left(i \, d x + i \, c\right)} - d e^{3}\right)}}"," ",0,"1/5*(sqrt(2)*(-4*I*a^4*e^(4*I*d*x + 4*I*c) + 4*I*a^4*e^(3*I*d*x + 3*I*c) + 28*I*a^4*e^(2*I*d*x + 2*I*c) + 14*I*a^4*e^(I*d*x + I*c) + 42*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 5*(d*e^3*e^(I*d*x + I*c) - d*e^3)*integral(1/5*sqrt(2)*(21*I*a^4*e^(2*I*d*x + 2*I*c) + 42*I*a^4*e^(I*d*x + I*c) + 21*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^3*e^(3*I*d*x + 3*I*c) - 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3*e^(I*d*x + I*c)), x))/(d*e^3*e^(I*d*x + I*c) - d*e^3)","F",0
218,0,0,0,0.630601," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{21 \, d e^{4} {\rm integral}\left(-\frac{5 i \, \sqrt{2} a^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{21 \, d e^{4}}, x\right) + \sqrt{2} {\left(-6 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 10 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{21 \, d e^{4}}"," ",0,"1/21*(21*d*e^4*integral(-5/21*I*sqrt(2)*a^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^4), x) + sqrt(2)*(-6*I*a^4*e^(4*I*d*x + 4*I*c) + 4*I*a^4*e^(2*I*d*x + 2*I*c) + 10*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^4)","F",0
219,0,0,0,0.631783," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(9/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-5 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 5 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} - 7 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 7 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} + 4 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a^{4} e^{\left(i \, d x + i \, c\right)} + 6 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 45 \, {\left(d e^{5} e^{\left(i \, d x + i \, c\right)} - d e^{5}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a^{4} e^{\left(i \, d x + i \, c\right)} + i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{15 \, {\left(d e^{5} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{5} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{45 \, {\left(d e^{5} e^{\left(i \, d x + i \, c\right)} - d e^{5}\right)}}"," ",0,"1/45*(sqrt(2)*(-5*I*a^4*e^(6*I*d*x + 6*I*c) + 5*I*a^4*e^(5*I*d*x + 5*I*c) - 7*I*a^4*e^(4*I*d*x + 4*I*c) + 7*I*a^4*e^(3*I*d*x + 3*I*c) + 4*I*a^4*e^(2*I*d*x + 2*I*c) + 2*I*a^4*e^(I*d*x + I*c) + 6*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 45*(d*e^5*e^(I*d*x + I*c) - d*e^5)*integral(1/15*sqrt(2)*(I*a^4*e^(2*I*d*x + 2*I*c) + 2*I*a^4*e^(I*d*x + I*c) + I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^5*e^(3*I*d*x + 3*I*c) - 2*d*e^5*e^(2*I*d*x + 2*I*c) + d*e^5*e^(I*d*x + I*c)), x))/(d*e^5*e^(I*d*x + I*c) - d*e^5)","F",0
220,0,0,0,0.585129," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(11/2),x, algorithm=""fricas"")","\frac{154 \, d e^{6} {\rm integral}\left(\frac{i \, \sqrt{2} a^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{77 \, d e^{6}}, x\right) + \sqrt{2} {\left(-7 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 20 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 17 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{154 \, d e^{6}}"," ",0,"1/154*(154*d*e^6*integral(1/77*I*sqrt(2)*a^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^6), x) + sqrt(2)*(-7*I*a^4*e^(6*I*d*x + 6*I*c) - 20*I*a^4*e^(4*I*d*x + 4*I*c) - 17*I*a^4*e^(2*I*d*x + 2*I*c) - 4*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^6)","F",0
221,0,0,0,0.517404," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(13/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-9 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 9 i \, a^{4} e^{\left(7 i \, d x + 7 i \, c\right)} - 37 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 37 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} - 59 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 59 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} - 55 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 31 i \, a^{4} e^{\left(i \, d x + i \, c\right)} - 24 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 468 \, {\left(d e^{7} e^{\left(i \, d x + i \, c\right)} - d e^{7}\right)} {\rm integral}\left(\frac{\sqrt{2} {\left(-i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, a^{4} e^{\left(i \, d x + i \, c\right)} - i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{39 \, {\left(d e^{7} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, d e^{7} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{7} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{468 \, {\left(d e^{7} e^{\left(i \, d x + i \, c\right)} - d e^{7}\right)}}"," ",0,"1/468*(sqrt(2)*(-9*I*a^4*e^(8*I*d*x + 8*I*c) + 9*I*a^4*e^(7*I*d*x + 7*I*c) - 37*I*a^4*e^(6*I*d*x + 6*I*c) + 37*I*a^4*e^(5*I*d*x + 5*I*c) - 59*I*a^4*e^(4*I*d*x + 4*I*c) + 59*I*a^4*e^(3*I*d*x + 3*I*c) - 55*I*a^4*e^(2*I*d*x + 2*I*c) + 31*I*a^4*e^(I*d*x + I*c) - 24*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 468*(d*e^7*e^(I*d*x + I*c) - d*e^7)*integral(1/39*sqrt(2)*(-I*a^4*e^(2*I*d*x + 2*I*c) - 2*I*a^4*e^(I*d*x + I*c) - I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^7*e^(3*I*d*x + 3*I*c) - 2*d*e^7*e^(2*I*d*x + 2*I*c) + d*e^7*e^(I*d*x + I*c)), x))/(d*e^7*e^(I*d*x + I*c) - d*e^7)","F",0
222,0,0,0,0.701624," ","integrate((a+I*a*tan(d*x+c))^4/(e*sec(d*x+c))^(15/2),x, algorithm=""fricas"")","\frac{1320 \, d e^{8} {\rm integral}\left(-\frac{i \, \sqrt{2} a^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{33 \, d e^{8}}, x\right) + \sqrt{2} {\left(-11 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} - 58 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} - 128 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 166 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 85 i \, a^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{1320 \, d e^{8}}"," ",0,"1/1320*(1320*d*e^8*integral(-1/33*I*sqrt(2)*a^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^8), x) + sqrt(2)*(-11*I*a^4*e^(8*I*d*x + 8*I*c) - 58*I*a^4*e^(6*I*d*x + 6*I*c) - 128*I*a^4*e^(4*I*d*x + 4*I*c) - 166*I*a^4*e^(2*I*d*x + 2*I*c) - 85*I*a^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^8)","F",0
223,0,0,0,0.514764," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-42 i \, e^{5} e^{\left(7 i \, d x + 7 i \, c\right)} - 154 i \, e^{5} e^{\left(5 i \, d x + 5 i \, c\right)} - 206 i \, e^{5} e^{\left(3 i \, d x + 3 i \, c\right)} - 14 i \, e^{5} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 35 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} {\rm integral}\left(\frac{3 i \, \sqrt{2} e^{5} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, a d}, x\right)}{35 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/35*(sqrt(2)*(-42*I*e^5*e^(7*I*d*x + 7*I*c) - 154*I*e^5*e^(5*I*d*x + 5*I*c) - 206*I*e^5*e^(3*I*d*x + 3*I*c) - 14*I*e^5*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 35*(a*d*e^(6*I*d*x + 6*I*c) + 3*a*d*e^(4*I*d*x + 4*I*c) + 3*a*d*e^(2*I*d*x + 2*I*c) + a*d)*integral(3/5*I*sqrt(2)*e^5*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a*d), x))/(a*d*e^(6*I*d*x + 6*I*c) + 3*a*d*e^(4*I*d*x + 4*I*c) + 3*a*d*e^(2*I*d*x + 2*I*c) + a*d)","F",0
224,0,0,0,0.578911," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-10 i \, e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 24 i \, e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 10 i \, e^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 15 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} e^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, a d}, x\right)}{15 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/15*(sqrt(2)*(-10*I*e^4*e^(4*I*d*x + 4*I*c) - 24*I*e^4*e^(2*I*d*x + 2*I*c) + 10*I*e^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 15*(a*d*e^(4*I*d*x + 4*I*c) + 2*a*d*e^(2*I*d*x + 2*I*c) + a*d)*integral(-1/3*I*sqrt(2)*e^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a*d), x))/(a*d*e^(4*I*d*x + 4*I*c) + 2*a*d*e^(2*I*d*x + 2*I*c) + a*d)","F",0
225,0,0,0,0.669875," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-6 i \, e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 10 i \, e^{3} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} {\rm integral}\left(\frac{i \, \sqrt{2} e^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a d}, x\right)}{3 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/3*(sqrt(2)*(-6*I*e^3*e^(3*I*d*x + 3*I*c) - 10*I*e^3*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 3*(a*d*e^(2*I*d*x + 2*I*c) + a*d)*integral(I*sqrt(2)*e^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a*d), x))/(a*d*e^(2*I*d*x + 2*I*c) + a*d)","F",0
226,0,0,0,0.655152," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-2 i \, \sqrt{2} e^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + a d {\rm integral}\left(-\frac{i \, \sqrt{2} e^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{a d}, x\right)}{a d}"," ",0,"(-2*I*sqrt(2)*e^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + a*d*integral(-I*sqrt(2)*e^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a*d), x))/(a*d)","F",0
227,0,0,0,0.591499," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a d e^{\left(i \, d x + i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} e \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a d}, x\right) + \sqrt{2} {\left(2 i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, e\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{a d}"," ",0,"(a*d*e^(I*d*x + I*c)*integral(-I*sqrt(2)*e*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a*d), x) + sqrt(2)*(2*I*e*e^(2*I*d*x + 2*I*c) + 2*I*e)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-I*d*x - I*c)/(a*d)","F",0
228,0,0,0,0.602845," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, a d}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{3 \, a d}"," ",0,"1/3*(3*a*d*e^(2*I*d*x + 2*I*c)*integral(-1/3*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a*d), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(2*I*d*x + 2*I*c) + I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-2*I*d*x - 2*I*c)/(a*d)","F",0
229,0,0,0,0.529021," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-5 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 7 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 8 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(i \, d x + i \, c\right)} - i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 10 \, {\left(a d e e^{\left(4 i \, d x + 4 i \, c\right)} - a d e e^{\left(3 i \, d x + 3 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, e^{\left(i \, d x + i \, c\right)} - 3 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(a d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a d e e^{\left(2 i \, d x + 2 i \, c\right)} + a d e e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{10 \, {\left(a d e e^{\left(4 i \, d x + 4 i \, c\right)} - a d e e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/10*(sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-5*I*e^(5*I*d*x + 5*I*c) - 7*I*e^(4*I*d*x + 4*I*c) - 4*I*e^(3*I*d*x + 3*I*c) - 8*I*e^(2*I*d*x + 2*I*c) + I*e^(I*d*x + I*c) - I)*e^(1/2*I*d*x + 1/2*I*c) + 10*(a*d*e*e^(4*I*d*x + 4*I*c) - a*d*e*e^(3*I*d*x + 3*I*c))*integral(1/5*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-3*I*e^(2*I*d*x + 2*I*c) - 6*I*e^(I*d*x + I*c) - 3*I)*e^(1/2*I*d*x + 1/2*I*c)/(a*d*e*e^(3*I*d*x + 3*I*c) - 2*a*d*e*e^(2*I*d*x + 2*I*c) + a*d*e*e^(I*d*x + I*c)), x))/(a*d*e*e^(4*I*d*x + 4*I*c) - a*d*e*e^(3*I*d*x + 3*I*c))","F",0
230,0,0,0,0.575569," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(84 \, a d e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} {\rm integral}\left(-\frac{5 i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{21 \, a d e^{2}}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-7 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 9 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 19 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{84 \, a d e^{2}}"," ",0,"1/84*(84*a*d*e^2*e^(4*I*d*x + 4*I*c)*integral(-5/21*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a*d*e^2), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-7*I*e^(6*I*d*x + 6*I*c) + 9*I*e^(4*I*d*x + 4*I*c) + 19*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-4*I*d*x - 4*I*c)/(a*d*e^2)","F",0
231,0,0,0,0.629490," ","integrate(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-9 i \, e^{\left(9 i \, d x + 9 i \, c\right)} + 9 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 162 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 174 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 124 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 212 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 34 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 34 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, e^{\left(i \, d x + i \, c\right)} - 5 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 360 \, {\left(a d e^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - a d e^{3} e^{\left(5 i \, d x + 5 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-7 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 14 i \, e^{\left(i \, d x + i \, c\right)} - 7 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{15 \, {\left(a d e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{3} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{360 \, {\left(a d e^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - a d e^{3} e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}"," ",0,"1/360*(sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-9*I*e^(9*I*d*x + 9*I*c) + 9*I*e^(8*I*d*x + 8*I*c) - 162*I*e^(7*I*d*x + 7*I*c) - 174*I*e^(6*I*d*x + 6*I*c) - 124*I*e^(5*I*d*x + 5*I*c) - 212*I*e^(4*I*d*x + 4*I*c) + 34*I*e^(3*I*d*x + 3*I*c) - 34*I*e^(2*I*d*x + 2*I*c) + 5*I*e^(I*d*x + I*c) - 5*I)*e^(1/2*I*d*x + 1/2*I*c) + 360*(a*d*e^3*e^(6*I*d*x + 6*I*c) - a*d*e^3*e^(5*I*d*x + 5*I*c))*integral(1/15*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-7*I*e^(2*I*d*x + 2*I*c) - 14*I*e^(I*d*x + I*c) - 7*I)*e^(1/2*I*d*x + 1/2*I*c)/(a*d*e^3*e^(3*I*d*x + 3*I*c) - 2*a*d*e^3*e^(2*I*d*x + 2*I*c) + a*d*e^3*e^(I*d*x + I*c)), x))/(a*d*e^3*e^(6*I*d*x + 6*I*c) - a*d*e^3*e^(5*I*d*x + 5*I*c))","F",0
232,0,0,0,0.581336," ","integrate(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(1232 \, a d e^{4} e^{\left(6 i \, d x + 6 i \, c\right)} {\rm integral}\left(-\frac{15 i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{77 \, a d e^{4}}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-11 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 121 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 70 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 226 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 53 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{1232 \, a d e^{4}}"," ",0,"1/1232*(1232*a*d*e^4*e^(6*I*d*x + 6*I*c)*integral(-15/77*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a*d*e^4), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-11*I*e^(10*I*d*x + 10*I*c) - 121*I*e^(8*I*d*x + 8*I*c) + 70*I*e^(6*I*d*x + 6*I*c) + 226*I*e^(4*I*d*x + 4*I*c) + 53*I*e^(2*I*d*x + 2*I*c) + 7*I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-6*I*d*x - 6*I*c)/(a*d*e^4)","F",0
233,0,0,0,0.646203," ","integrate((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-462 i \, e^{7} e^{\left(9 i \, d x + 9 i \, c\right)} - 2156 i \, e^{7} e^{\left(7 i \, d x + 7 i \, c\right)} - 3960 i \, e^{7} e^{\left(5 i \, d x + 5 i \, c\right)} - 3540 i \, e^{7} e^{\left(3 i \, d x + 3 i \, c\right)} - 154 i \, e^{7} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 315 \, {\left(a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} {\rm integral}\left(\frac{11 i \, \sqrt{2} e^{7} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{15 \, a^{2} d}, x\right)}{315 \, {\left(a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/315*(sqrt(2)*(-462*I*e^7*e^(9*I*d*x + 9*I*c) - 2156*I*e^7*e^(7*I*d*x + 7*I*c) - 3960*I*e^7*e^(5*I*d*x + 5*I*c) - 3540*I*e^7*e^(3*I*d*x + 3*I*c) - 154*I*e^7*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 315*(a^2*d*e^(8*I*d*x + 8*I*c) + 4*a^2*d*e^(6*I*d*x + 6*I*c) + 6*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*integral(11/15*I*sqrt(2)*e^7*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d), x))/(a^2*d*e^(8*I*d*x + 8*I*c) + 4*a^2*d*e^(6*I*d*x + 6*I*c) + 6*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","F",0
234,0,0,0,0.755522," ","integrate((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-30 i \, e^{6} e^{\left(6 i \, d x + 6 i \, c\right)} - 102 i \, e^{6} e^{\left(4 i \, d x + 4 i \, c\right)} - 122 i \, e^{6} e^{\left(2 i \, d x + 2 i \, c\right)} + 30 i \, e^{6}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 35 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} {\rm integral}\left(-\frac{3 i \, \sqrt{2} e^{6} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{7 \, a^{2} d}, x\right)}{35 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/35*(sqrt(2)*(-30*I*e^6*e^(6*I*d*x + 6*I*c) - 102*I*e^6*e^(4*I*d*x + 4*I*c) - 122*I*e^6*e^(2*I*d*x + 2*I*c) + 30*I*e^6)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 35*(a^2*d*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^(4*I*d*x + 4*I*c) + 3*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*integral(-3/7*I*sqrt(2)*e^6*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d), x))/(a^2*d*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^(4*I*d*x + 4*I*c) + 3*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","F",0
235,0,0,0,0.555516," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-42 i \, e^{5} e^{\left(5 i \, d x + 5 i \, c\right)} - 112 i \, e^{5} e^{\left(3 i \, d x + 3 i \, c\right)} - 94 i \, e^{5} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 15 \, {\left(a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} {\rm integral}\left(\frac{7 i \, \sqrt{2} e^{5} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, a^{2} d}, x\right)}{15 \, {\left(a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/15*(sqrt(2)*(-42*I*e^5*e^(5*I*d*x + 5*I*c) - 112*I*e^5*e^(3*I*d*x + 3*I*c) - 94*I*e^5*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 15*(a^2*d*e^(4*I*d*x + 4*I*c) + 2*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*integral(7/5*I*sqrt(2)*e^5*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d), x))/(a^2*d*e^(4*I*d*x + 4*I*c) + 2*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","F",0
236,0,0,0,0.809512," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-10 i \, e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 14 i \, e^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} {\rm integral}\left(-\frac{5 i \, \sqrt{2} e^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, a^{2} d}, x\right)}{3 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/3*(sqrt(2)*(-10*I*e^4*e^(2*I*d*x + 2*I*c) - 14*I*e^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 3*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*integral(-5/3*I*sqrt(2)*e^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d), x))/(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","F",0
237,0,0,0,0.544538," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} d e^{\left(i \, d x + i \, c\right)} {\rm integral}\left(-\frac{3 i \, \sqrt{2} e^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a^{2} d}, x\right) + \sqrt{2} {\left(6 i \, e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, e^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2} d}"," ",0,"(a^2*d*e^(I*d*x + I*c)*integral(-3*I*sqrt(2)*e^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d), x) + sqrt(2)*(6*I*e^3*e^(2*I*d*x + 2*I*c) + 4*I*e^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-I*d*x - I*c)/(a^2*d)","F",0
238,0,0,0,1.005770," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(\frac{i \, \sqrt{2} e^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, a^{2} d}, x\right) + \sqrt{2} {\left(2 i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, e^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{3 \, a^{2} d}"," ",0,"1/3*(3*a^2*d*e^(2*I*d*x + 2*I*c)*integral(1/3*I*sqrt(2)*e^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d), x) + sqrt(2)*(2*I*e^2*e^(2*I*d*x + 2*I*c) + 2*I*e^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-2*I*d*x - 2*I*c)/(a^2*d)","F",0
239,0,0,0,0.650359," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(5 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} e \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, a^{2} d}, x\right) + \sqrt{2} {\left(2 i \, e e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{5 \, a^{2} d}"," ",0,"1/5*(5*a^2*d*e^(3*I*d*x + 3*I*c)*integral(-1/5*I*sqrt(2)*e*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d), x) + sqrt(2)*(2*I*e*e^(4*I*d*x + 4*I*c) + 3*I*e*e^(2*I*d*x + 2*I*c) + I*e)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-3*I*d*x - 3*I*c)/(a^2*d)","F",0
240,0,0,0,0.547560," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(14 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{7 \, a^{2} d}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{14 \, a^{2} d}"," ",0,"1/14*(14*a^2*d*e^(4*I*d*x + 4*I*c)*integral(-1/7*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(3*I*e^(4*I*d*x + 4*I*c) + 4*I*e^(2*I*d*x + 2*I*c) + I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","F",0
241,0,0,0,0.616403," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-9 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 15 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 5 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 19 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(i \, d x + i \, c\right)} - i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 36 \, {\left(a^{2} d e e^{\left(6 i \, d x + 6 i \, c\right)} - a^{2} d e e^{\left(5 i \, d x + 5 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, e^{\left(i \, d x + i \, c\right)} - i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, {\left(a^{2} d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a^{2} d e e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{36 \, {\left(a^{2} d e e^{\left(6 i \, d x + 6 i \, c\right)} - a^{2} d e e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}"," ",0,"1/36*(sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-9*I*e^(7*I*d*x + 7*I*c) - 15*I*e^(6*I*d*x + 6*I*c) - 5*I*e^(5*I*d*x + 5*I*c) - 19*I*e^(4*I*d*x + 4*I*c) + 5*I*e^(3*I*d*x + 3*I*c) - 5*I*e^(2*I*d*x + 2*I*c) + I*e^(I*d*x + I*c) - I)*e^(1/2*I*d*x + 1/2*I*c) + 36*(a^2*d*e*e^(6*I*d*x + 6*I*c) - a^2*d*e*e^(5*I*d*x + 5*I*c))*integral(1/3*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-I*e^(2*I*d*x + 2*I*c) - 2*I*e^(I*d*x + I*c) - I)*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d*e*e^(3*I*d*x + 3*I*c) - 2*a^2*d*e*e^(2*I*d*x + 2*I*c) + a^2*d*e*e^(I*d*x + I*c)), x))/(a^2*d*e*e^(6*I*d*x + 6*I*c) - a^2*d*e*e^(5*I*d*x + 5*I*c))","F",0
242,0,0,0,0.703675," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(264 \, a^{2} d e^{2} e^{\left(6 i \, d x + 6 i \, c\right)} {\rm integral}\left(-\frac{5 i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{33 \, a^{2} d e^{2}}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-11 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 30 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 56 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 18 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{264 \, a^{2} d e^{2}}"," ",0,"1/264*(264*a^2*d*e^2*e^(6*I*d*x + 6*I*c)*integral(-5/33*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e^2), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-11*I*e^(8*I*d*x + 8*I*c) + 30*I*e^(6*I*d*x + 6*I*c) + 56*I*e^(4*I*d*x + 4*I*c) + 18*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-6*I*d*x - 6*I*c)/(a^2*d*e^2)","F",0
243,0,0,0,0.670877," ","integrate(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-13 i \, e^{\left(11 i \, d x + 11 i \, c\right)} + 13 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 299 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 373 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 198 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 474 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 118 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 118 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 35 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 35 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, e^{\left(i \, d x + i \, c\right)} - 5 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 1040 \, {\left(a^{2} d e^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - a^{2} d e^{3} e^{\left(7 i \, d x + 7 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-21 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 42 i \, e^{\left(i \, d x + i \, c\right)} - 21 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{65 \, {\left(a^{2} d e^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a^{2} d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{3} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{1040 \, {\left(a^{2} d e^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - a^{2} d e^{3} e^{\left(7 i \, d x + 7 i \, c\right)}\right)}}"," ",0,"1/1040*(sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-13*I*e^(11*I*d*x + 11*I*c) + 13*I*e^(10*I*d*x + 10*I*c) - 299*I*e^(9*I*d*x + 9*I*c) - 373*I*e^(8*I*d*x + 8*I*c) - 198*I*e^(7*I*d*x + 7*I*c) - 474*I*e^(6*I*d*x + 6*I*c) + 118*I*e^(5*I*d*x + 5*I*c) - 118*I*e^(4*I*d*x + 4*I*c) + 35*I*e^(3*I*d*x + 3*I*c) - 35*I*e^(2*I*d*x + 2*I*c) + 5*I*e^(I*d*x + I*c) - 5*I)*e^(1/2*I*d*x + 1/2*I*c) + 1040*(a^2*d*e^3*e^(8*I*d*x + 8*I*c) - a^2*d*e^3*e^(7*I*d*x + 7*I*c))*integral(1/65*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-21*I*e^(2*I*d*x + 2*I*c) - 42*I*e^(I*d*x + I*c) - 21*I)*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d*e^3*e^(3*I*d*x + 3*I*c) - 2*a^2*d*e^3*e^(2*I*d*x + 2*I*c) + a^2*d*e^3*e^(I*d*x + I*c)), x))/(a^2*d*e^3*e^(8*I*d*x + 8*I*c) - a^2*d*e^3*e^(7*I*d*x + 7*I*c))","F",0
244,0,0,0,0.813510," ","integrate(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(3360 \, a^{2} d e^{4} e^{\left(8 i \, d x + 8 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{7 \, a^{2} d e^{4}}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-15 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 200 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 245 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 592 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 211 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 56 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{3360 \, a^{2} d e^{4}}"," ",0,"1/3360*(3360*a^2*d*e^4*e^(8*I*d*x + 8*I*c)*integral(-1/7*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e^4), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-15*I*e^(12*I*d*x + 12*I*c) - 200*I*e^(10*I*d*x + 10*I*c) + 245*I*e^(8*I*d*x + 8*I*c) + 592*I*e^(6*I*d*x + 6*I*c) + 211*I*e^(4*I*d*x + 4*I*c) + 56*I*e^(2*I*d*x + 2*I*c) + 7*I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-8*I*d*x - 8*I*c)/(a^2*d*e^4)","F",0
245,0,0,0,0.473212," ","integrate((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-462 i \, e^{7} e^{\left(7 i \, d x + 7 i \, c\right)} - 1694 i \, e^{7} e^{\left(5 i \, d x + 5 i \, c\right)} - 2266 i \, e^{7} e^{\left(3 i \, d x + 3 i \, c\right)} - 1274 i \, e^{7} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 105 \, {\left(a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} {\rm integral}\left(\frac{11 i \, \sqrt{2} e^{7} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, a^{3} d}, x\right)}{105 \, {\left(a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/105*(sqrt(2)*(-462*I*e^7*e^(7*I*d*x + 7*I*c) - 1694*I*e^7*e^(5*I*d*x + 5*I*c) - 2266*I*e^7*e^(3*I*d*x + 3*I*c) - 1274*I*e^7*e^(I*d*x + I*c))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 105*(a^3*d*e^(6*I*d*x + 6*I*c) + 3*a^3*d*e^(4*I*d*x + 4*I*c) + 3*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*integral(11/5*I*sqrt(2)*e^7*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^3*d), x))/(a^3*d*e^(6*I*d*x + 6*I*c) + 3*a^3*d*e^(4*I*d*x + 4*I*c) + 3*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","F",0
246,0,0,0,0.642443," ","integrate((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-30 i \, e^{6} e^{\left(4 i \, d x + 4 i \, c\right)} - 72 i \, e^{6} e^{\left(2 i \, d x + 2 i \, c\right)} - 50 i \, e^{6}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 5 \, {\left(a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} {\rm integral}\left(-\frac{3 i \, \sqrt{2} e^{6} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{a^{3} d}, x\right)}{5 \, {\left(a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/5*(sqrt(2)*(-30*I*e^6*e^(4*I*d*x + 4*I*c) - 72*I*e^6*e^(2*I*d*x + 2*I*c) - 50*I*e^6)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 5*(a^3*d*e^(4*I*d*x + 4*I*c) + 2*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*integral(-3*I*sqrt(2)*e^6*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^3*d), x))/(a^3*d*e^(4*I*d*x + 4*I*c) + 2*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","F",0
247,0,0,0,0.616155," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(42 i \, e^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 70 i \, e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 24 i \, e^{5}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(-\frac{7 i \, \sqrt{2} e^{5} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a^{3} d}, x\right)}{3 \, {\left(a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{3} d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/3*(sqrt(2)*(42*I*e^5*e^(4*I*d*x + 4*I*c) + 70*I*e^5*e^(2*I*d*x + 2*I*c) + 24*I*e^5)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 3*(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))*integral(-7*I*sqrt(2)*e^5*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^3*d), x))/(a^3*d*e^(3*I*d*x + 3*I*c) + a^3*d*e^(I*d*x + I*c))","F",0
248,0,0,0,0.502091," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(\frac{5 i \, \sqrt{2} e^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, a^{3} d}, x\right) + \sqrt{2} {\left(10 i \, e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, e^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{3 \, a^{3} d}"," ",0,"1/3*(3*a^3*d*e^(2*I*d*x + 2*I*c)*integral(5/3*I*sqrt(2)*e^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^3*d), x) + sqrt(2)*(10*I*e^4*e^(2*I*d*x + 2*I*c) + 4*I*e^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-2*I*d*x - 2*I*c)/(a^3*d)","F",0
249,0,0,0,0.473722," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(5 \, a^{3} d e^{\left(3 i \, d x + 3 i \, c\right)} {\rm integral}\left(\frac{3 i \, \sqrt{2} e^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, a^{3} d}, x\right) + \sqrt{2} {\left(-6 i \, e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, e^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{5 \, a^{3} d}"," ",0,"1/5*(5*a^3*d*e^(3*I*d*x + 3*I*c)*integral(3/5*I*sqrt(2)*e^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^3*d), x) + sqrt(2)*(-6*I*e^3*e^(4*I*d*x + 4*I*c) - 4*I*e^3*e^(2*I*d*x + 2*I*c) + 2*I*e^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-3*I*d*x - 3*I*c)/(a^3*d)","F",0
250,0,0,0,0.578778," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(21 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} {\rm integral}\left(\frac{i \, \sqrt{2} e^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{21 \, a^{3} d}, x\right) + \sqrt{2} {\left(2 i \, e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, e^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{21 \, a^{3} d}"," ",0,"1/21*(21*a^3*d*e^(4*I*d*x + 4*I*c)*integral(1/21*I*sqrt(2)*e^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^3*d), x) + sqrt(2)*(2*I*e^2*e^(4*I*d*x + 4*I*c) + 5*I*e^2*e^(2*I*d*x + 2*I*c) + 3*I*e^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-4*I*d*x - 4*I*c)/(a^3*d)","F",0
251,0,0,0,0.838678," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(90 \, a^{3} d e^{\left(5 i \, d x + 5 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} e \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{15 \, a^{3} d}, x\right) + \sqrt{2} {\left(12 i \, e e^{\left(6 i \, d x + 6 i \, c\right)} + 23 i \, e e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, e\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{90 \, a^{3} d}"," ",0,"1/90*(90*a^3*d*e^(5*I*d*x + 5*I*c)*integral(-1/15*I*sqrt(2)*e*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^3*d), x) + sqrt(2)*(12*I*e*e^(6*I*d*x + 6*I*c) + 23*I*e*e^(4*I*d*x + 4*I*c) + 16*I*e*e^(2*I*d*x + 2*I*c) + 5*I*e)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-5*I*d*x - 5*I*c)/(a^3*d)","F",0
252,0,0,0,0.718035," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(308 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} {\rm integral}\left(-\frac{5 i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{77 \, a^{3} d}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(37 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 61 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 31 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{308 \, a^{3} d}"," ",0,"1/308*(308*a^3*d*e^(6*I*d*x + 6*I*c)*integral(-5/77*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^3*d), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(37*I*e^(6*I*d*x + 6*I*c) + 61*I*e^(4*I*d*x + 4*I*c) + 31*I*e^(2*I*d*x + 2*I*c) + 7*I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-6*I*d*x - 6*I*c)/(a^3*d)","F",0
253,0,0,0,0.824246," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-117 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 219 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 34 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 302 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 124 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 124 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 50 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 50 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 9 i \, e^{\left(i \, d x + i \, c\right)} - 9 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 936 \, {\left(a^{3} d e e^{\left(8 i \, d x + 8 i \, c\right)} - a^{3} d e e^{\left(7 i \, d x + 7 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-7 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 14 i \, e^{\left(i \, d x + i \, c\right)} - 7 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{39 \, {\left(a^{3} d e e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a^{3} d e e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d e e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{936 \, {\left(a^{3} d e e^{\left(8 i \, d x + 8 i \, c\right)} - a^{3} d e e^{\left(7 i \, d x + 7 i \, c\right)}\right)}}"," ",0,"1/936*(sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-117*I*e^(9*I*d*x + 9*I*c) - 219*I*e^(8*I*d*x + 8*I*c) - 34*I*e^(7*I*d*x + 7*I*c) - 302*I*e^(6*I*d*x + 6*I*c) + 124*I*e^(5*I*d*x + 5*I*c) - 124*I*e^(4*I*d*x + 4*I*c) + 50*I*e^(3*I*d*x + 3*I*c) - 50*I*e^(2*I*d*x + 2*I*c) + 9*I*e^(I*d*x + I*c) - 9*I)*e^(1/2*I*d*x + 1/2*I*c) + 936*(a^3*d*e*e^(8*I*d*x + 8*I*c) - a^3*d*e*e^(7*I*d*x + 7*I*c))*integral(1/39*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-7*I*e^(2*I*d*x + 2*I*c) - 14*I*e^(I*d*x + I*c) - 7*I)*e^(1/2*I*d*x + 1/2*I*c)/(a^3*d*e*e^(3*I*d*x + 3*I*c) - 2*a^3*d*e*e^(2*I*d*x + 2*I*c) + a^3*d*e*e^(I*d*x + I*c)), x))/(a^3*d*e*e^(8*I*d*x + 8*I*c) - a^3*d*e*e^(7*I*d*x + 7*I*c))","F",0
254,0,0,0,0.641730," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(2640 \, a^{3} d e^{2} e^{\left(8 i \, d x + 8 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{11 \, a^{3} d e^{2}}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-55 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 235 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 446 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 218 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 73 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 11 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{2640 \, a^{3} d e^{2}}"," ",0,"1/2640*(2640*a^3*d*e^2*e^(8*I*d*x + 8*I*c)*integral(-1/11*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^3*d*e^2), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-55*I*e^(10*I*d*x + 10*I*c) + 235*I*e^(8*I*d*x + 8*I*c) + 446*I*e^(6*I*d*x + 6*I*c) + 218*I*e^(4*I*d*x + 4*I*c) + 73*I*e^(2*I*d*x + 2*I*c) + 11*I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-8*I*d*x - 8*I*c)/(a^3*d*e^2)","F",0
255,0,0,0,0.423212," ","integrate((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(462 i \, e^{7} e^{\left(6 i \, d x + 6 i \, c\right)} + 1232 i \, e^{7} e^{\left(4 i \, d x + 4 i \, c\right)} + 1034 i \, e^{7} e^{\left(2 i \, d x + 2 i \, c\right)} + 240 i \, e^{7}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 15 \, {\left(a^{4} d e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{4} d e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(-\frac{77 i \, \sqrt{2} e^{7} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, a^{4} d}, x\right)}{15 \, {\left(a^{4} d e^{\left(5 i \, d x + 5 i \, c\right)} + 2 \, a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{4} d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/15*(sqrt(2)*(462*I*e^7*e^(6*I*d*x + 6*I*c) + 1232*I*e^7*e^(4*I*d*x + 4*I*c) + 1034*I*e^7*e^(2*I*d*x + 2*I*c) + 240*I*e^7)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 15*(a^4*d*e^(5*I*d*x + 5*I*c) + 2*a^4*d*e^(3*I*d*x + 3*I*c) + a^4*d*e^(I*d*x + I*c))*integral(-77/5*I*sqrt(2)*e^7*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^4*d), x))/(a^4*d*e^(5*I*d*x + 5*I*c) + 2*a^4*d*e^(3*I*d*x + 3*I*c) + a^4*d*e^(I*d*x + I*c))","F",0
256,0,0,0,0.557624," ","integrate((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(30 i \, e^{6} e^{\left(4 i \, d x + 4 i \, c\right)} + 42 i \, e^{6} e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, e^{6}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, {\left(a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)}\right)} {\rm integral}\left(\frac{5 i \, \sqrt{2} e^{6} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{a^{4} d}, x\right)}{3 \, {\left(a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/3*(sqrt(2)*(30*I*e^6*e^(4*I*d*x + 4*I*c) + 42*I*e^6*e^(2*I*d*x + 2*I*c) + 8*I*e^6)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 3*(a^4*d*e^(4*I*d*x + 4*I*c) + a^4*d*e^(2*I*d*x + 2*I*c))*integral(5*I*sqrt(2)*e^6*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^4*d), x))/(a^4*d*e^(4*I*d*x + 4*I*c) + a^4*d*e^(2*I*d*x + 2*I*c))","F",0
257,0,0,0,1.109570," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(5 \, a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} {\rm integral}\left(\frac{21 i \, \sqrt{2} e^{5} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, a^{4} d}, x\right) + \sqrt{2} {\left(-42 i \, e^{5} e^{\left(4 i \, d x + 4 i \, c\right)} - 28 i \, e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, e^{5}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{5 \, a^{4} d}"," ",0,"1/5*(5*a^4*d*e^(3*I*d*x + 3*I*c)*integral(21/5*I*sqrt(2)*e^5*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^4*d), x) + sqrt(2)*(-42*I*e^5*e^(4*I*d*x + 4*I*c) - 28*I*e^5*e^(2*I*d*x + 2*I*c) + 4*I*e^5)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-3*I*d*x - 3*I*c)/(a^4*d)","F",0
258,0,0,0,0.534750," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(21 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} {\rm integral}\left(-\frac{5 i \, \sqrt{2} e^{4} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{21 \, a^{4} d}, x\right) + \sqrt{2} {\left(-10 i \, e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, e^{4}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{21 \, a^{4} d}"," ",0,"1/21*(21*a^4*d*e^(4*I*d*x + 4*I*c)*integral(-5/21*I*sqrt(2)*e^4*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^4*d), x) + sqrt(2)*(-10*I*e^4*e^(4*I*d*x + 4*I*c) - 4*I*e^4*e^(2*I*d*x + 2*I*c) + 6*I*e^4)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-4*I*d*x - 4*I*c)/(a^4*d)","F",0
259,0,0,0,0.468853," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(45 \, a^{4} d e^{\left(5 i \, d x + 5 i \, c\right)} {\rm integral}\left(\frac{i \, \sqrt{2} e^{3} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{15 \, a^{4} d}, x\right) + \sqrt{2} {\left(-6 i \, e^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 4 i \, e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 7 i \, e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, e^{3}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{45 \, a^{4} d}"," ",0,"1/45*(45*a^4*d*e^(5*I*d*x + 5*I*c)*integral(1/15*I*sqrt(2)*e^3*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^4*d), x) + sqrt(2)*(-6*I*e^3*e^(6*I*d*x + 6*I*c) - 4*I*e^3*e^(4*I*d*x + 4*I*c) + 7*I*e^3*e^(2*I*d*x + 2*I*c) + 5*I*e^3)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-5*I*d*x - 5*I*c)/(a^4*d)","F",0
260,0,0,0,0.565462," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(154 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} {\rm integral}\left(\frac{i \, \sqrt{2} e^{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{77 \, a^{4} d}, x\right) + \sqrt{2} {\left(4 i \, e^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 17 i \, e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 20 i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, e^{2}\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{154 \, a^{4} d}"," ",0,"1/154*(154*a^4*d*e^(6*I*d*x + 6*I*c)*integral(1/77*I*sqrt(2)*e^2*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^4*d), x) + sqrt(2)*(4*I*e^2*e^(6*I*d*x + 6*I*c) + 17*I*e^2*e^(4*I*d*x + 4*I*c) + 20*I*e^2*e^(2*I*d*x + 2*I*c) + 7*I*e^2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-6*I*d*x - 6*I*c)/(a^4*d)","F",0
261,0,0,0,0.532993," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(468 \, a^{4} d e^{\left(7 i \, d x + 7 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} e \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{39 \, a^{4} d}, x\right) + \sqrt{2} {\left(24 i \, e e^{\left(8 i \, d x + 8 i \, c\right)} + 55 i \, e e^{\left(6 i \, d x + 6 i \, c\right)} + 59 i \, e e^{\left(4 i \, d x + 4 i \, c\right)} + 37 i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + 9 i \, e\right)} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{468 \, a^{4} d}"," ",0,"1/468*(468*a^4*d*e^(7*I*d*x + 7*I*c)*integral(-1/39*I*sqrt(2)*e*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(a^4*d), x) + sqrt(2)*(24*I*e*e^(8*I*d*x + 8*I*c) + 55*I*e*e^(6*I*d*x + 6*I*c) + 59*I*e*e^(4*I*d*x + 4*I*c) + 37*I*e*e^(2*I*d*x + 2*I*c) + 9*I*e)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-7*I*d*x - 7*I*c)/(a^4*d)","F",0
262,0,0,0,1.146380," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(1320 \, a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} {\rm integral}\left(-\frac{i \, \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{33 \, a^{4} d}, x\right) + \sqrt{2} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(85 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 166 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 128 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 58 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 11 i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{1320 \, a^{4} d}"," ",0,"1/1320*(1320*a^4*d*e^(8*I*d*x + 8*I*c)*integral(-1/33*I*sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a^4*d), x) + sqrt(2)*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(85*I*e^(8*I*d*x + 8*I*c) + 166*I*e^(6*I*d*x + 6*I*c) + 128*I*e^(4*I*d*x + 4*I*c) + 58*I*e^(2*I*d*x + 2*I*c) + 11*I)*e^(1/2*I*d*x + 1/2*I*c))*e^(-8*I*d*x - 8*I*c)/(a^4*d)","F",0
263,0,0,0,0.978201," ","integrate((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} {\left(-15 i \, a d e^{\left(3 i \, f x + 3 i \, e\right)} - 3 i \, a d e^{\left(i \, f x + i \, e\right)}\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)} + 10 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} {\rm integral}\left(\frac{i \cdot 2^{\frac{2}{3}} a d \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}}{2 \, f}, x\right)}{10 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/10*(2^(2/3)*(-15*I*a*d*e^(3*I*f*x + 3*I*e) - 3*I*a*d*e^(I*f*x + I*e))*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e) + 10*(f*e^(2*I*f*x + 2*I*e) + f)*integral(1/2*I*2^(2/3)*a*d*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e)/f, x))/(f*e^(2*I*f*x + 2*I*e) + f)","F",0
264,0,0,0,0.708079," ","integrate((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{3 i \cdot 2^{\frac{1}{3}} a \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{1}{3} i \, f x + \frac{1}{3} i \, e\right)} + f {\rm integral}\left(-\frac{i \cdot 2^{\frac{1}{3}} a \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(-\frac{2}{3} i \, f x - \frac{2}{3} i \, e\right)}}{f}, x\right)}{f}"," ",0,"(3*I*2^(1/3)*a*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(1/3*I*f*x + 1/3*I*e) + f*integral(-I*2^(1/3)*a*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(-2/3*I*f*x - 2/3*I*e)/f, x))/f","F",0
265,0,0,0,0.664714," ","integrate((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} {\left(-3 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - 3 i \, a\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)} + {\left(d f e^{\left(i \, f x + i \, e\right)} - d f\right)} {\rm integral}\left(\frac{2^{\frac{2}{3}} {\left(-2 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, a e^{\left(i \, f x + i \, e\right)} - 2 i \, a\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}}{d f e^{\left(3 i \, f x + 3 i \, e\right)} - 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f e^{\left(i \, f x + i \, e\right)}}, x\right)}{d f e^{\left(i \, f x + i \, e\right)} - d f}"," ",0,"(2^(2/3)*(-3*I*a*e^(2*I*f*x + 2*I*e) - 3*I*a)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e) + (d*f*e^(I*f*x + I*e) - d*f)*integral(2^(2/3)*(-2*I*a*e^(2*I*f*x + 2*I*e) - 2*I*a*e^(I*f*x + I*e) - 2*I*a)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e)/(d*f*e^(3*I*f*x + 3*I*e) - 2*d*f*e^(2*I*f*x + 2*I*e) + d*f*e^(I*f*x + I*e)), x))/(d*f*e^(I*f*x + I*e) - d*f)","F",0
266,0,0,0,0.690237," ","integrate((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x, algorithm=""fricas"")","\frac{10 \, d^{2} f {\rm integral}\left(-\frac{2 i \cdot 2^{\frac{1}{3}} a \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(-\frac{2}{3} i \, f x - \frac{2}{3} i \, e\right)}}{5 \, d^{2} f}, x\right) + 2^{\frac{1}{3}} {\left(-3 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} - 3 i \, a\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{1}{3} i \, f x + \frac{1}{3} i \, e\right)}}{10 \, d^{2} f}"," ",0,"1/10*(10*d^2*f*integral(-2/5*I*2^(1/3)*a*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(-2/3*I*f*x - 2/3*I*e)/(d^2*f), x) + 2^(1/3)*(-3*I*a*e^(2*I*f*x + 2*I*e) - 3*I*a)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(1/3*I*f*x + 1/3*I*e))/(d^2*f)","F",0
267,0,0,0,0.588732," ","integrate((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} {\left(-165 i \, a^{2} d e^{\left(5 i \, f x + 5 i \, e\right)} - 78 i \, a^{2} d e^{\left(3 i \, f x + 3 i \, e\right)} - 33 i \, a^{2} d e^{\left(i \, f x + i \, e\right)}\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)} + 80 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} {\rm integral}\left(\frac{11 i \cdot 2^{\frac{2}{3}} a^{2} d \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}}{16 \, f}, x\right)}{80 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/80*(2^(2/3)*(-165*I*a^2*d*e^(5*I*f*x + 5*I*e) - 78*I*a^2*d*e^(3*I*f*x + 3*I*e) - 33*I*a^2*d*e^(I*f*x + I*e))*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e) + 80*(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)*integral(11/16*I*2^(2/3)*a^2*d*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e)/f, x))/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","F",0
268,0,0,0,0.500051," ","integrate((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2^{\frac{1}{3}} {\left(27 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 21 i \, a^{2}\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{1}{3} i \, f x + \frac{1}{3} i \, e\right)} + 4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)} {\rm integral}\left(-\frac{7 i \cdot 2^{\frac{1}{3}} a^{2} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(-\frac{2}{3} i \, f x - \frac{2}{3} i \, e\right)}}{4 \, f}, x\right)}{4 \, {\left(f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/4*(2^(1/3)*(27*I*a^2*e^(2*I*f*x + 2*I*e) + 21*I*a^2)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(1/3*I*f*x + 1/3*I*e) + 4*(f*e^(2*I*f*x + 2*I*e) + f)*integral(-7/4*I*2^(1/3)*a^2*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(-2/3*I*f*x - 2/3*I*e)/f, x))/(f*e^(2*I*f*x + 2*I*e) + f)","F",0
269,0,0,0,0.678009," ","integrate((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} {\left(-12 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 3 i \, a^{2} e^{\left(i \, f x + i \, e\right)} - 15 i \, a^{2}\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)} + 2 \, {\left(d f e^{\left(i \, f x + i \, e\right)} - d f\right)} {\rm integral}\left(\frac{2^{\frac{2}{3}} {\left(-5 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 5 i \, a^{2} e^{\left(i \, f x + i \, e\right)} - 5 i \, a^{2}\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}}{d f e^{\left(3 i \, f x + 3 i \, e\right)} - 2 \, d f e^{\left(2 i \, f x + 2 i \, e\right)} + d f e^{\left(i \, f x + i \, e\right)}}, x\right)}{2 \, {\left(d f e^{\left(i \, f x + i \, e\right)} - d f\right)}}"," ",0,"1/2*(2^(2/3)*(-12*I*a^2*e^(2*I*f*x + 2*I*e) - 3*I*a^2*e^(I*f*x + I*e) - 15*I*a^2)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e) + 2*(d*f*e^(I*f*x + I*e) - d*f)*integral(2^(2/3)*(-5*I*a^2*e^(2*I*f*x + 2*I*e) - 5*I*a^2*e^(I*f*x + I*e) - 5*I*a^2)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e)/(d*f*e^(3*I*f*x + 3*I*e) - 2*d*f*e^(2*I*f*x + 2*I*e) + d*f*e^(I*f*x + I*e)), x))/(d*f*e^(I*f*x + I*e) - d*f)","F",0
270,0,0,0,0.584577," ","integrate((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x, algorithm=""fricas"")","\frac{5 \, d^{2} f {\rm integral}\left(\frac{i \cdot 2^{\frac{1}{3}} a^{2} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(-\frac{2}{3} i \, f x - \frac{2}{3} i \, e\right)}}{5 \, d^{2} f}, x\right) + 2^{\frac{1}{3}} {\left(-3 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 3 i \, a^{2}\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{1}{3} i \, f x + \frac{1}{3} i \, e\right)}}{5 \, d^{2} f}"," ",0,"1/5*(5*d^2*f*integral(1/5*I*2^(1/3)*a^2*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(-2/3*I*f*x - 2/3*I*e)/(d^2*f), x) + 2^(1/3)*(-3*I*a^2*e^(2*I*f*x + 2*I*e) - 3*I*a^2)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(1/3*I*f*x + 1/3*I*e))/(d^2*f)","F",0
271,0,0,0,0.787017," ","integrate((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a f e^{\left(i \, f x + i \, e\right)} {\rm integral}\left(-\frac{i \cdot 2^{\frac{2}{3}} d \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}}{a f}, x\right) + 2^{\frac{2}{3}} {\left(3 i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, d\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}\right)} e^{\left(-i \, f x - i \, e\right)}}{a f}"," ",0,"(a*f*e^(I*f*x + I*e)*integral(-I*2^(2/3)*d*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e)/(a*f), x) + 2^(2/3)*(3*I*d*e^(2*I*f*x + 2*I*e) + 3*I*d)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e))*e^(-I*f*x - I*e)/(a*f)","F",0
272,0,0,0,0.694684," ","integrate((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(10 \, a f e^{\left(2 i \, f x + 2 i \, e\right)} {\rm integral}\left(-\frac{2 i \cdot 2^{\frac{1}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(-\frac{2}{3} i \, f x - \frac{2}{3} i \, e\right)}}{5 \, a f}, x\right) + 2^{\frac{1}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} {\left(3 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)} e^{\left(\frac{1}{3} i \, f x + \frac{1}{3} i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}}{10 \, a f}"," ",0,"1/10*(10*a*f*e^(2*I*f*x + 2*I*e)*integral(-2/5*I*2^(1/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(-2/3*I*f*x - 2/3*I*e)/(a*f), x) + 2^(1/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*(3*I*e^(2*I*f*x + 2*I*e) + 3*I)*e^(1/3*I*f*x + 1/3*I*e))*e^(-2*I*f*x - 2*I*e)/(a*f)","F",0
273,0,0,0,0.922668," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(-21 i \, e^{\left(5 i \, f x + 5 i \, e\right)} - 27 i \, e^{\left(4 i \, f x + 4 i \, e\right)} - 18 i \, e^{\left(3 i \, f x + 3 i \, e\right)} - 30 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, e^{\left(i \, f x + i \, e\right)} - 3 i\right)} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)} + 28 \, {\left(a d f e^{\left(4 i \, f x + 4 i \, e\right)} - a d f e^{\left(3 i \, f x + 3 i \, e\right)}\right)} {\rm integral}\left(\frac{2^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(-8 i \, e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, e^{\left(i \, f x + i \, e\right)} - 8 i\right)} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}}{7 \, {\left(a d f e^{\left(3 i \, f x + 3 i \, e\right)} - 2 \, a d f e^{\left(2 i \, f x + 2 i \, e\right)} + a d f e^{\left(i \, f x + i \, e\right)}\right)}}, x\right)}{28 \, {\left(a d f e^{\left(4 i \, f x + 4 i \, e\right)} - a d f e^{\left(3 i \, f x + 3 i \, e\right)}\right)}}"," ",0,"1/28*(2^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(-21*I*e^(5*I*f*x + 5*I*e) - 27*I*e^(4*I*f*x + 4*I*e) - 18*I*e^(3*I*f*x + 3*I*e) - 30*I*e^(2*I*f*x + 2*I*e) + 3*I*e^(I*f*x + I*e) - 3*I)*e^(2/3*I*f*x + 2/3*I*e) + 28*(a*d*f*e^(4*I*f*x + 4*I*e) - a*d*f*e^(3*I*f*x + 3*I*e))*integral(1/7*2^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(-8*I*e^(2*I*f*x + 2*I*e) - 8*I*e^(I*f*x + I*e) - 8*I)*e^(2/3*I*f*x + 2/3*I*e)/(a*d*f*e^(3*I*f*x + 3*I*e) - 2*a*d*f*e^(2*I*f*x + 2*I*e) + a*d*f*e^(I*f*x + I*e)), x))/(a*d*f*e^(4*I*f*x + 4*I*e) - a*d*f*e^(3*I*f*x + 3*I*e))","F",0
274,0,0,0,0.518594," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(440 \, a d^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} {\rm integral}\left(-\frac{16 i \cdot 2^{\frac{1}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(-\frac{2}{3} i \, f x - \frac{2}{3} i \, e\right)}}{55 \, a d^{2} f}, x\right) + 2^{\frac{1}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} {\left(-33 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 45 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 93 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 15 i\right)} e^{\left(\frac{1}{3} i \, f x + \frac{1}{3} i \, e\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{440 \, a d^{2} f}"," ",0,"1/440*(440*a*d^2*f*e^(4*I*f*x + 4*I*e)*integral(-16/55*I*2^(1/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(-2/3*I*f*x - 2/3*I*e)/(a*d^2*f), x) + 2^(1/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*(-33*I*e^(6*I*f*x + 6*I*e) + 45*I*e^(4*I*f*x + 4*I*e) + 93*I*e^(2*I*f*x + 2*I*e) + 15*I)*e^(1/3*I*f*x + 1/3*I*e))*e^(-4*I*f*x - 4*I*e)/(a*d^2*f)","F",0
275,0,0,0,0.444798," ","integrate((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(14 \, a^{2} f e^{\left(3 i \, f x + 3 i \, e\right)} {\rm integral}\left(-\frac{i \cdot 2^{\frac{2}{3}} d \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}}{7 \, a^{2} f}, x\right) + 2^{\frac{2}{3}} {\left(6 i \, d e^{\left(4 i \, f x + 4 i \, e\right)} + 9 i \, d e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, d\right)} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}\right)} e^{\left(-3 i \, f x - 3 i \, e\right)}}{14 \, a^{2} f}"," ",0,"1/14*(14*a^2*f*e^(3*I*f*x + 3*I*e)*integral(-1/7*I*2^(2/3)*d*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e)/(a^2*f), x) + 2^(2/3)*(6*I*d*e^(4*I*f*x + 4*I*e) + 9*I*d*e^(2*I*f*x + 2*I*e) + 3*I*d)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2/3*I*f*x + 2/3*I*e))*e^(-3*I*f*x - 3*I*e)/(a^2*f)","F",0
276,0,0,0,1.200699," ","integrate((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(44 \, a^{2} f e^{\left(4 i \, f x + 4 i \, e\right)} {\rm integral}\left(-\frac{2 i \cdot 2^{\frac{1}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(-\frac{2}{3} i \, f x - \frac{2}{3} i \, e\right)}}{11 \, a^{2} f}, x\right) + 2^{\frac{1}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} {\left(9 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 12 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)} e^{\left(\frac{1}{3} i \, f x + \frac{1}{3} i \, e\right)}\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{44 \, a^{2} f}"," ",0,"1/44*(44*a^2*f*e^(4*I*f*x + 4*I*e)*integral(-2/11*I*2^(1/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(-2/3*I*f*x - 2/3*I*e)/(a^2*f), x) + 2^(1/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*(9*I*e^(4*I*f*x + 4*I*e) + 12*I*e^(2*I*f*x + 2*I*e) + 3*I)*e^(1/3*I*f*x + 1/3*I*e))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","F",0
277,0,0,0,0.577407," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{2^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(-39 i \, e^{\left(7 i \, f x + 7 i \, e\right)} - 57 i \, e^{\left(6 i \, f x + 6 i \, e\right)} - 27 i \, e^{\left(5 i \, f x + 5 i \, e\right)} - 69 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 15 i \, e^{\left(3 i \, f x + 3 i \, e\right)} - 15 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i \, e^{\left(i \, f x + i \, e\right)} - 3 i\right)} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)} + 104 \, {\left(a^{2} d f e^{\left(6 i \, f x + 6 i \, e\right)} - a^{2} d f e^{\left(5 i \, f x + 5 i \, e\right)}\right)} {\rm integral}\left(\frac{2^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(-8 i \, e^{\left(2 i \, f x + 2 i \, e\right)} - 8 i \, e^{\left(i \, f x + i \, e\right)} - 8 i\right)} e^{\left(\frac{2}{3} i \, f x + \frac{2}{3} i \, e\right)}}{13 \, {\left(a^{2} d f e^{\left(3 i \, f x + 3 i \, e\right)} - 2 \, a^{2} d f e^{\left(2 i \, f x + 2 i \, e\right)} + a^{2} d f e^{\left(i \, f x + i \, e\right)}\right)}}, x\right)}{104 \, {\left(a^{2} d f e^{\left(6 i \, f x + 6 i \, e\right)} - a^{2} d f e^{\left(5 i \, f x + 5 i \, e\right)}\right)}}"," ",0,"1/104*(2^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(-39*I*e^(7*I*f*x + 7*I*e) - 57*I*e^(6*I*f*x + 6*I*e) - 27*I*e^(5*I*f*x + 5*I*e) - 69*I*e^(4*I*f*x + 4*I*e) + 15*I*e^(3*I*f*x + 3*I*e) - 15*I*e^(2*I*f*x + 2*I*e) + 3*I*e^(I*f*x + I*e) - 3*I)*e^(2/3*I*f*x + 2/3*I*e) + 104*(a^2*d*f*e^(6*I*f*x + 6*I*e) - a^2*d*f*e^(5*I*f*x + 5*I*e))*integral(1/13*2^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(-8*I*e^(2*I*f*x + 2*I*e) - 8*I*e^(I*f*x + I*e) - 8*I)*e^(2/3*I*f*x + 2/3*I*e)/(a^2*d*f*e^(3*I*f*x + 3*I*e) - 2*a^2*d*f*e^(2*I*f*x + 2*I*e) + a^2*d*f*e^(I*f*x + I*e)), x))/(a^2*d*f*e^(6*I*f*x + 6*I*e) - a^2*d*f*e^(5*I*f*x + 5*I*e))","F",0
278,0,0,0,0.534605," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(1360 \, a^{2} d^{2} f e^{\left(6 i \, f x + 6 i \, e\right)} {\rm integral}\left(-\frac{16 i \cdot 2^{\frac{1}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} e^{\left(-\frac{2}{3} i \, f x - \frac{2}{3} i \, e\right)}}{85 \, a^{2} d^{2} f}, x\right) + 2^{\frac{1}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{1}{3}} {\left(-51 i \, e^{\left(8 i \, f x + 8 i \, e\right)} + 150 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 276 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 90 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 15 i\right)} e^{\left(\frac{1}{3} i \, f x + \frac{1}{3} i \, e\right)}\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{1360 \, a^{2} d^{2} f}"," ",0,"1/1360*(1360*a^2*d^2*f*e^(6*I*f*x + 6*I*e)*integral(-16/85*I*2^(1/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*e^(-2/3*I*f*x - 2/3*I*e)/(a^2*d^2*f), x) + 2^(1/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(1/3)*(-51*I*e^(8*I*f*x + 8*I*e) + 150*I*e^(6*I*f*x + 6*I*e) + 276*I*e^(4*I*f*x + 4*I*e) + 90*I*e^(2*I*f*x + 2*I*e) + 15*I)*e^(1/3*I*f*x + 1/3*I*e))*e^(-6*I*f*x - 6*I*e)/(a^2*d^2*f)","F",0
279,1,154,0,0.687984," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-4096 i \, e^{\left(15 i \, d x + 15 i \, c\right)} - 30720 i \, e^{\left(13 i \, d x + 13 i \, c\right)} - 99840 i \, e^{\left(11 i \, d x + 11 i \, c\right)} - 183040 i \, e^{\left(9 i \, d x + 9 i \, c\right)}\right)}}{6435 \, {\left(d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/6435*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-4096*I*e^(15*I*d*x + 15*I*c) - 30720*I*e^(13*I*d*x + 13*I*c) - 99840*I*e^(11*I*d*x + 11*I*c) - 183040*I*e^(9*I*d*x + 9*I*c))/(d*e^(14*I*d*x + 14*I*c) + 7*d*e^(12*I*d*x + 12*I*c) + 21*d*e^(10*I*d*x + 10*I*c) + 35*d*e^(8*I*d*x + 8*I*c) + 35*d*e^(6*I*d*x + 6*I*c) + 21*d*e^(4*I*d*x + 4*I*c) + 7*d*e^(2*I*d*x + 2*I*c) + d)","A",0
280,1,119,0,0.476800," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-512 i \, e^{\left(11 i \, d x + 11 i \, c\right)} - 2816 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 6336 i \, e^{\left(7 i \, d x + 7 i \, c\right)}\right)}}{693 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/693*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-512*I*e^(11*I*d*x + 11*I*c) - 2816*I*e^(9*I*d*x + 9*I*c) - 6336*I*e^(7*I*d*x + 7*I*c))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","A",0
281,1,84,0,0.460068," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-32 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 112 i \, e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}{35 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/35*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-32*I*e^(7*I*d*x + 7*I*c) - 112*I*e^(5*I*d*x + 5*I*c))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","A",0
282,1,46,0,0.473192," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{4 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(3 i \, d x + 3 i \, c\right)}}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-4/3*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(3*I*d*x + 3*I*c)/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
283,1,252,0,0.531990," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(8 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + 8 \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{1}{2} \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-8 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + 8 \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-i \, e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{8 \, d}"," ",0,"1/8*(3*sqrt(1/2)*d*sqrt(-a/d^2)*e^(I*d*x + I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(8*I*d*e^(2*I*d*x + 2*I*c) + 8*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + 8*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3*sqrt(1/2)*d*sqrt(-a/d^2)*e^(I*d*x + I*c)*log(1/2*(sqrt(2)*sqrt(1/2)*(-8*I*d*e^(2*I*d*x + 2*I*c) - 8*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + 8*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-I*e^(4*I*d*x + 4*I*c) + I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-I*d*x - I*c)/d","B",0
284,1,274,0,1.386805," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(105 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{1}{32} \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(128 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + 128 \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 105 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{1}{32} \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-128 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 128 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + 128 \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-6 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 45 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 41 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 88 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{384 \, d}"," ",0,"1/384*(105*sqrt(1/2)*d*sqrt(-a/d^2)*e^(3*I*d*x + 3*I*c)*log(1/32*(sqrt(2)*sqrt(1/2)*(128*I*d*e^(2*I*d*x + 2*I*c) + 128*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + 128*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 105*sqrt(1/2)*d*sqrt(-a/d^2)*e^(3*I*d*x + 3*I*c)*log(1/32*(sqrt(2)*sqrt(1/2)*(-128*I*d*e^(2*I*d*x + 2*I*c) - 128*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + 128*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-6*I*e^(8*I*d*x + 8*I*c) - 45*I*e^(6*I*d*x + 6*I*c) + 41*I*e^(4*I*d*x + 4*I*c) + 88*I*e^(2*I*d*x + 2*I*c) + 8*I))*e^(-3*I*d*x - 3*I*c)/d","A",0
285,1,296,0,0.578500," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3465 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{1}{256} \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(1024 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 1024 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + 1024 \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) - 3465 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(\frac{1}{256} \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-1024 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 1024 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + 1024 \, a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-40 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 350 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 1645 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 1433 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 3184 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 464 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 48 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{15360 \, d}"," ",0,"1/15360*(3465*sqrt(1/2)*d*sqrt(-a/d^2)*e^(5*I*d*x + 5*I*c)*log(1/256*(sqrt(2)*sqrt(1/2)*(1024*I*d*e^(2*I*d*x + 2*I*c) + 1024*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + 1024*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) - 3465*sqrt(1/2)*d*sqrt(-a/d^2)*e^(5*I*d*x + 5*I*c)*log(1/256*(sqrt(2)*sqrt(1/2)*(-1024*I*d*e^(2*I*d*x + 2*I*c) - 1024*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + 1024*a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-40*I*e^(12*I*d*x + 12*I*c) - 350*I*e^(10*I*d*x + 10*I*c) - 1645*I*e^(8*I*d*x + 8*I*c) + 1433*I*e^(6*I*d*x + 6*I*c) + 3184*I*e^(4*I*d*x + 4*I*c) + 464*I*e^(2*I*d*x + 2*I*c) + 48*I))*e^(-5*I*d*x - 5*I*c)/d","A",0
286,1,132,0,0.565762," ","integrate(sec(d*x+c)^7*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(54912 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 36608 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 13312 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2048 i\right)}}{3003 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3003*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(54912*I*e^(6*I*d*x + 6*I*c) + 36608*I*e^(4*I*d*x + 4*I*c) + 13312*I*e^(2*I*d*x + 2*I*c) + 2048*I)/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","A",0
287,1,97,0,1.464421," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(2016 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 1152 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 256 i\right)}}{315 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/315*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(2016*I*e^(4*I*d*x + 4*I*c) + 1152*I*e^(2*I*d*x + 2*I*c) + 256*I)/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","A",0
288,1,62,0,0.510591," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(40 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i\right)}}{15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/15*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(40*I*e^(2*I*d*x + 2*I*c) + 16*I)/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
289,1,25,0,0.526680," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{d}"," ",0,"2*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/d","A",0
290,1,183,0,0.737860," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} d \sqrt{-\frac{a}{d^{2}}} \log\left(\frac{2 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + i \, a\right)} e^{\left(-i \, d x - i \, c\right)}}{d}\right) - \sqrt{2} d \sqrt{-\frac{a}{d^{2}}} \log\left(-\frac{2 \, {\left({\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} - i \, a\right)} e^{\left(-i \, d x - i \, c\right)}}{d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i\right)}}{4 \, d}"," ",0,"1/4*(sqrt(2)*d*sqrt(-a/d^2)*log(2*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + I*a)*e^(-I*d*x - I*c)/d) - sqrt(2)*d*sqrt(-a/d^2)*log(-2*((d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) - I*a)*e^(-I*d*x - I*c)/d) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-2*I*e^(2*I*d*x + 2*I*c) - 2*I))/d","B",0
291,1,245,0,0.576775," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{5 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + i \, a\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, d}\right) - 15 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{5 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} - i \, a\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-2 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 16 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 11 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{48 \, d}"," ",0,"1/48*(15*sqrt(1/2)*d*sqrt(-a/d^2)*e^(2*I*d*x + 2*I*c)*log(5/4*(sqrt(2)*sqrt(1/2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + I*a)*e^(-I*d*x - I*c)/d) - 15*sqrt(1/2)*d*sqrt(-a/d^2)*e^(2*I*d*x + 2*I*c)*log(-5/4*(sqrt(2)*sqrt(1/2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) - I*a)*e^(-I*d*x - I*c)/d) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-2*I*e^(6*I*d*x + 6*I*c) - 16*I*e^(4*I*d*x + 4*I*c) - 11*I*e^(2*I*d*x + 2*I*c) + 3*I))*e^(-2*I*d*x - 2*I*c)/d","B",0
292,1,267,0,0.511000," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(315 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{63 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} + i \, a\right)} e^{\left(-i \, d x - i \, c\right)}}{64 \, d}\right) - 315 \, \sqrt{\frac{1}{2}} d \sqrt{-\frac{a}{d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{63 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{-\frac{a}{d^{2}}} - i \, a\right)} e^{\left(-i \, d x - i \, c\right)}}{64 \, d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-8 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 64 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 344 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 203 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 95 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 10 i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{1280 \, d}"," ",0,"1/1280*(315*sqrt(1/2)*d*sqrt(-a/d^2)*e^(4*I*d*x + 4*I*c)*log(63/64*(sqrt(2)*sqrt(1/2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) + I*a)*e^(-I*d*x - I*c)/d) - 315*sqrt(1/2)*d*sqrt(-a/d^2)*e^(4*I*d*x + 4*I*c)*log(-63/64*(sqrt(2)*sqrt(1/2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(-a/d^2) - I*a)*e^(-I*d*x - I*c)/d) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-8*I*e^(10*I*d*x + 10*I*c) - 64*I*e^(8*I*d*x + 8*I*c) - 344*I*e^(6*I*d*x + 6*I*c) - 203*I*e^(4*I*d*x + 4*I*c) + 95*I*e^(2*I*d*x + 2*I*c) + 10*I))*e^(-4*I*d*x - 4*I*c)/d","A",0
293,1,170,0,0.529325," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-8192 i \, a e^{\left(17 i \, d x + 17 i \, c\right)} - 69632 i \, a e^{\left(15 i \, d x + 15 i \, c\right)} - 261120 i \, a e^{\left(13 i \, d x + 13 i \, c\right)} - 565760 i \, a e^{\left(11 i \, d x + 11 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{12155 \, {\left(d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/12155*sqrt(2)*(-8192*I*a*e^(17*I*d*x + 17*I*c) - 69632*I*a*e^(15*I*d*x + 15*I*c) - 261120*I*a*e^(13*I*d*x + 13*I*c) - 565760*I*a*e^(11*I*d*x + 11*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(16*I*d*x + 16*I*c) + 8*d*e^(14*I*d*x + 14*I*c) + 28*d*e^(12*I*d*x + 12*I*c) + 56*d*e^(10*I*d*x + 10*I*c) + 70*d*e^(8*I*d*x + 8*I*c) + 56*d*e^(6*I*d*x + 6*I*c) + 28*d*e^(4*I*d*x + 4*I*c) + 8*d*e^(2*I*d*x + 2*I*c) + d)","A",0
294,1,134,0,0.537373," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-1024 i \, a e^{\left(13 i \, d x + 13 i \, c\right)} - 6656 i \, a e^{\left(11 i \, d x + 11 i \, c\right)} - 18304 i \, a e^{\left(9 i \, d x + 9 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{1287 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/1287*sqrt(2)*(-1024*I*a*e^(13*I*d*x + 13*I*c) - 6656*I*a*e^(11*I*d*x + 11*I*c) - 18304*I*a*e^(9*I*d*x + 9*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","B",0
295,1,98,0,0.631623," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-64 i \, a e^{\left(9 i \, d x + 9 i \, c\right)} - 288 i \, a e^{\left(7 i \, d x + 7 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{63 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/63*sqrt(2)*(-64*I*a*e^(9*I*d*x + 9*I*c) - 288*I*a*e^(7*I*d*x + 7*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
296,1,59,0,0.688273," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{8 i \, \sqrt{2} a \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(5 i \, d x + 5 i \, c\right)}}{5 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-8/5*I*sqrt(2)*a*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(5*I*d*x + 5*I*c)/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
297,1,241,0,0.464616," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(4 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 4 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) - \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-4 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 4 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{a}\right) + \sqrt{2} {\left(-i \, a e^{\left(3 i \, d x + 3 i \, c\right)} - i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{4 \, d}"," ",0,"1/4*(sqrt(1/2)*sqrt(-a^3/d^2)*d*log((sqrt(2)*sqrt(1/2)*(4*I*d*e^(2*I*d*x + 2*I*c) + 4*I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + 4*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - sqrt(1/2)*sqrt(-a^3/d^2)*d*log((sqrt(2)*sqrt(1/2)*(-4*I*d*e^(2*I*d*x + 2*I*c) - 4*I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + 4*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + sqrt(2)*(-I*a*e^(3*I*d*x + 3*I*c) - I*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","B",0
298,1,286,0,0.468229," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(15 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(64 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 64 i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 64 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{16 \, a}\right) - 15 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-64 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 64 i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 64 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{16 \, a}\right) + \sqrt{2} {\left(-2 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 11 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{64 \, d}"," ",0,"1/64*(15*sqrt(1/2)*sqrt(-a^3/d^2)*d*e^(I*d*x + I*c)*log(1/16*(sqrt(2)*sqrt(1/2)*(64*I*d*e^(2*I*d*x + 2*I*c) + 64*I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + 64*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 15*sqrt(1/2)*sqrt(-a^3/d^2)*d*e^(I*d*x + I*c)*log(1/16*(sqrt(2)*sqrt(1/2)*(-64*I*d*e^(2*I*d*x + 2*I*c) - 64*I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + 64*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + sqrt(2)*(-2*I*a*e^(6*I*d*x + 6*I*c) - 11*I*a*e^(4*I*d*x + 4*I*c) - I*a*e^(2*I*d*x + 2*I*c) + 8*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d","B",0
299,1,310,0,0.822959," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(315 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(512 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 512 i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 512 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{128 \, a}\right) - 315 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-512 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 512 i \, d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + 512 \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{128 \, a}\right) + \sqrt{2} {\left(-8 i \, a e^{\left(10 i \, d x + 10 i \, c\right)} - 58 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} - 215 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 43 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 224 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{1536 \, d}"," ",0,"1/1536*(315*sqrt(1/2)*sqrt(-a^3/d^2)*d*e^(3*I*d*x + 3*I*c)*log(1/128*(sqrt(2)*sqrt(1/2)*(512*I*d*e^(2*I*d*x + 2*I*c) + 512*I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + 512*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) - 315*sqrt(1/2)*sqrt(-a^3/d^2)*d*e^(3*I*d*x + 3*I*c)*log(1/128*(sqrt(2)*sqrt(1/2)*(-512*I*d*e^(2*I*d*x + 2*I*c) - 512*I*d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + 512*a^2*e^(I*d*x + I*c))*e^(-I*d*x - I*c)/a) + sqrt(2)*(-8*I*a*e^(10*I*d*x + 10*I*c) - 58*I*a*e^(8*I*d*x + 8*I*c) - 215*I*a*e^(6*I*d*x + 6*I*c) + 43*I*a*e^(4*I*d*x + 4*I*c) + 224*I*a*e^(2*I*d*x + 2*I*c) + 16*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-3*I*d*x - 3*I*c)/d","A",0
300,1,125,0,0.636652," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(14784 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 12672 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 5632 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 1024 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{1155 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/1155*sqrt(2)*(14784*I*a*e^(6*I*d*x + 6*I*c) + 12672*I*a*e^(4*I*d*x + 4*I*c) + 5632*I*a*e^(2*I*d*x + 2*I*c) + 1024*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","A",0
301,1,89,0,0.706113," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(560 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 448 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{105 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/105*sqrt(2)*(560*I*a*e^(4*I*d*x + 4*I*c) + 448*I*a*e^(2*I*d*x + 2*I*c) + 128*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","A",0
302,1,53,0,0.613879," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(12 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*sqrt(2)*(12*I*a*e^(2*I*d*x + 2*I*c) + 8*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
303,1,40,0,0.595431," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{d}"," ",0,"sqrt(2)*(-I*a*e^(2*I*d*x + 2*I*c) - I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/d","A",0
304,1,222,0,0.640445," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, a^{2}\right)} e^{\left(-i \, d x - i \, c\right)}}{d}\right) - 3 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d \log\left(-\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, a^{2}\right)} e^{\left(-i \, d x - i \, c\right)}}{d}\right) + \sqrt{2} {\left(-i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 5 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{12 \, d}"," ",0,"1/12*(3*sqrt(1/2)*sqrt(-a^3/d^2)*d*log((sqrt(2)*sqrt(1/2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + I*a^2)*e^(-I*d*x - I*c)/d) - 3*sqrt(1/2)*sqrt(-a^3/d^2)*d*log(-(sqrt(2)*sqrt(1/2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) - I*a^2)*e^(-I*d*x - I*c)/d) + sqrt(2)*(-I*a*e^(4*I*d*x + 4*I*c) - 5*I*a*e^(2*I*d*x + 2*I*c) - 4*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","B",0
305,1,274,0,0.500205," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(105 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{7 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} + i \, a^{2}\right)} e^{\left(-i \, d x - i \, c\right)}}{8 \, d}\right) - 105 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{3}}{d^{2}}} d e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{7 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{-\frac{a^{3}}{d^{2}}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} - i \, a^{2}\right)} e^{\left(-i \, d x - i \, c\right)}}{8 \, d}\right) + \sqrt{2} {\left(-6 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} - 38 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 148 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 101 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 15 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{480 \, d}"," ",0,"1/480*(105*sqrt(1/2)*sqrt(-a^3/d^2)*d*e^(2*I*d*x + 2*I*c)*log(7/8*(sqrt(2)*sqrt(1/2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) + I*a^2)*e^(-I*d*x - I*c)/d) - 105*sqrt(1/2)*sqrt(-a^3/d^2)*d*e^(2*I*d*x + 2*I*c)*log(-7/8*(sqrt(2)*sqrt(1/2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(-a^3/d^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)) - I*a^2)*e^(-I*d*x - I*c)/d) + sqrt(2)*(-6*I*a*e^(8*I*d*x + 8*I*c) - 38*I*a*e^(6*I*d*x + 6*I*c) - 148*I*a*e^(4*I*d*x + 4*I*c) - 101*I*a*e^(2*I*d*x + 2*I*c) + 15*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/d","A",0
306,1,190,0,0.657897," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-16384 i \, a^{2} e^{\left(19 i \, d x + 19 i \, c\right)} - 155648 i \, a^{2} e^{\left(17 i \, d x + 17 i \, c\right)} - 661504 i \, a^{2} e^{\left(15 i \, d x + 15 i \, c\right)} - 1653760 i \, a^{2} e^{\left(13 i \, d x + 13 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{20995 \, {\left(d e^{\left(18 i \, d x + 18 i \, c\right)} + 9 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 36 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 84 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 126 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 126 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 84 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 36 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 9 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/20995*sqrt(2)*(-16384*I*a^2*e^(19*I*d*x + 19*I*c) - 155648*I*a^2*e^(17*I*d*x + 17*I*c) - 661504*I*a^2*e^(15*I*d*x + 15*I*c) - 1653760*I*a^2*e^(13*I*d*x + 13*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(18*I*d*x + 18*I*c) + 9*d*e^(16*I*d*x + 16*I*c) + 36*d*e^(14*I*d*x + 14*I*c) + 84*d*e^(12*I*d*x + 12*I*c) + 126*d*e^(10*I*d*x + 10*I*c) + 126*d*e^(8*I*d*x + 8*I*c) + 84*d*e^(6*I*d*x + 6*I*c) + 36*d*e^(4*I*d*x + 4*I*c) + 9*d*e^(2*I*d*x + 2*I*c) + d)","B",0
307,1,152,0,0.678437," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-2048 i \, a^{2} e^{\left(15 i \, d x + 15 i \, c\right)} - 15360 i \, a^{2} e^{\left(13 i \, d x + 13 i \, c\right)} - 49920 i \, a^{2} e^{\left(11 i \, d x + 11 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{2145 \, {\left(d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/2145*sqrt(2)*(-2048*I*a^2*e^(15*I*d*x + 15*I*c) - 15360*I*a^2*e^(13*I*d*x + 13*I*c) - 49920*I*a^2*e^(11*I*d*x + 11*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(14*I*d*x + 14*I*c) + 7*d*e^(12*I*d*x + 12*I*c) + 21*d*e^(10*I*d*x + 10*I*c) + 35*d*e^(8*I*d*x + 8*I*c) + 35*d*e^(6*I*d*x + 6*I*c) + 21*d*e^(4*I*d*x + 4*I*c) + 7*d*e^(2*I*d*x + 2*I*c) + d)","B",0
308,1,114,0,0.463176," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-128 i \, a^{2} e^{\left(11 i \, d x + 11 i \, c\right)} - 704 i \, a^{2} e^{\left(9 i \, d x + 9 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{99 \, {\left(d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/99*sqrt(2)*(-128*I*a^2*e^(11*I*d*x + 11*I*c) - 704*I*a^2*e^(9*I*d*x + 9*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
309,1,73,0,0.672362," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{16 i \, \sqrt{2} a^{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(7 i \, d x + 7 i \, c\right)}}{7 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-16/7*I*sqrt(2)*a^2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(7*I*d*x + 7*I*c)/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
310,1,236,0,0.563711," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} d \log\left(\frac{2 \, {\left(2 \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(2 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - \sqrt{2} \sqrt{-\frac{a^{5}}{d^{2}}} d \log\left(\frac{2 \, {\left(2 \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-2 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2}}\right) - \sqrt{2} {\left(-2 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 2 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{4 \, d}"," ",0,"-1/4*(sqrt(2)*sqrt(-a^5/d^2)*d*log(2*(2*a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(2*I*d*e^(2*I*d*x + 2*I*c) + 2*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - sqrt(2)*sqrt(-a^5/d^2)*d*log(2*(2*a^3*e^(I*d*x + I*c) + sqrt(-a^5/d^2)*(-2*I*d*e^(2*I*d*x + 2*I*c) - 2*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - sqrt(2)*(-2*I*a^2*e^(3*I*d*x + 3*I*c) - 2*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","B",0
311,1,262,0,0.465692," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} d \log\left(\frac{{\left(32 \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(32 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{8 \, a^{2}}\right) - 3 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} d \log\left(\frac{{\left(32 \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-32 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 32 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{8 \, a^{2}}\right) + \sqrt{2} {\left(-2 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 7 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 5 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{32 \, d}"," ",0,"1/32*(3*sqrt(1/2)*sqrt(-a^5/d^2)*d*log(1/8*(32*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(1/2)*sqrt(-a^5/d^2)*(32*I*d*e^(2*I*d*x + 2*I*c) + 32*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 3*sqrt(1/2)*sqrt(-a^5/d^2)*d*log(1/8*(32*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(1/2)*sqrt(-a^5/d^2)*(-32*I*d*e^(2*I*d*x + 2*I*c) - 32*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) + sqrt(2)*(-2*I*a^2*e^(5*I*d*x + 5*I*c) - 7*I*a^2*e^(3*I*d*x + 3*I*c) - 5*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","B",0
312,1,308,0,0.647716," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(105 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left(256 \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(256 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 256 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{64 \, a^{2}}\right) - 105 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} d e^{\left(i \, d x + i \, c\right)} \log\left(\frac{{\left(256 \, a^{3} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(-256 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 256 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{64 \, a^{2}}\right) + \sqrt{2} {\left(-8 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 46 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 125 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 39 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 48 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{768 \, d}"," ",0,"1/768*(105*sqrt(1/2)*sqrt(-a^5/d^2)*d*e^(I*d*x + I*c)*log(1/64*(256*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(1/2)*sqrt(-a^5/d^2)*(256*I*d*e^(2*I*d*x + 2*I*c) + 256*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) - 105*sqrt(1/2)*sqrt(-a^5/d^2)*d*e^(I*d*x + I*c)*log(1/64*(256*a^3*e^(I*d*x + I*c) + sqrt(2)*sqrt(1/2)*sqrt(-a^5/d^2)*(-256*I*d*e^(2*I*d*x + 2*I*c) - 256*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^2) + sqrt(2)*(-8*I*a^2*e^(8*I*d*x + 8*I*c) - 46*I*a^2*e^(6*I*d*x + 6*I*c) - 125*I*a^2*e^(4*I*d*x + 4*I*c) - 39*I*a^2*e^(2*I*d*x + 2*I*c) + 48*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d","A",0
313,1,121,0,0.598986," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(3360 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 4032 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 2304 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 512 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{315 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/315*sqrt(2)*(3360*I*a^2*e^(6*I*d*x + 6*I*c) + 4032*I*a^2*e^(4*I*d*x + 4*I*c) + 2304*I*a^2*e^(2*I*d*x + 2*I*c) + 512*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","A",0
314,1,83,0,0.618906," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(120 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 160 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 64 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{15 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/15*sqrt(2)*(120*I*a^2*e^(4*I*d*x + 4*I*c) + 160*I*a^2*e^(2*I*d*x + 2*I*c) + 64*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
315,1,44,0,0.482996," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-2 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{d}"," ",0,"sqrt(2)*(-2*I*a^2*e^(2*I*d*x + 2*I*c) - 4*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/d","A",0
316,1,59,0,0.537197," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{6 \, d}"," ",0,"1/6*sqrt(2)*(-I*a^2*e^(4*I*d*x + 4*I*c) - 2*I*a^2*e^(2*I*d*x + 2*I*c) - I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/d","B",0
317,1,244,0,0.725768," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} d \log\left(\frac{{\left(i \, a^{3} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, d}\right) - 15 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} d \log\left(\frac{{\left(i \, a^{3} - \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, d}\right) + \sqrt{2} {\left(-3 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 14 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 34 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 23 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{120 \, d}"," ",0,"1/120*(15*sqrt(1/2)*sqrt(-a^5/d^2)*d*log(1/2*(I*a^3 + sqrt(2)*sqrt(1/2)*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) - 15*sqrt(1/2)*sqrt(-a^5/d^2)*d*log(1/2*(I*a^3 - sqrt(2)*sqrt(1/2)*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) + sqrt(2)*(-3*I*a^2*e^(6*I*d*x + 6*I*c) - 14*I*a^2*e^(4*I*d*x + 4*I*c) - 34*I*a^2*e^(2*I*d*x + 2*I*c) - 23*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","B",0
318,1,300,0,2.231655," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(315 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} d e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{9 \, {\left(-i \, a^{3} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{16 \, d}\right) - 315 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} d e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{9 \, {\left(-i \, a^{3} - \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{5}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{16 \, d}\right) - \sqrt{2} {\left(-10 i \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} - 68 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 214 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 544 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 353 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 35 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2240 \, d}"," ",0,"-1/2240*(315*sqrt(1/2)*sqrt(-a^5/d^2)*d*e^(2*I*d*x + 2*I*c)*log(-9/16*(-I*a^3 + sqrt(2)*sqrt(1/2)*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) - 315*sqrt(1/2)*sqrt(-a^5/d^2)*d*e^(2*I*d*x + 2*I*c)*log(-9/16*(-I*a^3 - sqrt(2)*sqrt(1/2)*sqrt(-a^5/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) - sqrt(2)*(-10*I*a^2*e^(10*I*d*x + 10*I*c) - 68*I*a^2*e^(8*I*d*x + 8*I*c) - 214*I*a^2*e^(6*I*d*x + 6*I*c) - 544*I*a^2*e^(4*I*d*x + 4*I*c) - 353*I*a^2*e^(2*I*d*x + 2*I*c) + 35*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/d","A",0
319,1,202,0,0.910092," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-32768 i \, a^{3} e^{\left(21 i \, d x + 21 i \, c\right)} - 344064 i \, a^{3} e^{\left(19 i \, d x + 19 i \, c\right)} - 1634304 i \, a^{3} e^{\left(17 i \, d x + 17 i \, c\right)} - 4630528 i \, a^{3} e^{\left(15 i \, d x + 15 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{33915 \, {\left(d e^{\left(20 i \, d x + 20 i \, c\right)} + 10 \, d e^{\left(18 i \, d x + 18 i \, c\right)} + 45 \, d e^{\left(16 i \, d x + 16 i \, c\right)} + 120 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 210 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 252 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 210 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 120 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 45 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 10 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/33915*sqrt(2)*(-32768*I*a^3*e^(21*I*d*x + 21*I*c) - 344064*I*a^3*e^(19*I*d*x + 19*I*c) - 1634304*I*a^3*e^(17*I*d*x + 17*I*c) - 4630528*I*a^3*e^(15*I*d*x + 15*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(20*I*d*x + 20*I*c) + 10*d*e^(18*I*d*x + 18*I*c) + 45*d*e^(16*I*d*x + 16*I*c) + 120*d*e^(14*I*d*x + 14*I*c) + 210*d*e^(12*I*d*x + 12*I*c) + 252*d*e^(10*I*d*x + 10*I*c) + 210*d*e^(8*I*d*x + 8*I*c) + 120*d*e^(6*I*d*x + 6*I*c) + 45*d*e^(4*I*d*x + 4*I*c) + 10*d*e^(2*I*d*x + 2*I*c) + d)","B",0
320,1,164,0,2.796716," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-4096 i \, a^{3} e^{\left(17 i \, d x + 17 i \, c\right)} - 34816 i \, a^{3} e^{\left(15 i \, d x + 15 i \, c\right)} - 130560 i \, a^{3} e^{\left(13 i \, d x + 13 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{3315 \, {\left(d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3315*sqrt(2)*(-4096*I*a^3*e^(17*I*d*x + 17*I*c) - 34816*I*a^3*e^(15*I*d*x + 15*I*c) - 130560*I*a^3*e^(13*I*d*x + 13*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(16*I*d*x + 16*I*c) + 8*d*e^(14*I*d*x + 14*I*c) + 28*d*e^(12*I*d*x + 12*I*c) + 56*d*e^(10*I*d*x + 10*I*c) + 70*d*e^(8*I*d*x + 8*I*c) + 56*d*e^(6*I*d*x + 6*I*c) + 28*d*e^(4*I*d*x + 4*I*c) + 8*d*e^(2*I*d*x + 2*I*c) + d)","B",0
321,1,126,0,0.466710," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-256 i \, a^{3} e^{\left(13 i \, d x + 13 i \, c\right)} - 1664 i \, a^{3} e^{\left(11 i \, d x + 11 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{143 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/143*sqrt(2)*(-256*I*a^3*e^(13*I*d*x + 13*I*c) - 1664*I*a^3*e^(11*I*d*x + 11*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(12*I*d*x + 12*I*c) + 6*d*e^(10*I*d*x + 10*I*c) + 15*d*e^(8*I*d*x + 8*I*c) + 20*d*e^(6*I*d*x + 6*I*c) + 15*d*e^(4*I*d*x + 4*I*c) + 6*d*e^(2*I*d*x + 2*I*c) + d)","B",0
322,1,85,0,0.460972," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{32 i \, \sqrt{2} a^{3} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(9 i \, d x + 9 i \, c\right)}}{9 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-32/9*I*sqrt(2)*a^3*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(9*I*d*x + 9*I*c)/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
323,1,235,0,2.466148," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{6 \, \sqrt{2} \sqrt{-\frac{a^{7}}{d^{2}}} d \log\left(\frac{4 \, {\left(a^{4} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{7}}{d^{2}}} {\left(i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3}}\right) - 6 \, \sqrt{2} \sqrt{-\frac{a^{7}}{d^{2}}} d \log\left(\frac{4 \, {\left(a^{4} e^{\left(i \, d x + i \, c\right)} + \sqrt{-\frac{a^{7}}{d^{2}}} {\left(-i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3}}\right) - \sqrt{2} {\left(-4 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 12 i \, a^{3} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{4 \, d}"," ",0,"-1/4*(6*sqrt(2)*sqrt(-a^7/d^2)*d*log(4*(a^4*e^(I*d*x + I*c) + sqrt(-a^7/d^2)*(I*d*e^(2*I*d*x + 2*I*c) + I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^3) - 6*sqrt(2)*sqrt(-a^7/d^2)*d*log(4*(a^4*e^(I*d*x + I*c) + sqrt(-a^7/d^2)*(-I*d*e^(2*I*d*x + 2*I*c) - I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^3) - sqrt(2)*(-4*I*a^3*e^(3*I*d*x + 3*I*c) - 12*I*a^3*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","B",0
324,1,262,0,0.700902," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d \log\left(\frac{{\left(16 \, a^{4} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(16 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{3}}\right) - \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d \log\left(\frac{{\left(16 \, a^{4} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(-16 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 16 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a^{3}}\right) - \sqrt{2} {\left(-2 i \, a^{3} e^{\left(5 i \, d x + 5 i \, c\right)} - 3 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - i \, a^{3} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{16 \, d}"," ",0,"-1/16*(sqrt(1/2)*sqrt(-a^7/d^2)*d*log(1/4*(16*a^4*e^(I*d*x + I*c) + sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(16*I*d*e^(2*I*d*x + 2*I*c) + 16*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^3) - sqrt(1/2)*sqrt(-a^7/d^2)*d*log(1/4*(16*a^4*e^(I*d*x + I*c) + sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(-16*I*d*e^(2*I*d*x + 2*I*c) - 16*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^3) - sqrt(2)*(-2*I*a^3*e^(5*I*d*x + 5*I*c) - 3*I*a^3*e^(3*I*d*x + 3*I*c) - I*a^3*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","B",0
325,1,276,0,0.891757," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d \log\left(\frac{{\left(128 \, a^{4} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(128 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{32 \, a^{3}}\right) - 15 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d \log\left(\frac{{\left(128 \, a^{4} e^{\left(i \, d x + i \, c\right)} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(-128 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 128 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{32 \, a^{3}}\right) + \sqrt{2} {\left(-8 i \, a^{3} e^{\left(7 i \, d x + 7 i \, c\right)} - 34 i \, a^{3} e^{\left(5 i \, d x + 5 i \, c\right)} - 59 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 33 i \, a^{3} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{384 \, d}"," ",0,"1/384*(15*sqrt(1/2)*sqrt(-a^7/d^2)*d*log(1/32*(128*a^4*e^(I*d*x + I*c) + sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(128*I*d*e^(2*I*d*x + 2*I*c) + 128*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^3) - 15*sqrt(1/2)*sqrt(-a^7/d^2)*d*log(1/32*(128*a^4*e^(I*d*x + I*c) + sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(-128*I*d*e^(2*I*d*x + 2*I*c) - 128*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/a^3) + sqrt(2)*(-8*I*a^3*e^(7*I*d*x + 7*I*c) - 34*I*a^3*e^(5*I*d*x + 5*I*c) - 59*I*a^3*e^(3*I*d*x + 3*I*c) - 33*I*a^3*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","B",0
326,1,109,0,1.837123," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(560 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 1120 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 896 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 256 i \, a^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{35 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/35*sqrt(2)*(560*I*a^3*e^(6*I*d*x + 6*I*c) + 1120*I*a^3*e^(4*I*d*x + 4*I*c) + 896*I*a^3*e^(2*I*d*x + 2*I*c) + 256*I*a^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","A",0
327,1,71,0,1.059242," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-12 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 48 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 32 i \, a^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*sqrt(2)*(-12*I*a^3*e^(4*I*d*x + 4*I*c) - 48*I*a^3*e^(2*I*d*x + 2*I*c) - 32*I*a^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
328,1,59,0,0.730303," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, a^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{3 \, d}"," ",0,"1/3*sqrt(2)*(-I*a^3*e^(4*I*d*x + 4*I*c) + I*a^3*e^(2*I*d*x + 2*I*c) + 2*I*a^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/d","A",0
329,1,73,0,1.954939," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(-i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 3 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 3 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{20 \, d}"," ",0,"1/20*sqrt(2)*(-I*a^3*e^(6*I*d*x + 6*I*c) - 3*I*a^3*e^(4*I*d*x + 4*I*c) - 3*I*a^3*e^(2*I*d*x + 2*I*c) - I*a^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/d","B",0
330,1,258,0,0.581230," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d \log\left(\frac{{\left(i \, a^{4} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, d}\right) - 105 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d \log\left(\frac{{\left(i \, a^{4} - \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, d}\right) + \sqrt{2} {\left(-15 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 81 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 188 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 298 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 176 i \, a^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{1680 \, d}"," ",0,"1/1680*(105*sqrt(1/2)*sqrt(-a^7/d^2)*d*log(1/4*(I*a^4 + sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) - 105*sqrt(1/2)*sqrt(-a^7/d^2)*d*log(1/4*(I*a^4 - sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) + sqrt(2)*(-15*I*a^3*e^(8*I*d*x + 8*I*c) - 81*I*a^3*e^(6*I*d*x + 6*I*c) - 188*I*a^3*e^(4*I*d*x + 4*I*c) - 298*I*a^3*e^(2*I*d*x + 2*I*c) - 176*I*a^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/d","A",0
331,1,314,0,1.406816," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{{\left(3465 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{11 \, {\left(-i \, a^{4} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{32 \, d}\right) - 3465 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-\frac{11 \, {\left(-i \, a^{4} - \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{32 \, d}\right) - \sqrt{2} {\left(-70 i \, a^{3} e^{\left(12 i \, d x + 12 i \, c\right)} - 530 i \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} - 1798 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 3754 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 7034 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 4303 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 315 i \, a^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{40320 \, d}"," ",0,"-1/40320*(3465*sqrt(1/2)*sqrt(-a^7/d^2)*d*e^(2*I*d*x + 2*I*c)*log(-11/32*(-I*a^4 + sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) - 3465*sqrt(1/2)*sqrt(-a^7/d^2)*d*e^(2*I*d*x + 2*I*c)*log(-11/32*(-I*a^4 - sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) - sqrt(2)*(-70*I*a^3*e^(12*I*d*x + 12*I*c) - 530*I*a^3*e^(10*I*d*x + 10*I*c) - 1798*I*a^3*e^(8*I*d*x + 8*I*c) - 3754*I*a^3*e^(6*I*d*x + 6*I*c) - 7034*I*a^3*e^(4*I*d*x + 4*I*c) - 4303*I*a^3*e^(2*I*d*x + 2*I*c) + 315*I*a^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-2*I*d*x - 2*I*c)/d","A",0
332,1,342,0,0.791533," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","-\frac{{\left(45045 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{195 \, {\left(-i \, a^{4} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{512 \, d}\right) - 45045 \, \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} d e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-\frac{195 \, {\left(-i \, a^{4} - \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{-\frac{a^{7}}{d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-i \, d x - i \, c\right)}}{512 \, d}\right) - \sqrt{2} {\left(-168 i \, a^{3} e^{\left(16 i \, d x + 16 i \, c\right)} - 1624 i \, a^{3} e^{\left(14 i \, d x + 14 i \, c\right)} - 7184 i \, a^{3} e^{\left(12 i \, d x + 12 i \, c\right)} - 19552 i \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} - 38512 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} - 78800 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 47413 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 7161 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 462 i \, a^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{473088 \, d}"," ",0,"-1/473088*(45045*sqrt(1/2)*sqrt(-a^7/d^2)*d*e^(4*I*d*x + 4*I*c)*log(-195/512*(-I*a^4 + sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) - 45045*sqrt(1/2)*sqrt(-a^7/d^2)*d*e^(4*I*d*x + 4*I*c)*log(-195/512*(-I*a^4 - sqrt(2)*sqrt(1/2)*sqrt(-a^7/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-I*d*x - I*c)/d) - sqrt(2)*(-168*I*a^3*e^(16*I*d*x + 16*I*c) - 1624*I*a^3*e^(14*I*d*x + 14*I*c) - 7184*I*a^3*e^(12*I*d*x + 12*I*c) - 19552*I*a^3*e^(10*I*d*x + 10*I*c) - 38512*I*a^3*e^(8*I*d*x + 8*I*c) - 78800*I*a^3*e^(6*I*d*x + 6*I*c) - 47413*I*a^3*e^(4*I*d*x + 4*I*c) + 7161*I*a^3*e^(2*I*d*x + 2*I*c) + 462*I*a^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))*e^(-4*I*d*x - 4*I*c)/d","A",0
333,1,150,0,1.931980," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-2048 i \, e^{\left(13 i \, d x + 13 i \, c\right)} - 13312 i \, e^{\left(11 i \, d x + 11 i \, c\right)} - 36608 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 54912 i \, e^{\left(7 i \, d x + 7 i \, c\right)}\right)}}{3003 \, {\left(a d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/3003*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-2048*I*e^(13*I*d*x + 13*I*c) - 13312*I*e^(11*I*d*x + 11*I*c) - 36608*I*e^(9*I*d*x + 9*I*c) - 54912*I*e^(7*I*d*x + 7*I*c))/(a*d*e^(12*I*d*x + 12*I*c) + 6*a*d*e^(10*I*d*x + 10*I*c) + 15*a*d*e^(8*I*d*x + 8*I*c) + 20*a*d*e^(6*I*d*x + 6*I*c) + 15*a*d*e^(4*I*d*x + 4*I*c) + 6*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
334,1,113,0,0.777665," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-256 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 1152 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 2016 i \, e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}{315 \, {\left(a d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/315*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-256*I*e^(9*I*d*x + 9*I*c) - 1152*I*e^(7*I*d*x + 7*I*c) - 2016*I*e^(5*I*d*x + 5*I*c))/(a*d*e^(8*I*d*x + 8*I*c) + 4*a*d*e^(6*I*d*x + 6*I*c) + 6*a*d*e^(4*I*d*x + 4*I*c) + 4*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
335,1,76,0,0.626325," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-16 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 40 i \, e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}{15 \, {\left(a d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/15*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-16*I*e^(5*I*d*x + 5*I*c) - 40*I*e^(3*I*d*x + 3*I*c))/(a*d*e^(4*I*d*x + 4*I*c) + 2*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
336,1,37,0,0.670033," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)}}{a d}"," ",0,"-2*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c)/(a*d)","A",0
337,1,271,0,1.306241," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(-15 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 15 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(3 i \, d x + 3 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-3 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 11 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 16 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{48 \, a d}"," ",0,"1/48*(-15*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(3*I*d*x + 3*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 15*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(3*I*d*x + 3*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-3*I*e^(6*I*d*x + 6*I*c) + 11*I*e^(4*I*d*x + 4*I*c) + 16*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-3*I*d*x - 3*I*c)/(a*d)","B",0
338,1,293,0,0.706468," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(-315 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 315 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-10 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 95 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 203 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 344 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 64 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{1280 \, a d}"," ",0,"1/1280*(-315*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 315*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-10*I*e^(10*I*d*x + 10*I*c) - 95*I*e^(8*I*d*x + 8*I*c) + 203*I*e^(6*I*d*x + 6*I*c) + 344*I*e^(4*I*d*x + 4*I*c) + 64*I*e^(2*I*d*x + 2*I*c) + 8*I))*e^(-5*I*d*x - 5*I*c)/(a*d)","A",0
339,1,315,0,0.938742," ","integrate(cos(d*x+c)^6/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(-45045 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 45045 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-280 i \, e^{\left(14 i \, d x + 14 i \, c\right)} - 2870 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 16345 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 27029 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 49792 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 11072 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 2304 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 240 i\right)}\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{215040 \, a d}"," ",0,"1/215040*(-45045*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(7*I*d*x + 7*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 45045*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(7*I*d*x + 7*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a*d*e^(2*I*d*x + 2*I*c) + a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-280*I*e^(14*I*d*x + 14*I*c) - 2870*I*e^(12*I*d*x + 12*I*c) - 16345*I*e^(10*I*d*x + 10*I*c) + 27029*I*e^(8*I*d*x + 8*I*c) + 49792*I*e^(6*I*d*x + 6*I*c) + 11072*I*e^(4*I*d*x + 4*I*c) + 2304*I*e^(2*I*d*x + 2*I*c) + 240*I))*e^(-7*I*d*x - 7*I*c)/(a*d)","A",0
340,1,153,0,0.789612," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(183040 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 99840 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 30720 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 4096 i\right)}}{6435 \, {\left(a d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, a d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, a d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/6435*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(183040*I*e^(6*I*d*x + 6*I*c) + 99840*I*e^(4*I*d*x + 4*I*c) + 30720*I*e^(2*I*d*x + 2*I*c) + 4096*I)/(a*d*e^(14*I*d*x + 14*I*c) + 7*a*d*e^(12*I*d*x + 12*I*c) + 21*a*d*e^(10*I*d*x + 10*I*c) + 35*a*d*e^(8*I*d*x + 8*I*c) + 35*a*d*e^(6*I*d*x + 6*I*c) + 21*a*d*e^(4*I*d*x + 4*I*c) + 7*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
341,1,116,0,0.918128," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(6336 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 2816 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 512 i\right)}}{693 \, {\left(a d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/693*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(6336*I*e^(4*I*d*x + 4*I*c) + 2816*I*e^(2*I*d*x + 2*I*c) + 512*I)/(a*d*e^(10*I*d*x + 10*I*c) + 5*a*d*e^(8*I*d*x + 8*I*c) + 10*a*d*e^(6*I*d*x + 6*I*c) + 10*a*d*e^(4*I*d*x + 4*I*c) + 5*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
342,1,79,0,0.789641," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(112 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 32 i\right)}}{35 \, {\left(a d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"1/35*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(112*I*e^(2*I*d*x + 2*I*c) + 32*I)/(a*d*e^(6*I*d*x + 6*I*c) + 3*a*d*e^(4*I*d*x + 4*I*c) + 3*a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
343,1,40,0,0.706930," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{3 \, {\left(a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d\right)}}"," ",0,"4/3*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(a*d*e^(2*I*d*x + 2*I*c) + a*d)","A",0
344,1,149,0,0.676442," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} i \, \sqrt{2} \sqrt{\frac{1}{a d^{2}}} \log\left(\frac{{\left(2 \, {\left(2 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + 4 i\right)} e^{\left(-i \, d x - i \, c\right)}}{d}\right) - \frac{1}{2} i \, \sqrt{2} \sqrt{\frac{1}{a d^{2}}} \log\left(\frac{{\left(2 \, {\left(-2 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + 4 i\right)} e^{\left(-i \, d x - i \, c\right)}}{d}\right)"," ",0,"1/2*I*sqrt(2)*sqrt(1/(a*d^2))*log((2*(2*I*d*e^(2*I*d*x + 2*I*c) + 2*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + 4*I)*e^(-I*d*x - I*c)/d) - 1/2*I*sqrt(2)*sqrt(1/(a*d^2))*log((2*(-2*I*d*e^(2*I*d*x + 2*I*c) - 2*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + 4*I)*e^(-I*d*x - I*c)/d)","B",0
345,1,245,0,0.682992," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(6 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + 6 i\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, d}\right) - 3 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-6 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + 6 i\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-2 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, a d}"," ",0,"1/8*(3*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(2*I*d*x + 2*I*c)*log(1/4*(sqrt(2)*sqrt(1/2)*(6*I*d*e^(2*I*d*x + 2*I*c) + 6*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + 6*I)*e^(-I*d*x - I*c)/d) - 3*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(2*I*d*x + 2*I*c)*log(1/4*(sqrt(2)*sqrt(1/2)*(-6*I*d*e^(2*I*d*x + 2*I*c) - 6*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + 6*I)*e^(-I*d*x - I*c)/d) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-2*I*e^(4*I*d*x + 4*I*c) - I*e^(2*I*d*x + 2*I*c) + I))*e^(-2*I*d*x - 2*I*c)/(a*d)","B",0
346,1,267,0,0.708882," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(105 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(1120 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} + 1120 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + 1120 i\right)} e^{\left(-i \, d x - i \, c\right)}}{1024 \, d}\right) - 105 i \, \sqrt{\frac{1}{2}} a d \sqrt{\frac{1}{a d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-1120 i \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 1120 i \, d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a d^{2}}} + 1120 i\right)} e^{\left(-i \, d x - i \, c\right)}}{1024 \, d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-8 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 88 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 41 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 45 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{384 \, a d}"," ",0,"1/384*(105*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(4*I*d*x + 4*I*c)*log(1/1024*(sqrt(2)*sqrt(1/2)*(1120*I*d*e^(2*I*d*x + 2*I*c) + 1120*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + 1120*I)*e^(-I*d*x - I*c)/d) - 105*I*sqrt(1/2)*a*d*sqrt(1/(a*d^2))*e^(4*I*d*x + 4*I*c)*log(1/1024*(sqrt(2)*sqrt(1/2)*(-1120*I*d*e^(2*I*d*x + 2*I*c) - 1120*I*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a*d^2)) + 1120*I)*e^(-I*d*x - I*c)/d) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-8*I*e^(8*I*d*x + 8*I*c) - 88*I*e^(6*I*d*x + 6*I*c) - 41*I*e^(4*I*d*x + 4*I*c) + 45*I*e^(2*I*d*x + 2*I*c) + 6*I))*e^(-4*I*d*x - 4*I*c)/(a*d)","A",0
347,1,149,0,0.799181," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-1024 i \, e^{\left(11 i \, d x + 11 i \, c\right)} - 5632 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 12672 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 14784 i \, e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}{1155 \, {\left(a^{2} d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/1155*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-1024*I*e^(11*I*d*x + 11*I*c) - 5632*I*e^(9*I*d*x + 9*I*c) - 12672*I*e^(7*I*d*x + 7*I*c) - 14784*I*e^(5*I*d*x + 5*I*c))/(a^2*d*e^(10*I*d*x + 10*I*c) + 5*a^2*d*e^(8*I*d*x + 8*I*c) + 10*a^2*d*e^(6*I*d*x + 6*I*c) + 10*a^2*d*e^(4*I*d*x + 4*I*c) + 5*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
348,1,108,0,0.574362," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-128 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 448 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 560 i \, e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}{105 \, {\left(a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/105*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-128*I*e^(7*I*d*x + 7*I*c) - 448*I*e^(5*I*d*x + 5*I*c) - 560*I*e^(3*I*d*x + 3*I*c))/(a^2*d*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^(4*I*d*x + 4*I*c) + 3*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
349,1,67,0,1.658813," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-8 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 12 i \, e^{\left(i \, d x + i \, c\right)}\right)}}{3 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/3*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-8*I*e^(3*I*d*x + 3*I*c) - 12*I*e^(I*d*x + I*c))/(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
350,1,49,0,0.714502," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2} d}"," ",0,"sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(2*I*d*x + 2*I*c) + I)*e^(-I*d*x - I*c)/(a^2*d)","B",0
351,1,294,0,0.467754," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(-105 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 105 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(5 i \, d x + 5 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-15 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 101 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 148 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 38 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{480 \, a^{2} d}"," ",0,"1/480*(-105*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(5*I*d*x + 5*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 105*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(5*I*d*x + 5*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-15*I*e^(8*I*d*x + 8*I*c) + 101*I*e^(6*I*d*x + 6*I*c) + 148*I*e^(4*I*d*x + 4*I*c) + 38*I*e^(2*I*d*x + 2*I*c) + 6*I))*e^(-5*I*d*x - 5*I*c)/(a^2*d)","B",0
352,1,316,0,0.710834," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(-3465 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 3465 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-70 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 805 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 2833 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 4584 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 1304 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 328 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 40 i\right)}\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{17920 \, a^{2} d}"," ",0,"1/17920*(-3465*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(7*I*d*x + 7*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 3465*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(7*I*d*x + 7*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-70*I*e^(12*I*d*x + 12*I*c) - 805*I*e^(10*I*d*x + 10*I*c) + 2833*I*e^(8*I*d*x + 8*I*c) + 4584*I*e^(6*I*d*x + 6*I*c) + 1304*I*e^(4*I*d*x + 4*I*c) + 328*I*e^(2*I*d*x + 2*I*c) + 40*I))*e^(-7*I*d*x - 7*I*c)/(a^2*d)","A",0
353,1,338,0,0.631338," ","integrate(cos(d*x+c)^6/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(-45045 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(9 i \, d x + 9 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 45045 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(9 i \, d x + 9 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-168 i \, e^{\left(16 i \, d x + 16 i \, c\right)} - 1974 i \, e^{\left(14 i \, d x + 14 i \, c\right)} - 13209 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 33301 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 57632 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 17344 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 5440 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 1136 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 112 i\right)}\right)} e^{\left(-9 i \, d x - 9 i \, c\right)}}{258048 \, a^{2} d}"," ",0,"1/258048*(-45045*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(9*I*d*x + 9*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 45045*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(9*I*d*x + 9*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-168*I*e^(16*I*d*x + 16*I*c) - 1974*I*e^(14*I*d*x + 14*I*c) - 13209*I*e^(12*I*d*x + 12*I*c) + 33301*I*e^(10*I*d*x + 10*I*c) + 57632*I*e^(8*I*d*x + 8*I*c) + 17344*I*e^(6*I*d*x + 6*I*c) + 5440*I*e^(4*I*d*x + 4*I*c) + 1136*I*e^(2*I*d*x + 2*I*c) + 112*I))*e^(-9*I*d*x - 9*I*c)/(a^2*d)","A",0
354,1,184,0,2.150990," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(565760 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 261120 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 69632 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8192 i\right)}}{12155 \, {\left(a^{2} d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, a^{2} d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, a^{2} d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, a^{2} d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/12155*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(565760*I*e^(6*I*d*x + 6*I*c) + 261120*I*e^(4*I*d*x + 4*I*c) + 69632*I*e^(2*I*d*x + 2*I*c) + 8192*I)/(a^2*d*e^(16*I*d*x + 16*I*c) + 8*a^2*d*e^(14*I*d*x + 14*I*c) + 28*a^2*d*e^(12*I*d*x + 12*I*c) + 56*a^2*d*e^(10*I*d*x + 10*I*c) + 70*a^2*d*e^(8*I*d*x + 8*I*c) + 56*a^2*d*e^(6*I*d*x + 6*I*c) + 28*a^2*d*e^(4*I*d*x + 4*I*c) + 8*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
355,1,143,0,0.717909," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(18304 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6656 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1024 i\right)}}{1287 \, {\left(a^{2} d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{2} d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/1287*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(18304*I*e^(4*I*d*x + 4*I*c) + 6656*I*e^(2*I*d*x + 2*I*c) + 1024*I)/(a^2*d*e^(12*I*d*x + 12*I*c) + 6*a^2*d*e^(10*I*d*x + 10*I*c) + 15*a^2*d*e^(8*I*d*x + 8*I*c) + 20*a^2*d*e^(6*I*d*x + 6*I*c) + 15*a^2*d*e^(4*I*d*x + 4*I*c) + 6*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
356,1,102,0,0.815215," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(288 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 64 i\right)}}{63 \, {\left(a^{2} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"1/63*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(288*I*e^(2*I*d*x + 2*I*c) + 64*I)/(a^2*d*e^(8*I*d*x + 8*I*c) + 4*a^2*d*e^(6*I*d*x + 6*I*c) + 6*a^2*d*e^(4*I*d*x + 4*I*c) + 4*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","A",0
357,1,59,0,0.565418," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{8 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{5 \, {\left(a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}"," ",0,"8/5*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(a^2*d*e^(4*I*d*x + 4*I*c) + 2*a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d)","B",0
358,1,196,0,0.597990," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{i \, \sqrt{2} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(\frac{{\left(2 \, {\left(4 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + 8 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a d}\right) - i \, \sqrt{2} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} \log\left(\frac{{\left(2 \, {\left(-4 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + 8 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a d}\right) - 2 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{a^{2} d}"," ",0,"(I*sqrt(2)*a^2*d*sqrt(1/(a^3*d^2))*log((2*(4*I*a*d*e^(2*I*d*x + 2*I*c) + 4*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + 8*I)*e^(-I*d*x - I*c)/(a*d)) - I*sqrt(2)*a^2*d*sqrt(1/(a^3*d^2))*log((2*(-4*I*a*d*e^(2*I*d*x + 2*I*c) - 4*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + 8*I)*e^(-I*d*x - I*c)/(a*d)) - 2*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1)))/(a^2*d)","B",0
359,1,246,0,0.735808," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + i\right)} e^{\left(-i \, d x - i \, c\right)}}{a d}\right) - i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + i\right)} e^{\left(-i \, d x - i \, c\right)}}{a d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{2} d}"," ",0,"1/4*(I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(2*I*d*x + 2*I*c)*log((sqrt(2)*sqrt(1/2)*(I*a*d*e^(2*I*d*x + 2*I*c) + I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + I)*e^(-I*d*x - I*c)/(a*d)) - I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(2*I*d*x + 2*I*c)*log((sqrt(2)*sqrt(1/2)*(-I*a*d*e^(2*I*d*x + 2*I*c) - I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + I)*e^(-I*d*x - I*c)/(a*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(2*I*d*x + 2*I*c) + I))*e^(-2*I*d*x - 2*I*c)/(a^2*d)","B",0
360,1,270,0,0.571996," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(15 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(240 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 240 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + 240 i\right)} e^{\left(-i \, d x - i \, c\right)}}{256 \, a d}\right) - 15 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-240 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 240 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + 240 i\right)} e^{\left(-i \, d x - i \, c\right)}}{256 \, a d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-8 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 11 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{64 \, a^{2} d}"," ",0,"1/64*(15*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(4*I*d*x + 4*I*c)*log(1/256*(sqrt(2)*sqrt(1/2)*(240*I*a*d*e^(2*I*d*x + 2*I*c) + 240*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + 240*I)*e^(-I*d*x - I*c)/(a*d)) - 15*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(4*I*d*x + 4*I*c)*log(1/256*(sqrt(2)*sqrt(1/2)*(-240*I*a*d*e^(2*I*d*x + 2*I*c) - 240*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + 240*I)*e^(-I*d*x - I*c)/(a*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-8*I*e^(6*I*d*x + 6*I*c) + I*e^(4*I*d*x + 4*I*c) + 11*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-4*I*d*x - 4*I*c)/(a^2*d)","B",0
361,1,292,0,0.578695," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(315 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(13440 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + 13440 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + 13440 i\right)} e^{\left(-i \, d x - i \, c\right)}}{16384 \, a d}\right) - 315 i \, \sqrt{\frac{1}{2}} a^{2} d \sqrt{\frac{1}{a^{3} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-13440 i \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - 13440 i \, a d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{3} d^{2}}} + 13440 i\right)} e^{\left(-i \, d x - i \, c\right)}}{16384 \, a d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-16 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 224 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 43 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 215 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 58 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{1536 \, a^{2} d}"," ",0,"1/1536*(315*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(6*I*d*x + 6*I*c)*log(1/16384*(sqrt(2)*sqrt(1/2)*(13440*I*a*d*e^(2*I*d*x + 2*I*c) + 13440*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + 13440*I)*e^(-I*d*x - I*c)/(a*d)) - 315*I*sqrt(1/2)*a^2*d*sqrt(1/(a^3*d^2))*e^(6*I*d*x + 6*I*c)*log(1/16384*(sqrt(2)*sqrt(1/2)*(-13440*I*a*d*e^(2*I*d*x + 2*I*c) - 13440*I*a*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^3*d^2)) + 13440*I)*e^(-I*d*x - I*c)/(a*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-16*I*e^(10*I*d*x + 10*I*c) - 224*I*e^(8*I*d*x + 8*I*c) - 43*I*e^(6*I*d*x + 6*I*c) + 215*I*e^(4*I*d*x + 4*I*c) + 58*I*e^(2*I*d*x + 2*I*c) + 8*I))*e^(-6*I*d*x - 6*I*c)/(a^2*d)","A",0
362,1,175,0,1.734170," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-16384 i \, e^{\left(13 i \, d x + 13 i \, c\right)} - 106496 i \, e^{\left(11 i \, d x + 11 i \, c\right)} - 292864 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 439296 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 384384 i \, e^{\left(5 i \, d x + 5 i \, c\right)}\right)}}{15015 \, {\left(a^{3} d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/15015*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-16384*I*e^(13*I*d*x + 13*I*c) - 106496*I*e^(11*I*d*x + 11*I*c) - 292864*I*e^(9*I*d*x + 9*I*c) - 439296*I*e^(7*I*d*x + 7*I*c) - 384384*I*e^(5*I*d*x + 5*I*c))/(a^3*d*e^(12*I*d*x + 12*I*c) + 6*a^3*d*e^(10*I*d*x + 10*I*c) + 15*a^3*d*e^(8*I*d*x + 8*I*c) + 20*a^3*d*e^(6*I*d*x + 6*I*c) + 15*a^3*d*e^(4*I*d*x + 4*I*c) + 6*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","A",0
363,1,134,0,0.650259," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-512 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 2304 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 4032 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 3360 i \, e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}{315 \, {\left(a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/315*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-512*I*e^(9*I*d*x + 9*I*c) - 2304*I*e^(7*I*d*x + 7*I*c) - 4032*I*e^(5*I*d*x + 5*I*c) - 3360*I*e^(3*I*d*x + 3*I*c))/(a^3*d*e^(8*I*d*x + 8*I*c) + 4*a^3*d*e^(6*I*d*x + 6*I*c) + 6*a^3*d*e^(4*I*d*x + 4*I*c) + 4*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","A",0
364,1,93,0,1.120129," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-64 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 160 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 120 i \, e^{\left(i \, d x + i \, c\right)}\right)}}{15 \, {\left(a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/15*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-64*I*e^(5*I*d*x + 5*I*c) - 160*I*e^(3*I*d*x + 3*I*c) - 120*I*e^(I*d*x + I*c))/(a^3*d*e^(4*I*d*x + 4*I*c) + 2*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","A",0
365,1,49,0,0.533973," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3} d}"," ",0,"sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(4*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-I*d*x - I*c)/(a^3*d)","A",0
366,1,61,0,0.513997," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{6 \, a^{3} d}"," ",0,"1/6*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(4*I*d*x + 4*I*c) + 2*I*e^(2*I*d*x + 2*I*c) + I)*e^(-3*I*d*x - 3*I*c)/(a^3*d)","B",0
367,1,305,0,0.750279," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(-315 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 315 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(7 i \, d x + 7 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-35 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 353 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 544 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 214 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 68 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 10 i\right)}\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{2240 \, a^{3} d}"," ",0,"1/2240*(-315*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(7*I*d*x + 7*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 315*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(7*I*d*x + 7*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-35*I*e^(10*I*d*x + 10*I*c) + 353*I*e^(8*I*d*x + 8*I*c) + 544*I*e^(6*I*d*x + 6*I*c) + 214*I*e^(4*I*d*x + 4*I*c) + 68*I*e^(2*I*d*x + 2*I*c) + 10*I))*e^(-7*I*d*x - 7*I*c)/(a^3*d)","B",0
368,1,327,0,0.859777," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(-45045 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(9 i \, d x + 9 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 45045 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(9 i \, d x + 9 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-630 i \, e^{\left(14 i \, d x + 14 i \, c\right)} - 8505 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 42709 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 69392 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 26752 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10144 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 2480 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 280 i\right)}\right)} e^{\left(-9 i \, d x - 9 i \, c\right)}}{322560 \, a^{3} d}"," ",0,"1/322560*(-45045*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(9*I*d*x + 9*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 45045*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(9*I*d*x + 9*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-630*I*e^(14*I*d*x + 14*I*c) - 8505*I*e^(12*I*d*x + 12*I*c) + 42709*I*e^(10*I*d*x + 10*I*c) + 69392*I*e^(8*I*d*x + 8*I*c) + 26752*I*e^(6*I*d*x + 6*I*c) + 10144*I*e^(4*I*d*x + 4*I*c) + 2480*I*e^(2*I*d*x + 2*I*c) + 280*I))*e^(-9*I*d*x - 9*I*c)/(a^3*d)","A",0
369,1,199,0,1.681727," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(1653760 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 661504 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 155648 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 16384 i\right)}}{20995 \, {\left(a^{3} d e^{\left(18 i \, d x + 18 i \, c\right)} + 9 \, a^{3} d e^{\left(16 i \, d x + 16 i \, c\right)} + 36 \, a^{3} d e^{\left(14 i \, d x + 14 i \, c\right)} + 84 \, a^{3} d e^{\left(12 i \, d x + 12 i \, c\right)} + 126 \, a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 126 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 84 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 36 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 9 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/20995*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(1653760*I*e^(6*I*d*x + 6*I*c) + 661504*I*e^(4*I*d*x + 4*I*c) + 155648*I*e^(2*I*d*x + 2*I*c) + 16384*I)/(a^3*d*e^(18*I*d*x + 18*I*c) + 9*a^3*d*e^(16*I*d*x + 16*I*c) + 36*a^3*d*e^(14*I*d*x + 14*I*c) + 84*a^3*d*e^(12*I*d*x + 12*I*c) + 126*a^3*d*e^(10*I*d*x + 10*I*c) + 126*a^3*d*e^(8*I*d*x + 8*I*c) + 84*a^3*d*e^(6*I*d*x + 6*I*c) + 36*a^3*d*e^(4*I*d*x + 4*I*c) + 9*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","A",0
370,1,158,0,0.753238," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(49920 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 15360 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2048 i\right)}}{2145 \, {\left(a^{3} d e^{\left(14 i \, d x + 14 i \, c\right)} + 7 \, a^{3} d e^{\left(12 i \, d x + 12 i \, c\right)} + 21 \, a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 35 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 35 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 21 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 7 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/2145*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(49920*I*e^(4*I*d*x + 4*I*c) + 15360*I*e^(2*I*d*x + 2*I*c) + 2048*I)/(a^3*d*e^(14*I*d*x + 14*I*c) + 7*a^3*d*e^(12*I*d*x + 12*I*c) + 21*a^3*d*e^(10*I*d*x + 10*I*c) + 35*a^3*d*e^(8*I*d*x + 8*I*c) + 35*a^3*d*e^(6*I*d*x + 6*I*c) + 21*a^3*d*e^(4*I*d*x + 4*I*c) + 7*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","A",0
371,1,117,0,0.719217," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(704 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 128 i\right)}}{99 \, {\left(a^{3} d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{3} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/99*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(704*I*e^(2*I*d*x + 2*I*c) + 128*I)/(a^3*d*e^(10*I*d*x + 10*I*c) + 5*a^3*d*e^(8*I*d*x + 8*I*c) + 10*a^3*d*e^(6*I*d*x + 6*I*c) + 10*a^3*d*e^(4*I*d*x + 4*I*c) + 5*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
372,1,74,0,0.513218," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{16 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{7 \, {\left(a^{3} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{3} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"16/7*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(a^3*d*e^(6*I*d*x + 6*I*c) + 3*a^3*d*e^(4*I*d*x + 4*I*c) + 3*a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
373,1,267,0,0.515639," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(6 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, a^{3} d\right)} \sqrt{\frac{1}{a^{5} d^{2}}} \log\left(\frac{{\left(2 \, {\left(8 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + 16 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2} d}\right) + \sqrt{2} {\left(-6 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, a^{3} d\right)} \sqrt{\frac{1}{a^{5} d^{2}}} \log\left(\frac{{\left(2 \, {\left(-8 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 8 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + 16 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-12 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 16 i\right)}}{3 \, {\left(a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{3} d\right)}}"," ",0,"1/3*(sqrt(2)*(6*I*a^3*d*e^(2*I*d*x + 2*I*c) + 6*I*a^3*d)*sqrt(1/(a^5*d^2))*log((2*(8*I*a^2*d*e^(2*I*d*x + 2*I*c) + 8*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + 16*I)*e^(-I*d*x - I*c)/(a^2*d)) + sqrt(2)*(-6*I*a^3*d*e^(2*I*d*x + 2*I*c) - 6*I*a^3*d)*sqrt(1/(a^5*d^2))*log((2*(-8*I*a^2*d*e^(2*I*d*x + 2*I*c) - 8*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + 16*I)*e^(-I*d*x - I*c)/(a^2*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-12*I*e^(2*I*d*x + 2*I*c) - 16*I))/(a^3*d*e^(2*I*d*x + 2*I*c) + a^3*d)","B",0
374,1,244,0,0.602078," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(i \, \sqrt{2} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left(2 \, {\left(i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - 2 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2} d}\right) - i \, \sqrt{2} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left(2 \, {\left(-i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} - 2 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{2} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, a^{3} d}"," ",0,"1/4*(I*sqrt(2)*a^3*d*sqrt(1/(a^5*d^2))*e^(2*I*d*x + 2*I*c)*log((2*(I*a^2*d*e^(2*I*d*x + 2*I*c) + I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - 2*I)*e^(-I*d*x - I*c)/(a^2*d)) - I*sqrt(2)*a^3*d*sqrt(1/(a^5*d^2))*e^(2*I*d*x + 2*I*c)*log((2*(-I*a^2*d*e^(2*I*d*x + 2*I*c) - I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) - 2*I)*e^(-I*d*x - I*c)/(a^2*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(2*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-2*I*d*x - 2*I*c)/(a^3*d)","B",0
375,1,267,0,0.496171," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(24 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 24 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + 24 i\right)} e^{\left(-i \, d x - i \, c\right)}}{64 \, a^{2} d}\right) - 3 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-24 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 24 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + 24 i\right)} e^{\left(-i \, d x - i \, c\right)}}{64 \, a^{2} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(5 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 7 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{32 \, a^{3} d}"," ",0,"1/32*(3*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(4*I*d*x + 4*I*c)*log(1/64*(sqrt(2)*sqrt(1/2)*(24*I*a^2*d*e^(2*I*d*x + 2*I*c) + 24*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + 24*I)*e^(-I*d*x - I*c)/(a^2*d)) - 3*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(4*I*d*x + 4*I*c)*log(1/64*(sqrt(2)*sqrt(1/2)*(-24*I*a^2*d*e^(2*I*d*x + 2*I*c) - 24*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + 24*I)*e^(-I*d*x - I*c)/(a^2*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(5*I*e^(4*I*d*x + 4*I*c) + 7*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-4*I*d*x - 4*I*c)/(a^3*d)","B",0
376,1,289,0,0.688364," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(105 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(2240 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 2240 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + 2240 i\right)} e^{\left(-i \, d x - i \, c\right)}}{4096 \, a^{2} d}\right) - 105 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-2240 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 2240 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + 2240 i\right)} e^{\left(-i \, d x - i \, c\right)}}{4096 \, a^{2} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-48 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 39 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 125 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 46 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{768 \, a^{3} d}"," ",0,"1/768*(105*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(6*I*d*x + 6*I*c)*log(1/4096*(sqrt(2)*sqrt(1/2)*(2240*I*a^2*d*e^(2*I*d*x + 2*I*c) + 2240*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + 2240*I)*e^(-I*d*x - I*c)/(a^2*d)) - 105*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(6*I*d*x + 6*I*c)*log(1/4096*(sqrt(2)*sqrt(1/2)*(-2240*I*a^2*d*e^(2*I*d*x + 2*I*c) - 2240*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + 2240*I)*e^(-I*d*x - I*c)/(a^2*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-48*I*e^(8*I*d*x + 8*I*c) + 39*I*e^(6*I*d*x + 6*I*c) + 125*I*e^(4*I*d*x + 4*I*c) + 46*I*e^(2*I*d*x + 2*I*c) + 8*I))*e^(-6*I*d*x - 6*I*c)/(a^3*d)","A",0
377,1,311,0,0.805050," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(3465 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(2365440 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + 2365440 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + 2365440 i\right)} e^{\left(-i \, d x - i \, c\right)}}{4194304 \, a^{2} d}\right) - 3465 i \, \sqrt{\frac{1}{2}} a^{3} d \sqrt{\frac{1}{a^{5} d^{2}}} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-2365440 i \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 2365440 i \, a^{2} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{5} d^{2}}} + 2365440 i\right)} e^{\left(-i \, d x - i \, c\right)}}{4194304 \, a^{2} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-128 i \, e^{\left(12 i \, d x + 12 i \, c\right)} - 2176 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 247 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 3325 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 1358 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 376 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 48 i\right)}\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{24576 \, a^{3} d}"," ",0,"1/24576*(3465*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(8*I*d*x + 8*I*c)*log(1/4194304*(sqrt(2)*sqrt(1/2)*(2365440*I*a^2*d*e^(2*I*d*x + 2*I*c) + 2365440*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + 2365440*I)*e^(-I*d*x - I*c)/(a^2*d)) - 3465*I*sqrt(1/2)*a^3*d*sqrt(1/(a^5*d^2))*e^(8*I*d*x + 8*I*c)*log(1/4194304*(sqrt(2)*sqrt(1/2)*(-2365440*I*a^2*d*e^(2*I*d*x + 2*I*c) - 2365440*I*a^2*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^5*d^2)) + 2365440*I)*e^(-I*d*x - I*c)/(a^2*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-128*I*e^(12*I*d*x + 12*I*c) - 2176*I*e^(10*I*d*x + 10*I*c) + 247*I*e^(8*I*d*x + 8*I*c) + 3325*I*e^(6*I*d*x + 6*I*c) + 1358*I*e^(4*I*d*x + 4*I*c) + 376*I*e^(2*I*d*x + 2*I*c) + 48*I))*e^(-8*I*d*x - 8*I*c)/(a^3*d)","A",0
378,1,160,0,0.778122," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-8192 i \, e^{\left(11 i \, d x + 11 i \, c\right)} - 45056 i \, e^{\left(9 i \, d x + 9 i \, c\right)} - 101376 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 118272 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 73920 i \, e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}{3465 \, {\left(a^{4} d e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/3465*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-8192*I*e^(11*I*d*x + 11*I*c) - 45056*I*e^(9*I*d*x + 9*I*c) - 101376*I*e^(7*I*d*x + 7*I*c) - 118272*I*e^(5*I*d*x + 5*I*c) - 73920*I*e^(3*I*d*x + 3*I*c))/(a^4*d*e^(10*I*d*x + 10*I*c) + 5*a^4*d*e^(8*I*d*x + 8*I*c) + 10*a^4*d*e^(6*I*d*x + 6*I*c) + 10*a^4*d*e^(4*I*d*x + 4*I*c) + 5*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","A",0
379,1,119,0,0.683946," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-256 i \, e^{\left(7 i \, d x + 7 i \, c\right)} - 896 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 1120 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 560 i \, e^{\left(i \, d x + i \, c\right)}\right)}}{35 \, {\left(a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/35*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-256*I*e^(7*I*d*x + 7*I*c) - 896*I*e^(5*I*d*x + 5*I*c) - 1120*I*e^(3*I*d*x + 3*I*c) - 560*I*e^(I*d*x + I*c))/(a^4*d*e^(6*I*d*x + 6*I*c) + 3*a^4*d*e^(4*I*d*x + 4*I*c) + 3*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","A",0
380,1,77,0,0.593713," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(32 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 48 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 12 i\right)}}{3 \, {\left(a^{4} d e^{\left(3 i \, d x + 3 i \, c\right)} + a^{4} d e^{\left(i \, d x + i \, c\right)}\right)}}"," ",0,"1/3*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(32*I*e^(4*I*d*x + 4*I*c) + 48*I*e^(2*I*d*x + 2*I*c) + 12*I)/(a^4*d*e^(3*I*d*x + 3*I*c) + a^4*d*e^(I*d*x + I*c))","A",0
381,1,61,0,0.617906," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-2 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{3 \, a^{4} d}"," ",0,"1/3*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-2*I*e^(4*I*d*x + 4*I*c) - I*e^(2*I*d*x + 2*I*c) + I)*e^(-3*I*d*x - 3*I*c)/(a^4*d)","A",0
382,1,72,0,2.145588," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{20 \, a^{4} d}"," ",0,"1/20*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(6*I*d*x + 6*I*c) + 3*I*e^(4*I*d*x + 4*I*c) + 3*I*e^(2*I*d*x + 2*I*c) + I)*e^(-5*I*d*x - 5*I*c)/(a^4*d)","B",0
383,1,316,0,0.524267," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(-3465 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(9 i \, d x + 9 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 3465 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(9 i \, d x + 9 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-315 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 4303 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 7034 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 3754 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 1798 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 530 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 70 i\right)}\right)} e^{\left(-9 i \, d x - 9 i \, c\right)}}{40320 \, a^{4} d}"," ",0,"1/40320*(-3465*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(9*I*d*x + 9*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 3465*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(9*I*d*x + 9*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-315*I*e^(12*I*d*x + 12*I*c) + 4303*I*e^(10*I*d*x + 10*I*c) + 7034*I*e^(8*I*d*x + 8*I*c) + 3754*I*e^(6*I*d*x + 6*I*c) + 1798*I*e^(4*I*d*x + 4*I*c) + 530*I*e^(2*I*d*x + 2*I*c) + 70*I))*e^(-9*I*d*x - 9*I*c)/(a^4*d)","A",0
384,1,338,0,0.679480," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(-45045 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(11 i \, d x + 11 i \, c\right)} \log\left(4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + 45045 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(11 i \, d x + 11 i \, c\right)} \log\left(-4 \, {\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} - a e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-462 i \, e^{\left(16 i \, d x + 16 i \, c\right)} - 7161 i \, e^{\left(14 i \, d x + 14 i \, c\right)} + 47413 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 78800 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 38512 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 19552 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 7184 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 1624 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 168 i\right)}\right)} e^{\left(-11 i \, d x - 11 i \, c\right)}}{473088 \, a^{4} d}"," ",0,"1/473088*(-45045*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(11*I*d*x + 11*I*c)*log(4*(sqrt(2)*sqrt(1/2)*(a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + 45045*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(11*I*d*x + 11*I*c)*log(-4*(sqrt(2)*sqrt(1/2)*(a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) - a*e^(I*d*x + I*c))*e^(-I*d*x - I*c)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-462*I*e^(16*I*d*x + 16*I*c) - 7161*I*e^(14*I*d*x + 14*I*c) + 47413*I*e^(12*I*d*x + 12*I*c) + 78800*I*e^(10*I*d*x + 10*I*c) + 38512*I*e^(8*I*d*x + 8*I*c) + 19552*I*e^(6*I*d*x + 6*I*c) + 7184*I*e^(4*I*d*x + 4*I*c) + 1624*I*e^(2*I*d*x + 2*I*c) + 168*I))*e^(-11*I*d*x - 11*I*c)/(a^4*d)","A",0
385,1,173,0,0.867154," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(130560 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 34816 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 4096 i\right)}}{3315 \, {\left(a^{4} d e^{\left(16 i \, d x + 16 i \, c\right)} + 8 \, a^{4} d e^{\left(14 i \, d x + 14 i \, c\right)} + 28 \, a^{4} d e^{\left(12 i \, d x + 12 i \, c\right)} + 56 \, a^{4} d e^{\left(10 i \, d x + 10 i \, c\right)} + 70 \, a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} + 56 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 28 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 8 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/3315*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(130560*I*e^(4*I*d*x + 4*I*c) + 34816*I*e^(2*I*d*x + 2*I*c) + 4096*I)/(a^4*d*e^(16*I*d*x + 16*I*c) + 8*a^4*d*e^(14*I*d*x + 14*I*c) + 28*a^4*d*e^(12*I*d*x + 12*I*c) + 56*a^4*d*e^(10*I*d*x + 10*I*c) + 70*a^4*d*e^(8*I*d*x + 8*I*c) + 56*a^4*d*e^(6*I*d*x + 6*I*c) + 28*a^4*d*e^(4*I*d*x + 4*I*c) + 8*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","B",0
386,1,132,0,0.669967," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(1664 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 256 i\right)}}{143 \, {\left(a^{4} d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, a^{4} d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/143*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(1664*I*e^(2*I*d*x + 2*I*c) + 256*I)/(a^4*d*e^(12*I*d*x + 12*I*c) + 6*a^4*d*e^(10*I*d*x + 10*I*c) + 15*a^4*d*e^(8*I*d*x + 8*I*c) + 20*a^4*d*e^(6*I*d*x + 6*I*c) + 15*a^4*d*e^(4*I*d*x + 4*I*c) + 6*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","B",0
387,1,89,0,0.765118," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{32 i \, \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}}}{9 \, {\left(a^{4} d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, a^{4} d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"32/9*I*sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))/(a^4*d*e^(8*I*d*x + 8*I*c) + 4*a^4*d*e^(6*I*d*x + 6*I*c) + 6*a^4*d*e^(4*I*d*x + 4*I*c) + 4*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","B",0
388,1,323,0,0.594788," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(60 i \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 120 i \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + 60 i \, a^{4} d\right)} \sqrt{\frac{1}{a^{7} d^{2}}} \log\left(\frac{{\left(2 \, {\left(16 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + 32 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3} d}\right) + \sqrt{2} {\left(-60 i \, a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} - 120 i \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} - 60 i \, a^{4} d\right)} \sqrt{\frac{1}{a^{7} d^{2}}} \log\left(\frac{{\left(2 \, {\left(-16 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 16 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + 32 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-120 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 280 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 184 i\right)}}{15 \, {\left(a^{4} d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{4} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{4} d\right)}}"," ",0,"1/15*(sqrt(2)*(60*I*a^4*d*e^(4*I*d*x + 4*I*c) + 120*I*a^4*d*e^(2*I*d*x + 2*I*c) + 60*I*a^4*d)*sqrt(1/(a^7*d^2))*log((2*(16*I*a^3*d*e^(2*I*d*x + 2*I*c) + 16*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + 32*I)*e^(-I*d*x - I*c)/(a^3*d)) + sqrt(2)*(-60*I*a^4*d*e^(4*I*d*x + 4*I*c) - 120*I*a^4*d*e^(2*I*d*x + 2*I*c) - 60*I*a^4*d)*sqrt(1/(a^7*d^2))*log((2*(-16*I*a^3*d*e^(2*I*d*x + 2*I*c) - 16*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + 32*I)*e^(-I*d*x - I*c)/(a^3*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-120*I*e^(4*I*d*x + 4*I*c) - 280*I*e^(2*I*d*x + 2*I*c) - 184*I))/(a^4*d*e^(4*I*d*x + 4*I*c) + 2*a^4*d*e^(2*I*d*x + 2*I*c) + a^4*d)","B",0
389,1,244,0,0.571378," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(3 i \, \sqrt{2} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left(2 \, {\left(6 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} - 12 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3} d}\right) - 3 i \, \sqrt{2} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{{\left(2 \, {\left(-6 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 6 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} - 12 i\right)} e^{\left(-i \, d x - i \, c\right)}}{a^{3} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a^{4} d}"," ",0,"1/2*(3*I*sqrt(2)*a^4*d*sqrt(1/(a^7*d^2))*e^(2*I*d*x + 2*I*c)*log((2*(6*I*a^3*d*e^(2*I*d*x + 2*I*c) + 6*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) - 12*I)*e^(-I*d*x - I*c)/(a^3*d)) - 3*I*sqrt(2)*a^4*d*sqrt(1/(a^7*d^2))*e^(2*I*d*x + 2*I*c)*log((2*(-6*I*a^3*d*e^(2*I*d*x + 2*I*c) - 6*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) - 12*I)*e^(-I*d*x - I*c)/(a^3*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(6*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-2*I*d*x - 2*I*c)/(a^4*d)","B",0
390,1,267,0,0.834458," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(4 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} - 4 i\right)} e^{\left(-i \, d x - i \, c\right)}}{16 \, a^{3} d}\right) - i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-4 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} - 4 i\right)} e^{\left(-i \, d x - i \, c\right)}}{16 \, a^{3} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)}\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{16 \, a^{4} d}"," ",0,"1/16*(I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(4*I*d*x + 4*I*c)*log(1/16*(sqrt(2)*sqrt(1/2)*(4*I*a^3*d*e^(2*I*d*x + 2*I*c) + 4*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) - 4*I)*e^(-I*d*x - I*c)/(a^3*d)) - I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(4*I*d*x + 4*I*c)*log(1/16*(sqrt(2)*sqrt(1/2)*(-4*I*a^3*d*e^(2*I*d*x + 2*I*c) - 4*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) - 4*I)*e^(-I*d*x - I*c)/(a^3*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(4*I*d*x + 4*I*c) + 3*I*e^(2*I*d*x + 2*I*c) + 2*I))*e^(-4*I*d*x - 4*I*c)/(a^4*d)","B",0
391,1,278,0,0.667059," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(15 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(160 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 160 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + 160 i\right)} e^{\left(-i \, d x - i \, c\right)}}{1024 \, a^{3} d}\right) - 15 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-160 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 160 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + 160 i\right)} e^{\left(-i \, d x - i \, c\right)}}{1024 \, a^{3} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(33 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 59 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 34 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i\right)}\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{384 \, a^{4} d}"," ",0,"1/384*(15*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(6*I*d*x + 6*I*c)*log(1/1024*(sqrt(2)*sqrt(1/2)*(160*I*a^3*d*e^(2*I*d*x + 2*I*c) + 160*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + 160*I)*e^(-I*d*x - I*c)/(a^3*d)) - 15*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(6*I*d*x + 6*I*c)*log(1/1024*(sqrt(2)*sqrt(1/2)*(-160*I*a^3*d*e^(2*I*d*x + 2*I*c) - 160*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + 160*I)*e^(-I*d*x - I*c)/(a^3*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(33*I*e^(6*I*d*x + 6*I*c) + 59*I*e^(4*I*d*x + 4*I*c) + 34*I*e^(2*I*d*x + 2*I*c) + 8*I))*e^(-6*I*d*x - 6*I*c)/(a^4*d)","B",0
392,1,300,0,0.780536," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(315 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(322560 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 322560 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + 322560 i\right)} e^{\left(-i \, d x - i \, c\right)}}{1048576 \, a^{3} d}\right) - 315 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-322560 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 322560 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + 322560 i\right)} e^{\left(-i \, d x - i \, c\right)}}{1048576 \, a^{3} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-128 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 197 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 535 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 298 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 104 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i\right)}\right)} e^{\left(-8 i \, d x - 8 i \, c\right)}}{4096 \, a^{4} d}"," ",0,"1/4096*(315*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(8*I*d*x + 8*I*c)*log(1/1048576*(sqrt(2)*sqrt(1/2)*(322560*I*a^3*d*e^(2*I*d*x + 2*I*c) + 322560*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + 322560*I)*e^(-I*d*x - I*c)/(a^3*d)) - 315*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(8*I*d*x + 8*I*c)*log(1/1048576*(sqrt(2)*sqrt(1/2)*(-322560*I*a^3*d*e^(2*I*d*x + 2*I*c) - 322560*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + 322560*I)*e^(-I*d*x - I*c)/(a^3*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-128*I*e^(10*I*d*x + 10*I*c) + 197*I*e^(8*I*d*x + 8*I*c) + 535*I*e^(6*I*d*x + 6*I*c) + 298*I*e^(4*I*d*x + 4*I*c) + 104*I*e^(2*I*d*x + 2*I*c) + 16*I))*e^(-8*I*d*x - 8*I*c)/(a^4*d)","A",0
393,1,322,0,0.608481," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(45045 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(24600576 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} + 24600576 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + 24600576 i\right)} e^{\left(-i \, d x - i \, c\right)}}{67108864 \, a^{3} d}\right) - 45045 i \, \sqrt{\frac{1}{2}} a^{4} d \sqrt{\frac{1}{a^{7} d^{2}}} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(\frac{{\left(\sqrt{2} \sqrt{\frac{1}{2}} {\left(-24600576 i \, a^{3} d e^{\left(2 i \, d x + 2 i \, c\right)} - 24600576 i \, a^{3} d\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{1}{a^{7} d^{2}}} + 24600576 i\right)} e^{\left(-i \, d x - i \, c\right)}}{67108864 \, a^{3} d}\right) + \sqrt{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-1280 i \, e^{\left(14 i \, d x + 14 i \, c\right)} - 25600 i \, e^{\left(12 i \, d x + 12 i \, c\right)} + 11275 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 56665 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 31094 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 12952 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3312 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 384 i\right)}\right)} e^{\left(-10 i \, d x - 10 i \, c\right)}}{491520 \, a^{4} d}"," ",0,"1/491520*(45045*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(10*I*d*x + 10*I*c)*log(1/67108864*(sqrt(2)*sqrt(1/2)*(24600576*I*a^3*d*e^(2*I*d*x + 2*I*c) + 24600576*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + 24600576*I)*e^(-I*d*x - I*c)/(a^3*d)) - 45045*I*sqrt(1/2)*a^4*d*sqrt(1/(a^7*d^2))*e^(10*I*d*x + 10*I*c)*log(1/67108864*(sqrt(2)*sqrt(1/2)*(-24600576*I*a^3*d*e^(2*I*d*x + 2*I*c) - 24600576*I*a^3*d)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(1/(a^7*d^2)) + 24600576*I)*e^(-I*d*x - I*c)/(a^3*d)) + sqrt(2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-1280*I*e^(14*I*d*x + 14*I*c) - 25600*I*e^(12*I*d*x + 12*I*c) + 11275*I*e^(10*I*d*x + 10*I*c) + 56665*I*e^(8*I*d*x + 8*I*c) + 31094*I*e^(6*I*d*x + 6*I*c) + 12952*I*e^(4*I*d*x + 4*I*c) + 3312*I*e^(2*I*d*x + 2*I*c) + 384*I))*e^(-10*I*d*x - 10*I*c)/(a^4*d)","A",0
394,1,418,0,0.546452," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 i \, e \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + \sqrt{\frac{i \, a e^{3}}{d^{2}}} d \log\left(\frac{2 \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 2 i \, \sqrt{\frac{i \, a e^{3}}{d^{2}}} d}{e}\right) - \sqrt{\frac{i \, a e^{3}}{d^{2}}} d \log\left(\frac{2 \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 2 i \, \sqrt{\frac{i \, a e^{3}}{d^{2}}} d}{e}\right) + \sqrt{-\frac{i \, a e^{3}}{d^{2}}} d \log\left(\frac{2 \, {\left({\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + i \, \sqrt{-\frac{i \, a e^{3}}{d^{2}}} d\right)}}{e}\right) - \sqrt{-\frac{i \, a e^{3}}{d^{2}}} d \log\left(\frac{2 \, {\left({\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - i \, \sqrt{-\frac{i \, a e^{3}}{d^{2}}} d\right)}}{e}\right)}{2 \, d}"," ",0,"1/2*(4*I*e*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + sqrt(I*a*e^3/d^2)*d*log((2*(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 2*I*sqrt(I*a*e^3/d^2)*d)/e) - sqrt(I*a*e^3/d^2)*d*log((2*(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 2*I*sqrt(I*a*e^3/d^2)*d)/e) + sqrt(-I*a*e^3/d^2)*d*log(2*((e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + I*sqrt(-I*a*e^3/d^2)*d)/e) - sqrt(-I*a*e^3/d^2)*d*log(2*((e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - I*sqrt(-I*a*e^3/d^2)*d)/e))/d","A",0
395,1,323,0,0.653094," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{4 i \, a e}{d^{2}}} \log\left(2 \, \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + d \sqrt{\frac{4 i \, a e}{d^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{4 i \, a e}{d^{2}}} \log\left(2 \, \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - d \sqrt{\frac{4 i \, a e}{d^{2}}}\right) - \frac{1}{2} \, \sqrt{-\frac{4 i \, a e}{d^{2}}} \log\left(2 \, \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + d \sqrt{-\frac{4 i \, a e}{d^{2}}}\right) + \frac{1}{2} \, \sqrt{-\frac{4 i \, a e}{d^{2}}} \log\left(2 \, \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - d \sqrt{-\frac{4 i \, a e}{d^{2}}}\right)"," ",0,"1/2*sqrt(4*I*a*e/d^2)*log(2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)*e^(1/2*I*d*x + 1/2*I*c) + d*sqrt(4*I*a*e/d^2)) - 1/2*sqrt(4*I*a*e/d^2)*log(2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)*e^(1/2*I*d*x + 1/2*I*c) - d*sqrt(4*I*a*e/d^2)) - 1/2*sqrt(-4*I*a*e/d^2)*log(2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)*e^(1/2*I*d*x + 1/2*I*c) + d*sqrt(-4*I*a*e/d^2)) + 1/2*sqrt(-4*I*a*e/d^2)*log(2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)*e^(1/2*I*d*x + 1/2*I*c) - d*sqrt(-4*I*a*e/d^2))","A",0
396,1,64,0,1.620932," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d e}"," ",0,"2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-I*e^(2*I*d*x + 2*I*c) - I)*e^(1/2*I*d*x + 1/2*I*c)/(d*e)","B",0
397,1,75,0,0.695224," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, d e^{2}}"," ",0,"1/3*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-I*e^(4*I*d*x + 4*I*c) + 2*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^2)","A",0
398,1,86,0,0.732942," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-3 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 33 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 25 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-\frac{3}{2} i \, d x - \frac{3}{2} i \, c\right)}}{30 \, d e^{3}}"," ",0,"1/30*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-3*I*e^(6*I*d*x + 6*I*c) - 33*I*e^(4*I*d*x + 4*I*c) - 25*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-3/2*I*d*x - 3/2*I*c)/(d*e^3)","A",0
399,1,97,0,0.635303," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-5 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 40 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 70 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 112 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i\right)} e^{\left(-\frac{5}{2} i \, d x - \frac{5}{2} i \, c\right)}}{140 \, d e^{4}}"," ",0,"1/140*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-5*I*e^(8*I*d*x + 8*I*c) - 40*I*e^(6*I*d*x + 6*I*c) + 70*I*e^(4*I*d*x + 4*I*c) + 112*I*e^(2*I*d*x + 2*I*c) + 7*I)*e^(-5/2*I*d*x - 5/2*I*c)/(d*e^4)","A",0
400,1,644,0,0.668320," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(-21 i \, a e^{2} e^{\left(5 i \, d x + 5 i \, c\right)} + 18 i \, a e^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 7 i \, a e^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 6 \, \sqrt{\frac{49 i \, a^{3} e^{5}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{2 \, {\left(7 \, {\left(a e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 8 \, \sqrt{\frac{49 i \, a^{3} e^{5}}{64 \, d^{2}}} d\right)}}{7 \, a e^{2}}\right) - 6 \, \sqrt{\frac{49 i \, a^{3} e^{5}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{2 \, {\left(7 \, {\left(a e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 8 \, \sqrt{\frac{49 i \, a^{3} e^{5}}{64 \, d^{2}}} d\right)}}{7 \, a e^{2}}\right) - 6 \, \sqrt{-\frac{49 i \, a^{3} e^{5}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{2 \, {\left(7 \, {\left(a e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 8 \, \sqrt{-\frac{49 i \, a^{3} e^{5}}{64 \, d^{2}}} d\right)}}{7 \, a e^{2}}\right) + 6 \, \sqrt{-\frac{49 i \, a^{3} e^{5}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{2 \, {\left(7 \, {\left(a e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 8 \, \sqrt{-\frac{49 i \, a^{3} e^{5}}{64 \, d^{2}}} d\right)}}{7 \, a e^{2}}\right)}{12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/12*((-21*I*a*e^2*e^(5*I*d*x + 5*I*c) + 18*I*a*e^2*e^(3*I*d*x + 3*I*c) + 7*I*a*e^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 6*sqrt(49/64*I*a^3*e^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(2/7*(7*(a*e^2*e^(2*I*d*x + 2*I*c) + a*e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 8*sqrt(49/64*I*a^3*e^5/d^2)*d)/(a*e^2)) - 6*sqrt(49/64*I*a^3*e^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(2/7*(7*(a*e^2*e^(2*I*d*x + 2*I*c) + a*e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 8*sqrt(49/64*I*a^3*e^5/d^2)*d)/(a*e^2)) - 6*sqrt(-49/64*I*a^3*e^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(2/7*(7*(a*e^2*e^(2*I*d*x + 2*I*c) + a*e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 8*sqrt(-49/64*I*a^3*e^5/d^2)*d)/(a*e^2)) + 6*sqrt(-49/64*I*a^3*e^5/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(2/7*(7*(a*e^2*e^(2*I*d*x + 2*I*c) + a*e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 8*sqrt(-49/64*I*a^3*e^5/d^2)*d)/(a*e^2)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
401,1,538,0,1.137126," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(9 i \, a e e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, a e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + \sqrt{\frac{25 i \, a^{3} e^{3}}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{10 \, {\left(a e e^{\left(2 i \, d x + 2 i \, c\right)} + a e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 8 i \, \sqrt{\frac{25 i \, a^{3} e^{3}}{16 \, d^{2}}} d}{5 \, a e}\right) - \sqrt{\frac{25 i \, a^{3} e^{3}}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{10 \, {\left(a e e^{\left(2 i \, d x + 2 i \, c\right)} + a e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 8 i \, \sqrt{\frac{25 i \, a^{3} e^{3}}{16 \, d^{2}}} d}{5 \, a e}\right) + \sqrt{-\frac{25 i \, a^{3} e^{3}}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{10 \, {\left(a e e^{\left(2 i \, d x + 2 i \, c\right)} + a e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 8 i \, \sqrt{-\frac{25 i \, a^{3} e^{3}}{16 \, d^{2}}} d}{5 \, a e}\right) - \sqrt{-\frac{25 i \, a^{3} e^{3}}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{10 \, {\left(a e e^{\left(2 i \, d x + 2 i \, c\right)} + a e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 8 i \, \sqrt{-\frac{25 i \, a^{3} e^{3}}{16 \, d^{2}}} d}{5 \, a e}\right)}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/2*((9*I*a*e*e^(2*I*d*x + 2*I*c) + 5*I*a*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + sqrt(25/16*I*a^3*e^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/5*(10*(a*e*e^(2*I*d*x + 2*I*c) + a*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 8*I*sqrt(25/16*I*a^3*e^3/d^2)*d)/(a*e)) - sqrt(25/16*I*a^3*e^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/5*(10*(a*e*e^(2*I*d*x + 2*I*c) + a*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 8*I*sqrt(25/16*I*a^3*e^3/d^2)*d)/(a*e)) + sqrt(-25/16*I*a^3*e^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/5*(10*(a*e*e^(2*I*d*x + 2*I*c) + a*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 8*I*sqrt(-25/16*I*a^3*e^3/d^2)*d)/(a*e)) - sqrt(-25/16*I*a^3*e^3/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(1/5*(10*(a*e*e^(2*I*d*x + 2*I*c) + a*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 8*I*sqrt(-25/16*I*a^3*e^3/d^2)*d)/(a*e)))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
402,1,420,0,0.590510," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{4 i \, a \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{3}{2} i \, d x + \frac{3}{2} i \, c\right)} + \sqrt{\frac{9 i \, a^{3} e}{d^{2}}} d \log\left(\frac{2 \, {\left(3 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + \sqrt{\frac{9 i \, a^{3} e}{d^{2}}} d\right)}}{3 \, a}\right) - \sqrt{\frac{9 i \, a^{3} e}{d^{2}}} d \log\left(\frac{2 \, {\left(3 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - \sqrt{\frac{9 i \, a^{3} e}{d^{2}}} d\right)}}{3 \, a}\right) - \sqrt{-\frac{9 i \, a^{3} e}{d^{2}}} d \log\left(\frac{2 \, {\left(3 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + \sqrt{-\frac{9 i \, a^{3} e}{d^{2}}} d\right)}}{3 \, a}\right) + \sqrt{-\frac{9 i \, a^{3} e}{d^{2}}} d \log\left(\frac{2 \, {\left(3 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - \sqrt{-\frac{9 i \, a^{3} e}{d^{2}}} d\right)}}{3 \, a}\right)}{2 \, d}"," ",0,"1/2*(4*I*a*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(3/2*I*d*x + 3/2*I*c) + sqrt(9*I*a^3*e/d^2)*d*log(2/3*(3*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + sqrt(9*I*a^3*e/d^2)*d)/a) - sqrt(9*I*a^3*e/d^2)*d*log(2/3*(3*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - sqrt(9*I*a^3*e/d^2)*d)/a) - sqrt(-9*I*a^3*e/d^2)*d*log(2/3*(3*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + sqrt(-9*I*a^3*e/d^2)*d)/a) + sqrt(-9*I*a^3*e/d^2)*d*log(2/3*(3*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - sqrt(-9*I*a^3*e/d^2)*d)/a))/d","A",0
403,1,460,0,0.567956," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{d e \sqrt{\frac{4 i \, a^{3}}{d^{2} e}} \log\left(\frac{2 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + i \, d e \sqrt{\frac{4 i \, a^{3}}{d^{2} e}}}{a}\right) - d e \sqrt{\frac{4 i \, a^{3}}{d^{2} e}} \log\left(\frac{2 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - i \, d e \sqrt{\frac{4 i \, a^{3}}{d^{2} e}}}{a}\right) + d e \sqrt{-\frac{4 i \, a^{3}}{d^{2} e}} \log\left(\frac{2 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + i \, d e \sqrt{-\frac{4 i \, a^{3}}{d^{2} e}}}{a}\right) - d e \sqrt{-\frac{4 i \, a^{3}}{d^{2} e}} \log\left(\frac{2 \, {\left(a e^{\left(2 i \, d x + 2 i \, c\right)} + a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - i \, d e \sqrt{-\frac{4 i \, a^{3}}{d^{2} e}}}{a}\right) - 2 \, {\left(-4 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{2 \, d e}"," ",0,"-1/2*(d*e*sqrt(4*I*a^3/(d^2*e))*log((2*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + I*d*e*sqrt(4*I*a^3/(d^2*e)))/a) - d*e*sqrt(4*I*a^3/(d^2*e))*log((2*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - I*d*e*sqrt(4*I*a^3/(d^2*e)))/a) + d*e*sqrt(-4*I*a^3/(d^2*e))*log((2*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + I*d*e*sqrt(-4*I*a^3/(d^2*e)))/a) - d*e*sqrt(-4*I*a^3/(d^2*e))*log((2*(a*e^(2*I*d*x + 2*I*c) + a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - I*d*e*sqrt(-4*I*a^3/(d^2*e)))/a) - 2*(-4*I*a*e^(2*I*d*x + 2*I*c) - 4*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e)","A",0
404,1,76,0,0.471726," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(-i \, a e^{\left(3 i \, d x + 3 i \, c\right)} - i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, d e^{2}}"," ",0,"2/3*(-I*a*e^(3*I*d*x + 3*I*c) - I*a*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^2)","B",0
405,1,79,0,0.784387," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(-i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 6 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 5 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, d e^{3}}"," ",0,"1/5*(-I*a*e^(4*I*d*x + 4*I*c) - 6*I*a*e^(2*I*d*x + 2*I*c) - 5*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^3)","A",0
406,1,91,0,0.559171," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(-3 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 17 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 7 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 21 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{42 \, d e^{4}}"," ",0,"1/42*(-3*I*a*e^(6*I*d*x + 6*I*c) - 17*I*a*e^(4*I*d*x + 4*I*c) + 7*I*a*e^(2*I*d*x + 2*I*c) + 21*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^4)","A",0
407,1,103,0,1.015513," ","integrate((a+I*a*tan(d*x+c))^(3/2)/(e*sec(d*x+c))^(9/2),x, algorithm=""fricas"")","\frac{{\left(-5 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} - 32 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 162 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 120 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 15 i \, a\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{3}{2} i \, d x - \frac{3}{2} i \, c\right)}}{180 \, d e^{5}}"," ",0,"1/180*(-5*I*a*e^(8*I*d*x + 8*I*c) - 32*I*a*e^(6*I*d*x + 6*I*c) - 162*I*a*e^(4*I*d*x + 4*I*c) - 120*I*a*e^(2*I*d*x + 2*I*c) + 15*I*a)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-3/2*I*d*x - 3/2*I*c)/(d*e^5)","A",0
408,1,635,0,0.554854," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(113 i \, a^{2} e e^{\left(4 i \, d x + 4 i \, c\right)} + 126 i \, a^{2} e e^{\left(2 i \, d x + 2 i \, c\right)} + 45 i \, a^{2} e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 6 \, \sqrt{\frac{225 i \, a^{5} e^{3}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{30 \, {\left(a^{2} e e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 16 i \, \sqrt{\frac{225 i \, a^{5} e^{3}}{64 \, d^{2}}} d}{15 \, a^{2} e}\right) - 6 \, \sqrt{\frac{225 i \, a^{5} e^{3}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{30 \, {\left(a^{2} e e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 16 i \, \sqrt{\frac{225 i \, a^{5} e^{3}}{64 \, d^{2}}} d}{15 \, a^{2} e}\right) + 6 \, \sqrt{-\frac{225 i \, a^{5} e^{3}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{30 \, {\left(a^{2} e e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 16 i \, \sqrt{-\frac{225 i \, a^{5} e^{3}}{64 \, d^{2}}} d}{15 \, a^{2} e}\right) - 6 \, \sqrt{-\frac{225 i \, a^{5} e^{3}}{64 \, d^{2}}} {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{30 \, {\left(a^{2} e e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 16 i \, \sqrt{-\frac{225 i \, a^{5} e^{3}}{64 \, d^{2}}} d}{15 \, a^{2} e}\right)}{12 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/12*((113*I*a^2*e*e^(4*I*d*x + 4*I*c) + 126*I*a^2*e*e^(2*I*d*x + 2*I*c) + 45*I*a^2*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 6*sqrt(225/64*I*a^5*e^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/15*(30*(a^2*e*e^(2*I*d*x + 2*I*c) + a^2*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 16*I*sqrt(225/64*I*a^5*e^3/d^2)*d)/(a^2*e)) - 6*sqrt(225/64*I*a^5*e^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/15*(30*(a^2*e*e^(2*I*d*x + 2*I*c) + a^2*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 16*I*sqrt(225/64*I*a^5*e^3/d^2)*d)/(a^2*e)) + 6*sqrt(-225/64*I*a^5*e^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/15*(30*(a^2*e*e^(2*I*d*x + 2*I*c) + a^2*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 16*I*sqrt(-225/64*I*a^5*e^3/d^2)*d)/(a^2*e)) - 6*sqrt(-225/64*I*a^5*e^3/d^2)*(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)*log(1/15*(30*(a^2*e*e^(2*I*d*x + 2*I*c) + a^2*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 16*I*sqrt(-225/64*I*a^5*e^3/d^2)*d)/(a^2*e)))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
409,1,525,0,0.650612," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(11 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 7 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + \sqrt{\frac{441 i \, a^{5} e}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{2 \, {\left(21 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 4 \, \sqrt{\frac{441 i \, a^{5} e}{16 \, d^{2}}} d\right)}}{21 \, a^{2}}\right) - \sqrt{\frac{441 i \, a^{5} e}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{2 \, {\left(21 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 4 \, \sqrt{\frac{441 i \, a^{5} e}{16 \, d^{2}}} d\right)}}{21 \, a^{2}}\right) - \sqrt{-\frac{441 i \, a^{5} e}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{2 \, {\left(21 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 4 \, \sqrt{-\frac{441 i \, a^{5} e}{16 \, d^{2}}} d\right)}}{21 \, a^{2}}\right) + \sqrt{-\frac{441 i \, a^{5} e}{16 \, d^{2}}} {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)} \log\left(\frac{2 \, {\left(21 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 4 \, \sqrt{-\frac{441 i \, a^{5} e}{16 \, d^{2}}} d\right)}}{21 \, a^{2}}\right)}{2 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/2*((11*I*a^2*e^(3*I*d*x + 3*I*c) + 7*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + sqrt(441/16*I*a^5*e/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(2/21*(21*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 4*sqrt(441/16*I*a^5*e/d^2)*d)/a^2) - sqrt(441/16*I*a^5*e/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(2/21*(21*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 4*sqrt(441/16*I*a^5*e/d^2)*d)/a^2) - sqrt(-441/16*I*a^5*e/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(2/21*(21*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 4*sqrt(-441/16*I*a^5*e/d^2)*d)/a^2) + sqrt(-441/16*I*a^5*e/d^2)*(d*e^(2*I*d*x + 2*I*c) + d)*log(2/21*(21*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 4*sqrt(-441/16*I*a^5*e/d^2)*d)/a^2))/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
410,1,484,0,0.487576," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{25 i \, a^{5}}{d^{2} e}} d e \log\left(\frac{10 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 2 i \, \sqrt{\frac{25 i \, a^{5}}{d^{2} e}} d e}{5 \, a^{2}}\right) - \sqrt{\frac{25 i \, a^{5}}{d^{2} e}} d e \log\left(\frac{10 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 2 i \, \sqrt{\frac{25 i \, a^{5}}{d^{2} e}} d e}{5 \, a^{2}}\right) + \sqrt{-\frac{25 i \, a^{5}}{d^{2} e}} d e \log\left(\frac{10 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 2 i \, \sqrt{-\frac{25 i \, a^{5}}{d^{2} e}} d e}{5 \, a^{2}}\right) - \sqrt{-\frac{25 i \, a^{5}}{d^{2} e}} d e \log\left(\frac{10 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - 2 i \, \sqrt{-\frac{25 i \, a^{5}}{d^{2} e}} d e}{5 \, a^{2}}\right) - 2 \, {\left(-8 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 10 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{2 \, d e}"," ",0,"-1/2*(sqrt(25*I*a^5/(d^2*e))*d*e*log(1/5*(10*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 2*I*sqrt(25*I*a^5/(d^2*e))*d*e)/a^2) - sqrt(25*I*a^5/(d^2*e))*d*e*log(1/5*(10*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 2*I*sqrt(25*I*a^5/(d^2*e))*d*e)/a^2) + sqrt(-25*I*a^5/(d^2*e))*d*e*log(1/5*(10*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + 2*I*sqrt(-25*I*a^5/(d^2*e))*d*e)/a^2) - sqrt(-25*I*a^5/(d^2*e))*d*e*log(1/5*(10*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - 2*I*sqrt(-25*I*a^5/(d^2*e))*d*e)/a^2) - 2*(-8*I*a^2*e^(2*I*d*x + 2*I*c) - 10*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e)","A",0
411,1,505,0,0.556456," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, d e^{2} \sqrt{\frac{4 i \, a^{5}}{d^{2} e^{3}}} \log\left(\frac{d e^{2} \sqrt{\frac{4 i \, a^{5}}{d^{2} e^{3}}} + 2 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a^{2}}\right) - 3 \, d e^{2} \sqrt{\frac{4 i \, a^{5}}{d^{2} e^{3}}} \log\left(-\frac{d e^{2} \sqrt{\frac{4 i \, a^{5}}{d^{2} e^{3}}} - 2 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a^{2}}\right) - 3 \, d e^{2} \sqrt{-\frac{4 i \, a^{5}}{d^{2} e^{3}}} \log\left(\frac{d e^{2} \sqrt{-\frac{4 i \, a^{5}}{d^{2} e^{3}}} + 2 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a^{2}}\right) + 3 \, d e^{2} \sqrt{-\frac{4 i \, a^{5}}{d^{2} e^{3}}} \log\left(-\frac{d e^{2} \sqrt{-\frac{4 i \, a^{5}}{d^{2} e^{3}}} - 2 \, {\left(a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a^{2}}\right) - 2 \, {\left(-4 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{6 \, d e^{2}}"," ",0,"-1/6*(3*d*e^2*sqrt(4*I*a^5/(d^2*e^3))*log((d*e^2*sqrt(4*I*a^5/(d^2*e^3)) + 2*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/a^2) - 3*d*e^2*sqrt(4*I*a^5/(d^2*e^3))*log(-(d*e^2*sqrt(4*I*a^5/(d^2*e^3)) - 2*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/a^2) - 3*d*e^2*sqrt(-4*I*a^5/(d^2*e^3))*log((d*e^2*sqrt(-4*I*a^5/(d^2*e^3)) + 2*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/a^2) + 3*d*e^2*sqrt(-4*I*a^5/(d^2*e^3))*log(-(d*e^2*sqrt(-4*I*a^5/(d^2*e^3)) - 2*(a^2*e^(2*I*d*x + 2*I*c) + a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/a^2) - 2*(-4*I*a^2*e^(3*I*d*x + 3*I*c) - 4*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/(d*e^2)","A",0
412,1,80,0,0.611328," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(-i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, d e^{3}}"," ",0,"2/5*(-I*a^2*e^(4*I*d*x + 4*I*c) - I*a^2*e^(2*I*d*x + 2*I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^3)","B",0
413,1,94,0,0.628146," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{{\left(-3 i \, a^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 10 i \, a^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 7 i \, a^{2} e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{21 \, d e^{4}}"," ",0,"1/21*(-3*I*a^2*e^(5*I*d*x + 5*I*c) - 10*I*a^2*e^(3*I*d*x + 3*I*c) - 7*I*a^2*e^(I*d*x + I*c))*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^4)","A",0
414,1,99,0,0.689938," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(9/2),x, algorithm=""fricas"")","\frac{{\left(-5 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 23 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 63 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 45 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{90 \, d e^{5}}"," ",0,"1/90*(-5*I*a^2*e^(6*I*d*x + 6*I*c) - 23*I*a^2*e^(4*I*d*x + 4*I*c) - 63*I*a^2*e^(2*I*d*x + 2*I*c) - 45*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/(d*e^5)","A",0
415,1,99,0,0.447157," ","integrate((a+I*a*tan(d*x+c))^(5/2)/(e*sec(d*x+c))^(11/2),x, algorithm=""fricas"")","\frac{{\left(-7 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 40 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 110 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 77 i \, a^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{308 \, d e^{6}}"," ",0,"1/308*(-7*I*a^2*e^(8*I*d*x + 8*I*c) - 40*I*a^2*e^(6*I*d*x + 6*I*c) - 110*I*a^2*e^(4*I*d*x + 4*I*c) + 77*I*a^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^6)","A",0
416,1,461,0,0.818568," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{-4 i \, e^{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{3}{2} i \, d x + \frac{3}{2} i \, c\right)} + \sqrt{\frac{i \, e^{5}}{a d^{2}}} a d \log\left(\frac{2 \, {\left({\left(e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + \sqrt{\frac{i \, e^{5}}{a d^{2}}} a d\right)}}{e^{2}}\right) - \sqrt{\frac{i \, e^{5}}{a d^{2}}} a d \log\left(\frac{2 \, {\left({\left(e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - \sqrt{\frac{i \, e^{5}}{a d^{2}}} a d\right)}}{e^{2}}\right) - \sqrt{-\frac{i \, e^{5}}{a d^{2}}} a d \log\left(\frac{2 \, {\left({\left(e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + \sqrt{-\frac{i \, e^{5}}{a d^{2}}} a d\right)}}{e^{2}}\right) + \sqrt{-\frac{i \, e^{5}}{a d^{2}}} a d \log\left(\frac{2 \, {\left({\left(e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - \sqrt{-\frac{i \, e^{5}}{a d^{2}}} a d\right)}}{e^{2}}\right)}{2 \, a d}"," ",0,"1/2*(-4*I*e^2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(3/2*I*d*x + 3/2*I*c) + sqrt(I*e^5/(a*d^2))*a*d*log(2*((e^2*e^(2*I*d*x + 2*I*c) + e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + sqrt(I*e^5/(a*d^2))*a*d)/e^2) - sqrt(I*e^5/(a*d^2))*a*d*log(2*((e^2*e^(2*I*d*x + 2*I*c) + e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - sqrt(I*e^5/(a*d^2))*a*d)/e^2) - sqrt(-I*e^5/(a*d^2))*a*d*log(2*((e^2*e^(2*I*d*x + 2*I*c) + e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + sqrt(-I*e^5/(a*d^2))*a*d)/e^2) + sqrt(-I*e^5/(a*d^2))*a*d*log(2*((e^2*e^(2*I*d*x + 2*I*c) + e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - sqrt(-I*e^5/(a*d^2))*a*d)/e^2))/(a*d)","A",0
417,1,385,0,1.241870," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{4 i \, e^{3}}{a d^{2}}} \log\left(\frac{2 \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + i \, a d \sqrt{\frac{4 i \, e^{3}}{a d^{2}}}}{e}\right) - \frac{1}{2} \, \sqrt{\frac{4 i \, e^{3}}{a d^{2}}} \log\left(\frac{2 \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - i \, a d \sqrt{\frac{4 i \, e^{3}}{a d^{2}}}}{e}\right) + \frac{1}{2} \, \sqrt{-\frac{4 i \, e^{3}}{a d^{2}}} \log\left(\frac{2 \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + i \, a d \sqrt{-\frac{4 i \, e^{3}}{a d^{2}}}}{e}\right) - \frac{1}{2} \, \sqrt{-\frac{4 i \, e^{3}}{a d^{2}}} \log\left(\frac{2 \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - i \, a d \sqrt{-\frac{4 i \, e^{3}}{a d^{2}}}}{e}\right)"," ",0,"1/2*sqrt(4*I*e^3/(a*d^2))*log((2*(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + I*a*d*sqrt(4*I*e^3/(a*d^2)))/e) - 1/2*sqrt(4*I*e^3/(a*d^2))*log((2*(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - I*a*d*sqrt(4*I*e^3/(a*d^2)))/e) + 1/2*sqrt(-4*I*e^3/(a*d^2))*log((2*(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) + I*a*d*sqrt(-4*I*e^3/(a*d^2)))/e) - 1/2*sqrt(-4*I*e^3/(a*d^2))*log((2*(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - I*a*d*sqrt(-4*I*e^3/(a*d^2)))/e)","A",0
418,1,64,0,0.420075," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{a d}"," ",0,"2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(I*e^(2*I*d*x + 2*I*c) + I)*e^(-1/2*I*d*x - 1/2*I*c)/(a*d)","B",0
419,1,78,0,1.122383," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-\frac{3}{2} i \, d x - \frac{3}{2} i \, c\right)}}{3 \, a d e}"," ",0,"1/3*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-3*I*e^(4*I*d*x + 4*I*c) - 2*I*e^(2*I*d*x + 2*I*c) + I)*e^(-3/2*I*d*x - 3/2*I*c)/(a*d*e)","A",0
420,1,89,0,0.799013," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-5 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 25 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 33 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-\frac{5}{2} i \, d x - \frac{5}{2} i \, c\right)}}{30 \, a d e^{2}}"," ",0,"1/30*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-5*I*e^(6*I*d*x + 6*I*c) + 25*I*e^(4*I*d*x + 4*I*c) + 33*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-5/2*I*d*x - 5/2*I*c)/(a*d*e^2)","A",0
421,1,100,0,0.565372," ","integrate(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-7 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 112 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 70 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 40 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-\frac{7}{2} i \, d x - \frac{7}{2} i \, c\right)}}{140 \, a d e^{3}}"," ",0,"1/140*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-7*I*e^(8*I*d*x + 8*I*c) - 112*I*e^(6*I*d*x + 6*I*c) - 70*I*e^(4*I*d*x + 4*I*c) + 40*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-7/2*I*d*x - 7/2*I*c)/(a*d*e^3)","A",0
422,1,111,0,0.681736," ","integrate(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-45 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 465 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 1470 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 2142 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 287 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 35 i\right)} e^{\left(-\frac{9}{2} i \, d x - \frac{9}{2} i \, c\right)}}{2520 \, a d e^{4}}"," ",0,"1/2520*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-45*I*e^(10*I*d*x + 10*I*c) - 465*I*e^(8*I*d*x + 8*I*c) + 1470*I*e^(6*I*d*x + 6*I*c) + 2142*I*e^(4*I*d*x + 4*I*c) + 287*I*e^(2*I*d*x + 2*I*c) + 35*I)*e^(-9/2*I*d*x - 9/2*I*c)/(a*d*e^4)","A",0
423,1,483,0,0.697345," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{-4 i \, e^{3} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - \sqrt{\frac{9 i \, e^{7}}{a^{3} d^{2}}} a^{2} d \log\left(-\frac{2 \, {\left(i \, \sqrt{\frac{9 i \, e^{7}}{a^{3} d^{2}}} a^{2} d - 3 \, {\left(e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)}}{3 \, e^{3}}\right) + \sqrt{\frac{9 i \, e^{7}}{a^{3} d^{2}}} a^{2} d \log\left(-\frac{2 \, {\left(-i \, \sqrt{\frac{9 i \, e^{7}}{a^{3} d^{2}}} a^{2} d - 3 \, {\left(e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)}}{3 \, e^{3}}\right) + \sqrt{-\frac{9 i \, e^{7}}{a^{3} d^{2}}} a^{2} d \log\left(\frac{2 i \, \sqrt{-\frac{9 i \, e^{7}}{a^{3} d^{2}}} a^{2} d + 6 \, {\left(e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, e^{3}}\right) - \sqrt{-\frac{9 i \, e^{7}}{a^{3} d^{2}}} a^{2} d \log\left(\frac{-2 i \, \sqrt{-\frac{9 i \, e^{7}}{a^{3} d^{2}}} a^{2} d + 6 \, {\left(e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{3 \, e^{3}}\right)}{2 \, a^{2} d}"," ",0,"1/2*(-4*I*e^3*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - sqrt(9*I*e^7/(a^3*d^2))*a^2*d*log(-2/3*(I*sqrt(9*I*e^7/(a^3*d^2))*a^2*d - 3*(e^3*e^(2*I*d*x + 2*I*c) + e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^3) + sqrt(9*I*e^7/(a^3*d^2))*a^2*d*log(-2/3*(-I*sqrt(9*I*e^7/(a^3*d^2))*a^2*d - 3*(e^3*e^(2*I*d*x + 2*I*c) + e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^3) + sqrt(-9*I*e^7/(a^3*d^2))*a^2*d*log(1/3*(2*I*sqrt(-9*I*e^7/(a^3*d^2))*a^2*d + 6*(e^3*e^(2*I*d*x + 2*I*c) + e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^3) - sqrt(-9*I*e^7/(a^3*d^2))*a^2*d*log(1/3*(-2*I*sqrt(-9*I*e^7/(a^3*d^2))*a^2*d + 6*(e^3*e^(2*I*d*x + 2*I*c) + e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^3))/(a^2*d)","A",0
424,1,539,0,0.658678," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} d \sqrt{\frac{4 i \, e^{5}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{a^{2} d \sqrt{\frac{4 i \, e^{5}}{a^{3} d^{2}}} + 2 \, {\left(e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{e^{2}}\right) - a^{2} d \sqrt{\frac{4 i \, e^{5}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{a^{2} d \sqrt{\frac{4 i \, e^{5}}{a^{3} d^{2}}} - 2 \, {\left(e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{e^{2}}\right) - a^{2} d \sqrt{-\frac{4 i \, e^{5}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(\frac{a^{2} d \sqrt{-\frac{4 i \, e^{5}}{a^{3} d^{2}}} + 2 \, {\left(e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{e^{2}}\right) + a^{2} d \sqrt{-\frac{4 i \, e^{5}}{a^{3} d^{2}}} e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{a^{2} d \sqrt{-\frac{4 i \, e^{5}}{a^{3} d^{2}}} - 2 \, {\left(e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{e^{2}}\right) - 2 \, {\left(4 i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a^{2} d}"," ",0,"-1/2*(a^2*d*sqrt(4*I*e^5/(a^3*d^2))*e^(I*d*x + I*c)*log((a^2*d*sqrt(4*I*e^5/(a^3*d^2)) + 2*(e^2*e^(2*I*d*x + 2*I*c) + e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^2) - a^2*d*sqrt(4*I*e^5/(a^3*d^2))*e^(I*d*x + I*c)*log(-(a^2*d*sqrt(4*I*e^5/(a^3*d^2)) - 2*(e^2*e^(2*I*d*x + 2*I*c) + e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^2) - a^2*d*sqrt(-4*I*e^5/(a^3*d^2))*e^(I*d*x + I*c)*log((a^2*d*sqrt(-4*I*e^5/(a^3*d^2)) + 2*(e^2*e^(2*I*d*x + 2*I*c) + e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^2) + a^2*d*sqrt(-4*I*e^5/(a^3*d^2))*e^(I*d*x + I*c)*log(-(a^2*d*sqrt(-4*I*e^5/(a^3*d^2)) - 2*(e^2*e^(2*I*d*x + 2*I*c) + e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^2) - 2*(4*I*e^2*e^(2*I*d*x + 2*I*c) + 4*I*e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-I*d*x - I*c)/(a^2*d)","A",0
425,1,67,0,0.666183," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{3}{2} i \, d x - \frac{3}{2} i \, c\right)}}{3 \, a^{2} d}"," ",0,"2/3*(I*e*e^(2*I*d*x + 2*I*c) + I*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-3/2*I*d*x - 3/2*I*c)/(a^2*d)","B",0
426,1,75,0,0.541083," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(5 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-\frac{5}{2} i \, d x - \frac{5}{2} i \, c\right)}}{5 \, a^{2} d}"," ",0,"1/5*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(5*I*e^(4*I*d*x + 4*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + I)*e^(-5/2*I*d*x - 5/2*I*c)/(a^2*d)","A",0
427,1,89,0,0.503502," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-21 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 7 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 17 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(-\frac{7}{2} i \, d x - \frac{7}{2} i \, c\right)}}{42 \, a^{2} d e}"," ",0,"1/42*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-21*I*e^(6*I*d*x + 6*I*c) - 7*I*e^(4*I*d*x + 4*I*c) + 17*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(-7/2*I*d*x - 7/2*I*c)/(a^2*d*e)","A",0
428,1,100,0,0.696144," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-15 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 120 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 162 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 32 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-\frac{9}{2} i \, d x - \frac{9}{2} i \, c\right)}}{180 \, a^{2} d e^{2}}"," ",0,"1/180*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-15*I*e^(8*I*d*x + 8*I*c) + 120*I*e^(6*I*d*x + 6*I*c) + 162*I*e^(4*I*d*x + 4*I*c) + 32*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-9/2*I*d*x - 9/2*I*c)/(a^2*d*e^2)","A",0
429,1,111,0,0.655184," ","integrate(1/(e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-77 i \, e^{\left(10 i \, d x + 10 i \, c\right)} - 1617 i \, e^{\left(8 i \, d x + 8 i \, c\right)} - 770 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 990 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 255 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 35 i\right)} e^{\left(-\frac{11}{2} i \, d x - \frac{11}{2} i \, c\right)}}{3080 \, a^{2} d e^{3}}"," ",0,"1/3080*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-77*I*e^(10*I*d*x + 10*I*c) - 1617*I*e^(8*I*d*x + 8*I*c) - 770*I*e^(6*I*d*x + 6*I*c) + 990*I*e^(4*I*d*x + 4*I*c) + 255*I*e^(2*I*d*x + 2*I*c) + 35*I)*e^(-11/2*I*d*x - 11/2*I*c)/(a^2*d*e^3)","A",0
430,1,541,0,0.705101," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(\sqrt{\frac{25 i \, e^{9}}{a^{5} d^{2}}} a^{3} d e^{\left(i \, d x + i \, c\right)} \log\left(\frac{2 \, {\left(\sqrt{\frac{25 i \, e^{9}}{a^{5} d^{2}}} a^{3} d + 5 \, {\left(e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{4}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)}}{5 \, e^{4}}\right) - \sqrt{\frac{25 i \, e^{9}}{a^{5} d^{2}}} a^{3} d e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{2 \, {\left(\sqrt{\frac{25 i \, e^{9}}{a^{5} d^{2}}} a^{3} d - 5 \, {\left(e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{4}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)}}{5 \, e^{4}}\right) - \sqrt{-\frac{25 i \, e^{9}}{a^{5} d^{2}}} a^{3} d e^{\left(i \, d x + i \, c\right)} \log\left(\frac{2 \, {\left(\sqrt{-\frac{25 i \, e^{9}}{a^{5} d^{2}}} a^{3} d + 5 \, {\left(e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{4}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)}}{5 \, e^{4}}\right) + \sqrt{-\frac{25 i \, e^{9}}{a^{5} d^{2}}} a^{3} d e^{\left(i \, d x + i \, c\right)} \log\left(-\frac{2 \, {\left(\sqrt{-\frac{25 i \, e^{9}}{a^{5} d^{2}}} a^{3} d - 5 \, {\left(e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{4}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)}}{5 \, e^{4}}\right) - 2 \, {\left(10 i \, e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i \, e^{4}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a^{3} d}"," ",0,"-1/2*(sqrt(25*I*e^9/(a^5*d^2))*a^3*d*e^(I*d*x + I*c)*log(2/5*(sqrt(25*I*e^9/(a^5*d^2))*a^3*d + 5*(e^4*e^(2*I*d*x + 2*I*c) + e^4)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^4) - sqrt(25*I*e^9/(a^5*d^2))*a^3*d*e^(I*d*x + I*c)*log(-2/5*(sqrt(25*I*e^9/(a^5*d^2))*a^3*d - 5*(e^4*e^(2*I*d*x + 2*I*c) + e^4)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^4) - sqrt(-25*I*e^9/(a^5*d^2))*a^3*d*e^(I*d*x + I*c)*log(2/5*(sqrt(-25*I*e^9/(a^5*d^2))*a^3*d + 5*(e^4*e^(2*I*d*x + 2*I*c) + e^4)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^4) + sqrt(-25*I*e^9/(a^5*d^2))*a^3*d*e^(I*d*x + I*c)*log(-2/5*(sqrt(-25*I*e^9/(a^5*d^2))*a^3*d - 5*(e^4*e^(2*I*d*x + 2*I*c) + e^4)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^4) - 2*(10*I*e^4*e^(2*I*d*x + 2*I*c) + 8*I*e^4)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-I*d*x - I*c)/(a^3*d)","A",0
431,1,543,0,0.632088," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} d \sqrt{\frac{4 i \, e^{7}}{a^{5} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{i \, a^{3} d \sqrt{\frac{4 i \, e^{7}}{a^{5} d^{2}}} + 2 \, {\left(e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{e^{3}}\right) - 3 \, a^{3} d \sqrt{\frac{4 i \, e^{7}}{a^{5} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{-i \, a^{3} d \sqrt{\frac{4 i \, e^{7}}{a^{5} d^{2}}} + 2 \, {\left(e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{e^{3}}\right) + 3 \, a^{3} d \sqrt{-\frac{4 i \, e^{7}}{a^{5} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{i \, a^{3} d \sqrt{-\frac{4 i \, e^{7}}{a^{5} d^{2}}} + 2 \, {\left(e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{e^{3}}\right) - 3 \, a^{3} d \sqrt{-\frac{4 i \, e^{7}}{a^{5} d^{2}}} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(\frac{-i \, a^{3} d \sqrt{-\frac{4 i \, e^{7}}{a^{5} d^{2}}} + 2 \, {\left(e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{e^{3}}\right) - 2 \, {\left(4 i \, e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 4 i \, e^{3}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{6 \, a^{3} d}"," ",0,"-1/6*(3*a^3*d*sqrt(4*I*e^7/(a^5*d^2))*e^(2*I*d*x + 2*I*c)*log((I*a^3*d*sqrt(4*I*e^7/(a^5*d^2)) + 2*(e^3*e^(2*I*d*x + 2*I*c) + e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^3) - 3*a^3*d*sqrt(4*I*e^7/(a^5*d^2))*e^(2*I*d*x + 2*I*c)*log((-I*a^3*d*sqrt(4*I*e^7/(a^5*d^2)) + 2*(e^3*e^(2*I*d*x + 2*I*c) + e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^3) + 3*a^3*d*sqrt(-4*I*e^7/(a^5*d^2))*e^(2*I*d*x + 2*I*c)*log((I*a^3*d*sqrt(-4*I*e^7/(a^5*d^2)) + 2*(e^3*e^(2*I*d*x + 2*I*c) + e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^3) - 3*a^3*d*sqrt(-4*I*e^7/(a^5*d^2))*e^(2*I*d*x + 2*I*c)*log((-I*a^3*d*sqrt(-4*I*e^7/(a^5*d^2)) + 2*(e^3*e^(2*I*d*x + 2*I*c) + e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))/e^3) - 2*(4*I*e^3*e^(2*I*d*x + 2*I*c) + 4*I*e^3)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c))*e^(-2*I*d*x - 2*I*c)/(a^3*d)","A",0
432,1,71,0,0.717163," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{2}\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{5}{2} i \, d x - \frac{5}{2} i \, c\right)}}{5 \, a^{3} d}"," ",0,"2/5*(I*e^2*e^(2*I*d*x + 2*I*c) + I*e^2)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-5/2*I*d*x - 5/2*I*c)/(a^3*d)","B",0
433,1,79,0,0.646848," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(7 i \, e e^{\left(4 i \, d x + 4 i \, c\right)} + 10 i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{7}{2} i \, d x - \frac{7}{2} i \, c\right)}}{21 \, a^{3} d}"," ",0,"1/21*(7*I*e*e^(4*I*d*x + 4*I*c) + 10*I*e*e^(2*I*d*x + 2*I*c) + 3*I*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(-7/2*I*d*x - 7/2*I*c)/(a^3*d)","A",0
434,1,86,0,1.506720," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(45 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 63 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 23 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i\right)} e^{\left(-\frac{9}{2} i \, d x - \frac{9}{2} i \, c\right)}}{90 \, a^{3} d}"," ",0,"1/90*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(45*I*e^(6*I*d*x + 6*I*c) + 63*I*e^(4*I*d*x + 4*I*c) + 23*I*e^(2*I*d*x + 2*I*c) + 5*I)*e^(-9/2*I*d*x - 9/2*I*c)/(a^3*d)","A",0
435,1,89,0,2.469666," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-77 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 110 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 40 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i\right)} e^{\left(-\frac{11}{2} i \, d x - \frac{11}{2} i \, c\right)}}{308 \, a^{3} d e}"," ",0,"1/308*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-77*I*e^(8*I*d*x + 8*I*c) + 110*I*e^(4*I*d*x + 4*I*c) + 40*I*e^(2*I*d*x + 2*I*c) + 7*I)*e^(-11/2*I*d*x - 11/2*I*c)/(a^3*d*e)","A",0
436,1,111,0,0.829521," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-195 i \, e^{\left(10 i \, d x + 10 i \, c\right)} + 2145 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 3042 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 962 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 305 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 45 i\right)} e^{\left(-\frac{13}{2} i \, d x - \frac{13}{2} i \, c\right)}}{4680 \, a^{3} d e^{2}}"," ",0,"1/4680*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(-195*I*e^(10*I*d*x + 10*I*c) + 2145*I*e^(8*I*d*x + 8*I*c) + 3042*I*e^(6*I*d*x + 6*I*c) + 962*I*e^(4*I*d*x + 4*I*c) + 305*I*e^(2*I*d*x + 2*I*c) + 45*I)*e^(-13/2*I*d*x - 13/2*I*c)/(a^3*d*e^2)","A",0
437,0,0,0,0.605961," ","integrate((e*sec(d*x+c))^(7/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{-6 i \cdot 2^{\frac{5}{6}} e^{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{4}{3} i \, d x + \frac{4}{3} i \, c\right)} + 5 \, a d {\rm integral}\left(-\frac{2 i \cdot 2^{\frac{5}{6}} e^{2} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{1}{3} i \, d x + \frac{1}{3} i \, c\right)}}{5 \, a d}, x\right)}{5 \, a d}"," ",0,"1/5*(-6*I*2^(5/6)*e^2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(4/3*I*d*x + 4/3*I*c) + 5*a*d*integral(-2/5*I*2^(5/6)*e^2*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(1/3*I*d*x + 1/3*I*c)/(a*d), x))/(a*d)","F",0
438,0,0,0,0.763134," ","integrate((e*sec(d*x+c))^(5/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \cdot 2^{\frac{1}{6}} {\left(-3 i \, e e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + a d {\rm integral}\left(\frac{2^{\frac{1}{6}} {\left(i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} e^{\left(-\frac{4}{3} i \, d x - \frac{4}{3} i \, c\right)}}{a d}, x\right)}{a d}"," ",0,"(2*2^(1/6)*(-3*I*e*e^(2*I*d*x + 2*I*c) - 3*I*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*e^(2/3*I*d*x + 2/3*I*c) + a*d*integral(2^(1/6)*(I*e*e^(2*I*d*x + 2*I*c) + I*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*e^(-4/3*I*d*x - 4/3*I*c)/(a*d), x))/(a*d)","F",0
439,0,0,0,0.813818," ","integrate((e*sec(d*x+c))^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2^{\frac{1}{6}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + {\left(a d e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}\right)} {\rm integral}\left(\frac{2^{\frac{1}{6}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 7 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 5 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, e^{\left(i \, d x + i \, c\right)} + 4 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}}{a d e^{\left(4 i \, d x + 4 i \, c\right)} - 3 \, a d e^{\left(3 i \, d x + 3 i \, c\right)} + 3 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} - a d e^{\left(i \, d x + i \, c\right)}}, x\right)}{a d e^{\left(3 i \, d x + 3 i \, c\right)} - 2 \, a d e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{\left(i \, d x + i \, c\right)}}"," ",0,"(2^(1/6)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(3*I*e^(4*I*d*x + 4*I*c) + 6*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(2/3*I*d*x + 2/3*I*c) + (a*d*e^(3*I*d*x + 3*I*c) - 2*a*d*e^(2*I*d*x + 2*I*c) + a*d*e^(I*d*x + I*c))*integral(2^(1/6)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(I*e^(4*I*d*x + 4*I*c) + 7*I*e^(3*I*d*x + 3*I*c) + 5*I*e^(2*I*d*x + 2*I*c) + 7*I*e^(I*d*x + I*c) + 4*I)*e^(2/3*I*d*x + 2/3*I*c)/(a*d*e^(4*I*d*x + 4*I*c) - 3*a*d*e^(3*I*d*x + 3*I*c) + 3*a*d*e^(2*I*d*x + 2*I*c) - a*d*e^(I*d*x + I*c)), x))/(a*d*e^(3*I*d*x + 3*I*c) - 2*a*d*e^(2*I*d*x + 2*I*c) + a*d*e^(I*d*x + I*c))","F",0
440,0,0,0,0.725299," ","integrate((e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(4 \, a d e^{\left(i \, d x + i \, c\right)} {\rm integral}\left(-\frac{i \cdot 2^{\frac{5}{6}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} e^{\left(\frac{1}{3} i \, d x + \frac{1}{3} i \, c\right)}}{4 \, a d}, x\right) + 2^{\frac{5}{6}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{1}{3}} {\left(3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i\right)} e^{\left(\frac{1}{3} i \, d x + \frac{1}{3} i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{4 \, a d}"," ",0,"1/4*(4*a*d*e^(I*d*x + I*c)*integral(-1/4*I*2^(5/6)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*e^(1/3*I*d*x + 1/3*I*c)/(a*d), x) + 2^(5/6)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(1/3)*(3*I*e^(2*I*d*x + 2*I*c) + 3*I)*e^(1/3*I*d*x + 1/3*I*c))*e^(-I*d*x - I*c)/(a*d)","F",0
441,0,0,0,0.736694," ","integrate(1/(e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2^{\frac{1}{6}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-12 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 27 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 18 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 8 \, {\left(a d e e^{\left(4 i \, d x + 4 i \, c\right)} - a d e e^{\left(2 i \, d x + 2 i \, c\right)}\right)} {\rm integral}\left(\frac{2^{\frac{1}{6}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-45 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 60 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 15 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}}{16 \, {\left(a d e e^{\left(6 i \, d x + 6 i \, c\right)} - 2 \, a d e e^{\left(4 i \, d x + 4 i \, c\right)} + a d e e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}, x\right)}{8 \, {\left(a d e e^{\left(4 i \, d x + 4 i \, c\right)} - a d e e^{\left(2 i \, d x + 2 i \, c\right)}\right)}}"," ",0,"1/8*(2^(1/6)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-12*I*e^(6*I*d*x + 6*I*c) - 27*I*e^(4*I*d*x + 4*I*c) - 18*I*e^(2*I*d*x + 2*I*c) - 3*I)*e^(2/3*I*d*x + 2/3*I*c) + 8*(a*d*e*e^(4*I*d*x + 4*I*c) - a*d*e*e^(2*I*d*x + 2*I*c))*integral(1/16*2^(1/6)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-45*I*e^(4*I*d*x + 4*I*c) - 60*I*e^(2*I*d*x + 2*I*c) - 15*I)*e^(2/3*I*d*x + 2/3*I*c)/(a*d*e*e^(6*I*d*x + 6*I*c) - 2*a*d*e*e^(4*I*d*x + 4*I*c) + a*d*e*e^(2*I*d*x + 2*I*c)), x))/(a*d*e*e^(4*I*d*x + 4*I*c) - a*d*e*e^(2*I*d*x + 2*I*c))","F",0
442,0,0,0,0.686217," ","integrate(1/(e*sec(d*x+c))^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2^{\frac{1}{6}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(-21 i \, e^{\left(8 i \, d x + 8 i \, c\right)} + 42 i \, e^{\left(7 i \, d x + 7 i \, c\right)} + 114 i \, e^{\left(6 i \, d x + 6 i \, c\right)} + 60 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 303 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 6 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 180 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 24 i \, e^{\left(i \, d x + i \, c\right)} + 12 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)} + 112 \, {\left(a d e^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{2} e^{\left(3 i \, d x + 3 i \, c\right)}\right)} {\rm integral}\left(\frac{2^{\frac{1}{6}} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} \left(\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{\frac{2}{3}} {\left(55 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 385 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 275 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 385 i \, e^{\left(i \, d x + i \, c\right)} + 220 i\right)} e^{\left(\frac{2}{3} i \, d x + \frac{2}{3} i \, c\right)}}{112 \, {\left(a d e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 3 \, a d e^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + 3 \, a d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - a d e^{2} e^{\left(i \, d x + i \, c\right)}\right)}}, x\right)}{112 \, {\left(a d e^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 2 \, a d e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + a d e^{2} e^{\left(3 i \, d x + 3 i \, c\right)}\right)}}"," ",0,"1/112*(2^(1/6)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(-21*I*e^(8*I*d*x + 8*I*c) + 42*I*e^(7*I*d*x + 7*I*c) + 114*I*e^(6*I*d*x + 6*I*c) + 60*I*e^(5*I*d*x + 5*I*c) + 303*I*e^(4*I*d*x + 4*I*c) - 6*I*e^(3*I*d*x + 3*I*c) + 180*I*e^(2*I*d*x + 2*I*c) - 24*I*e^(I*d*x + I*c) + 12*I)*e^(2/3*I*d*x + 2/3*I*c) + 112*(a*d*e^2*e^(5*I*d*x + 5*I*c) - 2*a*d*e^2*e^(4*I*d*x + 4*I*c) + a*d*e^2*e^(3*I*d*x + 3*I*c))*integral(1/112*2^(1/6)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e/(e^(2*I*d*x + 2*I*c) + 1))^(2/3)*(55*I*e^(4*I*d*x + 4*I*c) + 385*I*e^(3*I*d*x + 3*I*c) + 275*I*e^(2*I*d*x + 2*I*c) + 385*I*e^(I*d*x + I*c) + 220*I)*e^(2/3*I*d*x + 2/3*I*c)/(a*d*e^2*e^(4*I*d*x + 4*I*c) - 3*a*d*e^2*e^(3*I*d*x + 3*I*c) + 3*a*d*e^2*e^(2*I*d*x + 2*I*c) - a*d*e^2*e^(I*d*x + I*c)), x))/(a*d*e^2*e^(5*I*d*x + 5*I*c) - 2*a*d*e^2*e^(4*I*d*x + 4*I*c) + a*d*e^2*e^(3*I*d*x + 3*I*c))","F",0
443,1,529,0,0.963615," ","integrate((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(7/3),x, algorithm=""fricas"")","\frac{{\left(48 \, a^{3} f \left(\frac{125 i \, d^{2}}{186624 \, a^{7} f^{3}}\right)^{\frac{1}{3}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(-\frac{2}{5} \, {\left(72 i \, a^{3} f \left(\frac{125 i \, d^{2}}{186624 \, a^{7} f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)} - 5 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(8 i \, e^{\left(6 i \, f x + 6 i \, e\right)} + 19 i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 14 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - 24 \, {\left(-i \, \sqrt{3} a^{3} f + a^{3} f\right)} \left(\frac{125 i \, d^{2}}{186624 \, a^{7} f^{3}}\right)^{\frac{1}{3}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{1}{5} \, {\left(10 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(72 \, \sqrt{3} a^{3} f + 72 i \, a^{3} f\right)} \left(\frac{125 i \, d^{2}}{186624 \, a^{7} f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 24 \, {\left(i \, \sqrt{3} a^{3} f + a^{3} f\right)} \left(\frac{125 i \, d^{2}}{186624 \, a^{7} f^{3}}\right)^{\frac{1}{3}} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(\frac{1}{5} \, {\left(10 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(72 \, \sqrt{3} a^{3} f - 72 i \, a^{3} f\right)} \left(\frac{125 i \, d^{2}}{186624 \, a^{7} f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right)\right)} e^{\left(-6 i \, f x - 6 i \, e\right)}}{48 \, a^{3} f}"," ",0,"1/48*(48*a^3*f*(125/186624*I*d^2/(a^7*f^3))^(1/3)*e^(6*I*f*x + 6*I*e)*log(-2/5*(72*I*a^3*f*(125/186624*I*d^2/(a^7*f^3))^(1/3)*e^(2*I*f*x + 2*I*e) - 5*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) + 2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(8*I*e^(6*I*f*x + 6*I*e) + 19*I*e^(4*I*f*x + 4*I*e) + 14*I*e^(2*I*f*x + 2*I*e) + 3*I)*e^(2*I*f*x + 2*I*e) - 24*(-I*sqrt(3)*a^3*f + a^3*f)*(125/186624*I*d^2/(a^7*f^3))^(1/3)*e^(6*I*f*x + 6*I*e)*log(1/5*(10*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e) + (72*sqrt(3)*a^3*f + 72*I*a^3*f)*(125/186624*I*d^2/(a^7*f^3))^(1/3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 24*(I*sqrt(3)*a^3*f + a^3*f)*(125/186624*I*d^2/(a^7*f^3))^(1/3)*e^(6*I*f*x + 6*I*e)*log(1/5*(10*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e) - (72*sqrt(3)*a^3*f - 72*I*a^3*f)*(125/186624*I*d^2/(a^7*f^3))^(1/3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)))*e^(-6*I*f*x - 6*I*e)/(a^3*f)","A",0
444,1,515,0,0.629500," ","integrate((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(4/3),x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} f \left(\frac{i \, d^{2}}{108 \, a^{4} f^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left({\left(-12 i \, a^{2} f \left(\frac{i \, d^{2}}{108 \, a^{4} f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(i \, e^{\left(4 i \, f x + 4 i \, e\right)} + 2 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - 2 \, {\left(-i \, \sqrt{3} a^{2} f + a^{2} f\right)} \left(\frac{i \, d^{2}}{108 \, a^{4} f^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left({\left(2 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(6 \, \sqrt{3} a^{2} f + 6 i \, a^{2} f\right)} \left(\frac{i \, d^{2}}{108 \, a^{4} f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) - 2 \, {\left(i \, \sqrt{3} a^{2} f + a^{2} f\right)} \left(\frac{i \, d^{2}}{108 \, a^{4} f^{3}}\right)^{\frac{1}{3}} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left({\left(2 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(6 \, \sqrt{3} a^{2} f - 6 i \, a^{2} f\right)} \left(\frac{i \, d^{2}}{108 \, a^{4} f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right)\right)} e^{\left(-4 i \, f x - 4 i \, e\right)}}{4 \, a^{2} f}"," ",0,"1/4*(4*a^2*f*(1/108*I*d^2/(a^4*f^3))^(1/3)*e^(4*I*f*x + 4*I*e)*log((-12*I*a^2*f*(1/108*I*d^2/(a^4*f^3))^(1/3)*e^(2*I*f*x + 2*I*e) + 2*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) + 2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(I*e^(4*I*f*x + 4*I*e) + 2*I*e^(2*I*f*x + 2*I*e) + I)*e^(2*I*f*x + 2*I*e) - 2*(-I*sqrt(3)*a^2*f + a^2*f)*(1/108*I*d^2/(a^4*f^3))^(1/3)*e^(4*I*f*x + 4*I*e)*log((2*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e) + (6*sqrt(3)*a^2*f + 6*I*a^2*f)*(1/108*I*d^2/(a^4*f^3))^(1/3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) - 2*(I*sqrt(3)*a^2*f + a^2*f)*(1/108*I*d^2/(a^4*f^3))^(1/3)*e^(4*I*f*x + 4*I*e)*log((2*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e) - (6*sqrt(3)*a^2*f - 6*I*a^2*f)*(1/108*I*d^2/(a^4*f^3))^(1/3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)))*e^(-4*I*f*x - 4*I*e)/(a^2*f)","A",0
445,1,369,0,1.681414," ","integrate((d*sec(f*x+e))^(2/3)/(a+I*a*tan(f*x+e))^(1/3),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(\frac{i \, d^{2}}{4 \, a f^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(2 \, \sqrt{3} a f + 2 i \, a f\right)} \left(\frac{i \, d^{2}}{4 \, a f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(\frac{i \, d^{2}}{4 \, a f^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - {\left(2 \, \sqrt{3} a f - 2 i \, a f\right)} \left(\frac{i \, d^{2}}{4 \, a f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right) + \left(\frac{i \, d^{2}}{4 \, a f^{3}}\right)^{\frac{1}{3}} \log\left({\left(2 \cdot 2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)} e^{\left(2 i \, f x + 2 i \, e\right)} - 4 i \, a f \left(\frac{i \, d^{2}}{4 \, a f^{3}}\right)^{\frac{1}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}\right)} e^{\left(-2 i \, f x - 2 i \, e\right)}\right)"," ",0,"1/2*(I*sqrt(3) - 1)*(1/4*I*d^2/(a*f^3))^(1/3)*log((2*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e) + (2*sqrt(3)*a*f + 2*I*a*f)*(1/4*I*d^2/(a*f^3))^(1/3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) + 1/2*(-I*sqrt(3) - 1)*(1/4*I*d^2/(a*f^3))^(1/3)*log((2*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e) - (2*sqrt(3)*a*f - 2*I*a*f)*(1/4*I*d^2/(a*f^3))^(1/3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e)) + (1/4*I*d^2/(a*f^3))^(1/3)*log((2*2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(e^(2*I*f*x + 2*I*e) + 1)*e^(2*I*f*x + 2*I*e) - 4*I*a*f*(1/4*I*d^2/(a*f^3))^(1/3)*e^(2*I*f*x + 2*I*e))*e^(-2*I*f*x - 2*I*e))","A",0
446,1,54,0,0.638380," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(2/3),x, algorithm=""fricas"")","\frac{2^{\frac{1}{3}} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} {\left(3 i \, e^{\left(2 i \, f x + 2 i \, e\right)} + 3 i\right)}}{f}"," ",0,"2^(1/3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(3*I*e^(2*I*f*x + 2*I*e) + 3*I)/f","A",0
447,1,58,0,0.445741," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(5/3),x, algorithm=""fricas"")","\frac{2^{\frac{1}{3}} {\left(12 i \, a e^{\left(2 i \, f x + 2 i \, e\right)} + 9 i \, a\right)} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}}}{2 \, f}"," ",0,"1/2*2^(1/3)*(12*I*a*e^(2*I*f*x + 2*I*e) + 9*I*a)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)/f","A",0
448,1,107,0,0.728416," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(8/3),x, algorithm=""fricas"")","\frac{2 \cdot 2^{\frac{1}{3}} {\left(42 i \, a^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 63 i \, a^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 27 i \, a^{2}\right)} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}}{7 \, {\left(f e^{\left(4 i \, f x + 4 i \, e\right)} + f e^{\left(2 i \, f x + 2 i \, e\right)}\right)}}"," ",0,"2/7*2^(1/3)*(42*I*a^2*e^(4*I*f*x + 4*I*e) + 63*I*a^2*e^(2*I*f*x + 2*I*e) + 27*I*a^2)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2*I*f*x + 2*I*e)/(f*e^(4*I*f*x + 4*I*e) + f*e^(2*I*f*x + 2*I*e))","A",0
449,1,133,0,0.684446," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(11/3),x, algorithm=""fricas"")","\frac{2 \cdot 2^{\frac{1}{3}} {\left(420 i \, a^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + 945 i \, a^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 810 i \, a^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 243 i \, a^{3}\right)} \left(\frac{a}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} \left(\frac{d}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{\frac{2}{3}} e^{\left(2 i \, f x + 2 i \, e\right)}}{35 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 2 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + f e^{\left(2 i \, f x + 2 i \, e\right)}\right)}}"," ",0,"2/35*2^(1/3)*(420*I*a^3*e^(6*I*f*x + 6*I*e) + 945*I*a^3*e^(4*I*f*x + 4*I*e) + 810*I*a^3*e^(2*I*f*x + 2*I*e) + 243*I*a^3)*(a/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*(d/(e^(2*I*f*x + 2*I*e) + 1))^(2/3)*e^(2*I*f*x + 2*I*e)/(f*e^(6*I*f*x + 6*I*e) + 2*f*e^(4*I*f*x + 4*I*e) + f*e^(2*I*f*x + 2*I*e))","A",0
450,0,0,0,0.704045," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{32 \, a^{5} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} e^{\left(10 i \, d x + 10 i \, c\right)}}{e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(32*a^5*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(10*I*d*x + 10*I*c)/(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
451,0,0,0,1.810984," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{8 \, a^{3} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} e^{\left(6 i \, d x + 6 i \, c\right)}}{e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(8*a^3*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(6*I*d*x + 6*I*c)/(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
452,0,0,0,0.650170," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, a^{2} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} e^{\left(4 i \, d x + 4 i \, c\right)}}{e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(4*a^2*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(4*I*d*x + 4*I*c)/(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
453,0,0,0,0.654848," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(2*a*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
454,0,0,0,0.521434," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(e^(2*I*d*x + 2*I*c) + 1)*e^(-2*I*d*x - 2*I*c)/a, x)","F",0
455,0,0,0,0.579011," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*e^(-4*I*d*x - 4*I*c)/a^2, x)","F",0
456,0,0,0,0.780402," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}}{8 \, a^{3}}, x\right)"," ",0,"integral(1/8*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*e^(-6*I*d*x - 6*I*c)/a^3, x)","F",0
457,0,0,0,1.512610," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{8 \, \sqrt{2} a^{3} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(7 i \, d x + 7 i \, c\right)}}{e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(8*sqrt(2)*a^3*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(7*I*d*x + 7*I*c)/(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
458,0,0,0,0.850288," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, \sqrt{2} a^{2} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(5 i \, d x + 5 i \, c\right)}}{e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(4*sqrt(2)*a^2*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(5*I*d*x + 5*I*c)/(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
459,0,0,0,0.618169," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \sqrt{2} a \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(3 i \, d x + 3 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(2*sqrt(2)*a*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(3*I*d*x + 3*I*c)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
460,0,0,0,0.574360," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{2} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)}, x\right)"," ",0,"integral(sqrt(2)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c), x)","F",0
461,0,0,0,0.548942," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*sqrt(2)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)*e^(-I*d*x - I*c)/a, x)","F",0
462,0,0,0,0.570879," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*sqrt(2)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*e^(-3*I*d*x - 3*I*c)/a^2, x)","F",0
463,0,0,0,0.577145," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{8 \, a^{3}}, x\right)"," ",0,"integral(1/8*sqrt(2)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*e^(-5*I*d*x - 5*I*c)/a^3, x)","F",0
464,0,0,0,0.916615," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{m} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}, x\right)"," ",0,"integral((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^m*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)), x)","F",0
465,1,245,0,0.520407," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left({\left(-64 i \, n - 320 i\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-32 i \, n^{2} - 288 i \, n - 640 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} - 64 i \, e^{\left(10 i \, d x + 10 i \, c\right)}\right)} \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n}}{d n^{3} + 12 \, d n^{2} + 47 \, d n + {\left(d n^{3} + 12 \, d n^{2} + 47 \, d n + 60 \, d\right)} e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, {\left(d n^{3} + 12 \, d n^{2} + 47 \, d n + 60 \, d\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, {\left(d n^{3} + 12 \, d n^{2} + 47 \, d n + 60 \, d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, {\left(d n^{3} + 12 \, d n^{2} + 47 \, d n + 60 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, {\left(d n^{3} + 12 \, d n^{2} + 47 \, d n + 60 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 60 \, d}"," ",0,"((-64*I*n - 320*I)*e^(8*I*d*x + 8*I*c) + (-32*I*n^2 - 288*I*n - 640*I)*e^(6*I*d*x + 6*I*c) - 64*I*e^(10*I*d*x + 10*I*c))*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(d*n^3 + 12*d*n^2 + 47*d*n + (d*n^3 + 12*d*n^2 + 47*d*n + 60*d)*e^(10*I*d*x + 10*I*c) + 5*(d*n^3 + 12*d*n^2 + 47*d*n + 60*d)*e^(8*I*d*x + 8*I*c) + 10*(d*n^3 + 12*d*n^2 + 47*d*n + 60*d)*e^(6*I*d*x + 6*I*c) + 10*(d*n^3 + 12*d*n^2 + 47*d*n + 60*d)*e^(4*I*d*x + 4*I*c) + 5*(d*n^3 + 12*d*n^2 + 47*d*n + 60*d)*e^(2*I*d*x + 2*I*c) + 60*d)","B",0
466,1,141,0,0.689740," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left({\left(-8 i \, n - 24 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 8 i \, e^{\left(6 i \, d x + 6 i \, c\right)}\right)} \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n}}{d n^{2} + 5 \, d n + {\left(d n^{2} + 5 \, d n + 6 \, d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, {\left(d n^{2} + 5 \, d n + 6 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(d n^{2} + 5 \, d n + 6 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 \, d}"," ",0,"((-8*I*n - 24*I)*e^(4*I*d*x + 4*I*c) - 8*I*e^(6*I*d*x + 6*I*c))*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n/(d*n^2 + 5*d*n + (d*n^2 + 5*d*n + 6*d)*e^(6*I*d*x + 6*I*c) + 3*(d*n^2 + 5*d*n + 6*d)*e^(4*I*d*x + 4*I*c) + 3*(d*n^2 + 5*d*n + 6*d)*e^(2*I*d*x + 2*I*c) + 6*d)","B",0
467,1,60,0,0.698076," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","-\frac{2 i \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} e^{\left(2 i \, d x + 2 i \, c\right)}}{d n + {\left(d n + d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"-2*I*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*e^(2*I*d*x + 2*I*c)/(d*n + (d*n + d)*e^(2*I*d*x + 2*I*c) + d)","B",0
468,0,0,0,1.051236," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{4} \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}, x\right)"," ",0,"integral(1/4*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*e^(-2*I*d*x - 2*I*c), x)","F",0
469,0,0,0,1.479164," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{16} \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} {\left(e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}, x\right)"," ",0,"integral(1/16*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*(e^(8*I*d*x + 8*I*c) + 4*e^(6*I*d*x + 6*I*c) + 6*e^(4*I*d*x + 4*I*c) + 4*e^(2*I*d*x + 2*I*c) + 1)*e^(-4*I*d*x - 4*I*c), x)","F",0
470,0,0,0,0.577595," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{64} \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} {\left(e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-6 i \, d x - 6 i \, c\right)}, x\right)"," ",0,"integral(1/64*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*(e^(12*I*d*x + 12*I*c) + 6*e^(10*I*d*x + 10*I*c) + 15*e^(8*I*d*x + 8*I*c) + 20*e^(6*I*d*x + 6*I*c) + 15*e^(4*I*d*x + 4*I*c) + 6*e^(2*I*d*x + 2*I*c) + 1)*e^(-6*I*d*x - 6*I*c), x)","F",0
471,0,0,0,0.468856," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{32 \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} e^{\left(5 i \, d x + 5 i \, c\right)}}{e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(32*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*e^(5*I*d*x + 5*I*c)/(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
472,0,0,0,0.923027," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{8 \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} e^{\left(3 i \, d x + 3 i \, c\right)}}{e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(8*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*e^(3*I*d*x + 3*I*c)/(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
473,0,0,0,0.491320," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(2*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
474,0,0,0,0.575082," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{2} \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-i \, d x - i \, c\right)}, x\right)"," ",0,"integral(1/2*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*(e^(2*I*d*x + 2*I*c) + 1)*e^(-I*d*x - I*c), x)","F",0
475,0,0,0,0.647280," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{8} \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}, x\right)"," ",0,"integral(1/8*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*e^(-3*I*d*x - 3*I*c), x)","F",0
476,0,0,0,0.773120," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{32} \, \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} {\left(e^{\left(10 i \, d x + 10 i \, c\right)} + 5 \, e^{\left(8 i \, d x + 8 i \, c\right)} + 10 \, e^{\left(6 i \, d x + 6 i \, c\right)} + 10 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 5 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}, x\right)"," ",0,"integral(1/32*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*(e^(10*I*d*x + 10*I*c) + 5*e^(8*I*d*x + 8*I*c) + 10*e^(6*I*d*x + 6*I*c) + 10*e^(4*I*d*x + 4*I*c) + 5*e^(2*I*d*x + 2*I*c) + 1)*e^(-5*I*d*x - 5*I*c), x)","F",0
477,0,0,0,0.647441," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, \sqrt{2} e^{2} \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{5}{2} i \, d x + \frac{5}{2} i \, c\right)}}{e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(4*sqrt(2)*e^2*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(5/2*I*d*x + 5/2*I*c)/(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
478,0,0,0,0.596322," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \sqrt{2} e \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{3}{2} i \, d x + \frac{3}{2} i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(2*sqrt(2)*e*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(3/2*I*d*x + 3/2*I*c)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
479,0,0,0,0.576523," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{2} \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}, x\right)"," ",0,"integral(sqrt(2)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c), x)","F",0
480,0,0,0,0.661581," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{2 \, e}, x\right)"," ",0,"integral(1/2*sqrt(2)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)*e^(-1/2*I*d*x - 1/2*I*c)/e, x)","F",0
481,0,0,0,0.769934," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-\frac{3}{2} i \, d x - \frac{3}{2} i \, c\right)}}{4 \, e^{2}}, x\right)"," ",0,"integral(1/4*sqrt(2)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*e^(-3/2*I*d*x - 3/2*I*c)/e^2, x)","F",0
482,0,0,0,0.584217," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} \sqrt{\frac{e}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-\frac{5}{2} i \, d x - \frac{5}{2} i \, c\right)}}{8 \, e^{3}}, x\right)"," ",0,"integral(1/8*sqrt(2)*(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*sqrt(e/(e^(2*I*d*x + 2*I*c) + 1))*(e^(6*I*d*x + 6*I*c) + 3*e^(4*I*d*x + 4*I*c) + 3*e^(2*I*d*x + 2*I*c) + 1)*e^(-5/2*I*d*x - 5/2*I*c)/e^3, x)","F",0
483,1,332,0,1.100668," ","integrate((e*sec(d*x+c))^(-4-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left(-i \, n^{4} - 4 i \, n^{3} + 4 i \, n^{2} + {\left(-i \, n^{4} + 4 i \, n^{3} + 4 i \, n^{2} - 16 i \, n\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + {\left(-4 i \, n^{4} + 8 i \, n^{3} + 64 i \, n^{2} - 128 i \, n\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-6 i \, n^{4} + 120 i \, n^{2} - 384 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-4 i \, n^{4} - 8 i \, n^{3} + 64 i \, n^{2} + 128 i \, n\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 16 i \, n\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n - 4} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}}{d n^{5} - 20 \, d n^{3} + 64 \, d n + {\left(d n^{5} - 20 \, d n^{3} + 64 \, d n\right)} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, {\left(d n^{5} - 20 \, d n^{3} + 64 \, d n\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, {\left(d n^{5} - 20 \, d n^{3} + 64 \, d n\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, {\left(d n^{5} - 20 \, d n^{3} + 64 \, d n\right)} e^{\left(2 i \, d x + 2 i \, c\right)}}"," ",0,"(-I*n^4 - 4*I*n^3 + 4*I*n^2 + (-I*n^4 + 4*I*n^3 + 4*I*n^2 - 16*I*n)*e^(8*I*d*x + 8*I*c) + (-4*I*n^4 + 8*I*n^3 + 64*I*n^2 - 128*I*n)*e^(6*I*d*x + 6*I*c) + (-6*I*n^4 + 120*I*n^2 - 384*I)*e^(4*I*d*x + 4*I*c) + (-4*I*n^4 - 8*I*n^3 + 64*I*n^2 + 128*I*n)*e^(2*I*d*x + 2*I*c) + 16*I*n)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n - 4)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e))/(d*n^5 - 20*d*n^3 + 64*d*n + (d*n^5 - 20*d*n^3 + 64*d*n)*e^(8*I*d*x + 8*I*c) + 4*(d*n^5 - 20*d*n^3 + 64*d*n)*e^(6*I*d*x + 6*I*c) + 6*(d*n^5 - 20*d*n^3 + 64*d*n)*e^(4*I*d*x + 4*I*c) + 4*(d*n^5 - 20*d*n^3 + 64*d*n)*e^(2*I*d*x + 2*I*c))","A",0
484,1,263,0,0.576295," ","integrate((e*sec(d*x+c))^(-3-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left(-i \, n^{3} - 3 i \, n^{2} + {\left(-i \, n^{3} + 3 i \, n^{2} + i \, n - 3 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-3 i \, n^{3} + 3 i \, n^{2} + 27 i \, n - 27 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-3 i \, n^{3} - 3 i \, n^{2} + 27 i \, n + 27 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i \, n + 3 i\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n - 3} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}}{d n^{4} - 10 \, d n^{2} + {\left(d n^{4} - 10 \, d n^{2} + 9 \, d\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, {\left(d n^{4} - 10 \, d n^{2} + 9 \, d\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, {\left(d n^{4} - 10 \, d n^{2} + 9 \, d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + 9 \, d}"," ",0,"(-I*n^3 - 3*I*n^2 + (-I*n^3 + 3*I*n^2 + I*n - 3*I)*e^(6*I*d*x + 6*I*c) + (-3*I*n^3 + 3*I*n^2 + 27*I*n - 27*I)*e^(4*I*d*x + 4*I*c) + (-3*I*n^3 - 3*I*n^2 + 27*I*n + 27*I)*e^(2*I*d*x + 2*I*c) + I*n + 3*I)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n - 3)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e))/(d*n^4 - 10*d*n^2 + (d*n^4 - 10*d*n^2 + 9*d)*e^(6*I*d*x + 6*I*c) + 3*(d*n^4 - 10*d*n^2 + 9*d)*e^(4*I*d*x + 4*I*c) + 3*(d*n^4 - 10*d*n^2 + 9*d)*e^(2*I*d*x + 2*I*c) + 9*d)","A",0
485,1,177,0,0.532434," ","integrate((e*sec(d*x+c))^(-2-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left(-i \, n^{2} + {\left(-i \, n^{2} + 2 i \, n\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-2 i \, n^{2} + 8 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i \, n\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n - 2} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}}{d n^{3} - 4 \, d n + {\left(d n^{3} - 4 \, d n\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(d n^{3} - 4 \, d n\right)} e^{\left(2 i \, d x + 2 i \, c\right)}}"," ",0,"(-I*n^2 + (-I*n^2 + 2*I*n)*e^(4*I*d*x + 4*I*c) + (-2*I*n^2 + 8*I)*e^(2*I*d*x + 2*I*c) - 2*I*n)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n - 2)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e))/(d*n^3 - 4*d*n + (d*n^3 - 4*d*n)*e^(4*I*d*x + 4*I*c) + 2*(d*n^3 - 4*d*n)*e^(2*I*d*x + 2*I*c))","A",0
486,1,129,0,0.698061," ","integrate((e*sec(d*x+c))^(-1-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left({\left(-i \, n + i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - i \, n - i\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n - 1} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}}{d n^{2} + {\left(d n^{2} - d\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - d}"," ",0,"((-I*n + I)*e^(2*I*d*x + 2*I*c) - I*n - I)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n - 1)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e))/(d*n^2 + (d*n^2 - d)*e^(2*I*d*x + 2*I*c) - d)","A",0
487,1,84,0,0.663482," ","integrate((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^n),x, algorithm=""fricas"")","-\frac{i \, e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}}{d n \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n}}"," ",0,"-I*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e))/(d*n*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n)","B",0
488,0,0,0,0.606749," ","integrate((e*sec(d*x+c))^(1-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n + 1} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}, x\right)"," ",0,"integral((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n + 1)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)), x)","F",0
489,0,0,0,0.572865," ","integrate((e*sec(d*x+c))^(2-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n + 2} {\left(i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(\frac{1}{2} \, {\left(n e^{\left(2 i \, d x + 2 i \, c\right)} + n\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n + 2} e^{\left(i \, d n x + i \, c n - 2 i \, d x + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right) - 2 i \, c\right)}, x\right)\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, d}"," ",0,"1/2*((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n + 2)*(I*e^(2*I*d*x + 2*I*c) + I)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)) + 2*d*e^(2*I*d*x + 2*I*c)*integral(1/2*(n*e^(2*I*d*x + 2*I*c) + n)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n + 2)*e^(I*d*n*x + I*c*n - 2*I*d*x + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e) - 2*I*c), x))*e^(-2*I*d*x - 2*I*c)/d","F",0
490,0,0,0,0.636027," ","integrate((e*sec(d*x+c))^(3-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left({\left({\left(-i \, n - i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} - 2 i \, n e^{\left(2 i \, d x + 2 i \, c\right)} - i \, n + i\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n + 3} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)} + 8 \, d e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(-\frac{1}{8} \, {\left(n^{2} + {\left(n^{2} - 1\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, {\left(n^{2} - 1\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 1\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-n + 3} e^{\left(i \, d n x + i \, c n - 2 i \, d x + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right) - 2 i \, c\right)}, x\right)\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{8 \, d}"," ",0,"1/8*(((-I*n - I)*e^(4*I*d*x + 4*I*c) - 2*I*n*e^(2*I*d*x + 2*I*c) - I*n + I)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n + 3)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)) + 8*d*e^(2*I*d*x + 2*I*c)*integral(-1/8*(n^2 + (n^2 - 1)*e^(4*I*d*x + 4*I*c) + 2*(n^2 - 1)*e^(2*I*d*x + 2*I*c) - 1)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-n + 3)*e^(I*d*n*x + I*c*n - 2*I*d*x + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e) - 2*I*c), x))*e^(-2*I*d*x - 2*I*c)/d","F",0
491,1,165,0,0.579197," ","integrate((e*sec(d*x+c))^(6-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left({\left(-i \, n^{2} + 9 i \, n - 20 i\right)} e^{\left(6 i \, d x + 6 i \, c\right)} + {\left(-i \, n^{2} + 11 i \, n - 30 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(2 i \, n - 12 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} - 2 i\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n + 6} e^{\left(i \, d n x + i \, c n - 6 i \, d x + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right) - 6 i \, c\right)}}{2 \, {\left(d n^{3} - 12 \, d n^{2} + 47 \, d n - 60 \, d\right)}}"," ",0,"1/2*((-I*n^2 + 9*I*n - 20*I)*e^(6*I*d*x + 6*I*c) + (-I*n^2 + 11*I*n - 30*I)*e^(4*I*d*x + 4*I*c) + (2*I*n - 12*I)*e^(2*I*d*x + 2*I*c) - 2*I)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n + 6)*e^(I*d*n*x + I*c*n - 6*I*d*x + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e) - 6*I*c)/(d*n^3 - 12*d*n^2 + 47*d*n - 60*d)","A",0
492,0,0,0,0.797615," ","integrate((e*sec(d*x+c))^(5-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n + 5} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}, x\right)"," ",0,"integral((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n + 5)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)), x)","F",0
493,1,134,0,0.676054," ","integrate((e*sec(d*x+c))^(4-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left({\left(-i \, n + 3 i\right)} e^{\left(4 i \, d x + 4 i \, c\right)} + {\left(-i \, n + 4 i\right)} e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} \left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n + 4} e^{\left(i \, d n x + i \, c n - 4 i \, d x + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right) - 4 i \, c\right)}}{2 \, {\left(d n^{2} - 5 \, d n + 6 \, d\right)}}"," ",0,"1/2*((-I*n + 3*I)*e^(4*I*d*x + 4*I*c) + (-I*n + 4*I)*e^(2*I*d*x + 2*I*c) + I)*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n + 4)*e^(I*d*n*x + I*c*n - 4*I*d*x + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e) - 4*I*c)/(d*n^2 - 5*d*n + 6*d)","A",0
494,0,0,0,0.762959," ","integrate((e*sec(d*x+c))^(3-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n + 3} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}, x\right)"," ",0,"integral((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n + 3)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)), x)","F",0
495,1,109,0,0.669805," ","integrate((e*sec(d*x+c))^(2-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n + 2} {\left(-i \, e^{\left(2 i \, d x + 2 i \, c\right)} - i\right)} e^{\left(i \, d n x + i \, c n - 2 i \, d x + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right) - 2 i \, c\right)}}{2 \, {\left(d n - d\right)}}"," ",0,"1/2*(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n + 2)*(-I*e^(2*I*d*x + 2*I*c) - I)*e^(I*d*n*x + I*c*n - 2*I*d*x + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e) - 2*I*c)/(d*n - d)","B",0
496,0,0,0,0.611194," ","integrate((e*sec(d*x+c))^(1-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n + 1} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}, x\right)"," ",0,"integral((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n + 1)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)), x)","F",0
497,0,0,0,0.582101," ","integrate((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}}{\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{2 \, n}}, x\right)"," ",0,"integral(e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e))/(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(2*n), x)","F",0
498,0,0,0,0.593627," ","integrate((e*sec(d*x+c))^(-1-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n - 1} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}, x\right)"," ",0,"integral((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n - 1)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)), x)","F",0
499,0,0,0,0.680867," ","integrate((e*sec(d*x+c))^(-2-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n - 2} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}, x\right)"," ",0,"integral((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n - 2)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)), x)","F",0
500,0,0,0,1.565353," ","integrate((e*sec(d*x+c))^(-3-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{-2 \, n - 3} e^{\left(i \, d n x + i \, c n + n \log\left(\frac{2 \, e e^{\left(i \, d x + i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right) + n \log\left(\frac{a}{e}\right)\right)}, x\right)"," ",0,"integral((2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1))^(-2*n - 3)*e^(I*d*n*x + I*c*n + n*log(2*e*e^(I*d*x + I*c)/(e^(2*I*d*x + 2*I*c) + 1)) + n*log(a/e)), x)","F",0
501,0,0,0,0.694578," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-2-n),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{2 \, n} e^{\left(-i \, e n + {\left(-i \, f n - 2 i \, f\right)} x - {\left(n + 2\right)} \log\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) - {\left(n + 2\right)} \log\left(\frac{a}{d}\right) - 2 i \, e\right)}, x\right)"," ",0,"integral((2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1))^(2*n)*e^(-I*e*n + (-I*f*n - 2*I*f)*x - (n + 2)*log(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1)) - (n + 2)*log(a/d) - 2*I*e), x)","F",0
502,0,0,0,0.780418," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-1-n),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{2 \, n} e^{\left(-i \, e n + {\left(-i \, f n - i \, f\right)} x - {\left(n + 1\right)} \log\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) - {\left(n + 1\right)} \log\left(\frac{a}{d}\right) - i \, e\right)}, x\right)"," ",0,"integral((2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1))^(2*n)*e^(-I*e*n + (-I*f*n - I*f)*x - (n + 1)*log(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1)) - (n + 1)*log(a/d) - I*e), x)","F",0
503,0,0,0,0.633066," ","integrate((d*sec(f*x+e))^(2*n)/((a+I*a*tan(f*x+e))^n),x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{2 \, n} e^{\left(-i \, f n x - i \, e n - n \log\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) - n \log\left(\frac{a}{d}\right)\right)}, x\right)"," ",0,"integral((2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1))^(2*n)*e^(-I*f*n*x - I*e*n - n*log(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1)) - n*log(a/d)), x)","F",0
504,1,115,0,0.756843," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(1-n),x, algorithm=""fricas"")","\frac{\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{2 \, n} {\left(i \, e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} e^{\left(-i \, e n + {\left(-i \, f n + i \, f\right)} x - 2 i \, f x - {\left(n - 1\right)} \log\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) - {\left(n - 1\right)} \log\left(\frac{a}{d}\right) - i \, e\right)}}{2 \, f n}"," ",0,"1/2*(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1))^(2*n)*(I*e^(2*I*f*x + 2*I*e) + I)*e^(-I*e*n + (-I*f*n + I*f)*x - 2*I*f*x - (n - 1)*log(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1)) - (n - 1)*log(a/d) - I*e)/(f*n)","B",0
505,1,139,0,0.973065," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(2-n),x, algorithm=""fricas"")","\frac{{\left({\left(i \, n + i\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(i \, n + 2 i\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + i\right)} \left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{2 \, n} e^{\left(-i \, e n + {\left(-i \, f n + 2 i \, f\right)} x - 4 i \, f x - {\left(n - 2\right)} \log\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) - {\left(n - 2\right)} \log\left(\frac{a}{d}\right) - 2 i \, e\right)}}{2 \, {\left(f n^{2} + f n\right)}}"," ",0,"1/2*((I*n + I)*e^(4*I*f*x + 4*I*e) + (I*n + 2*I)*e^(2*I*f*x + 2*I*e) + I)*(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1))^(2*n)*e^(-I*e*n + (-I*f*n + 2*I*f)*x - 4*I*f*x - (n - 2)*log(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1)) - (n - 2)*log(a/d) - 2*I*e)/(f*n^2 + f*n)","A",0
506,1,171,0,0.611375," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(3-n),x, algorithm=""fricas"")","\frac{{\left({\left(i \, n^{2} + 3 i \, n + 2 i\right)} e^{\left(6 i \, f x + 6 i \, e\right)} + {\left(i \, n^{2} + 5 i \, n + 6 i\right)} e^{\left(4 i \, f x + 4 i \, e\right)} + {\left(2 i \, n + 6 i\right)} e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i\right)} \left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right)^{2 \, n} e^{\left(-i \, e n + {\left(-i \, f n + 3 i \, f\right)} x - 6 i \, f x - {\left(n - 3\right)} \log\left(\frac{2 \, d e^{\left(i \, f x + i \, e\right)}}{e^{\left(2 i \, f x + 2 i \, e\right)} + 1}\right) - {\left(n - 3\right)} \log\left(\frac{a}{d}\right) - 3 i \, e\right)}}{2 \, {\left(f n^{3} + 3 \, f n^{2} + 2 \, f n\right)}}"," ",0,"1/2*((I*n^2 + 3*I*n + 2*I)*e^(6*I*f*x + 6*I*e) + (I*n^2 + 5*I*n + 6*I)*e^(4*I*f*x + 4*I*e) + (2*I*n + 6*I)*e^(2*I*f*x + 2*I*e) + 2*I)*(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1))^(2*n)*e^(-I*e*n + (-I*f*n + 3*I*f)*x - 6*I*f*x - (n - 3)*log(2*d*e^(I*f*x + I*e)/(e^(2*I*f*x + 2*I*e) + 1)) - (n - 3)*log(a/d) - 3*I*e)/(f*n^3 + 3*f*n^2 + 2*f*n)","A",0
507,1,57,0,1.635329," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a \cos\left(d x + c\right)^{5} + 4 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 5 \, b}{30 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/30*(2*(8*a*cos(d*x + c)^5 + 4*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c) + 5*b)/(d*cos(d*x + c)^6)","A",0
508,1,88,0,0.596045," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, a \cos\left(d x + c\right)^{5} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, a \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 10 \, {\left(3 \, a \cos\left(d x + c\right)^{3} + 2 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 16 \, b}{80 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/80*(15*a*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*a*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 10*(3*a*cos(d*x + c)^3 + 2*a*cos(d*x + c))*sin(d*x + c) + 16*b)/(d*cos(d*x + c)^5)","A",0
509,1,45,0,0.701883," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 3 \, b}{12 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/12*(4*(2*a*cos(d*x + c)^3 + a*cos(d*x + c))*sin(d*x + c) + 3*b)/(d*cos(d*x + c)^4)","A",0
510,1,74,0,0.701884," ","integrate(sec(d*x+c)^3*(a+b*tan(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) + 6 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, b}{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) + 6*a*cos(d*x + c)*sin(d*x + c) + 4*b)/(d*cos(d*x + c)^3)","A",0
511,1,30,0,0.788881," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) + b}{2 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/2*(2*a*cos(d*x + c)*sin(d*x + c) + b)/(d*cos(d*x + c)^2)","A",0
512,1,54,0,1.804363," ","integrate(sec(d*x+c)*(a+b*tan(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}{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)/(d*cos(d*x + c))","B",0
513,1,23,0,0.678202," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right) - a \sin\left(d x + c\right)}{d}"," ",0,"-(b*cos(d*x + c) - a*sin(d*x + c))/d","A",0
514,1,35,0,0.655022," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{a d x - b \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*d*x - b*cos(d*x + c)^2 + a*cos(d*x + c)*sin(d*x + c))/d","A",0
515,1,38,0,0.660073," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right)^{3} - {\left(a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(b*cos(d*x + c)^3 - (a*cos(d*x + c)^2 + 2*a)*sin(d*x + c))/d","A",0
516,1,51,0,0.639483," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b \cos\left(d x + c\right)^{4} - 3 \, a d x - {\left(2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(2*b*cos(d*x + c)^4 - 3*a*d*x - (2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
517,1,122,0,0.679941," ","integrate(sec(d*x+c)^8*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{315 \, a b \cos\left(d x + c\right) + 4 \, {\left(16 \, {\left(9 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{8} + 8 \, {\left(9 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(9 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(9 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 35 \, b^{2}\right)} \sin\left(d x + c\right)}{1260 \, d \cos\left(d x + c\right)^{9}}"," ",0,"1/1260*(315*a*b*cos(d*x + c) + 4*(16*(9*a^2 - b^2)*cos(d*x + c)^8 + 8*(9*a^2 - b^2)*cos(d*x + c)^6 + 6*(9*a^2 - b^2)*cos(d*x + c)^4 + 5*(9*a^2 - b^2)*cos(d*x + c)^2 + 35*b^2)*sin(d*x + c))/(d*cos(d*x + c)^9)","A",0
518,1,100,0,0.642991," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{35 \, a b \cos\left(d x + c\right) + {\left(8 \, {\left(7 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(7 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 15 \, b^{2}\right)} \sin\left(d x + c\right)}{105 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/105*(35*a*b*cos(d*x + c) + (8*(7*a^2 - b^2)*cos(d*x + c)^6 + 4*(7*a^2 - b^2)*cos(d*x + c)^4 + 3*(7*a^2 - b^2)*cos(d*x + c)^2 + 15*b^2)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
519,1,79,0,0.621163," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, a b \cos\left(d x + c\right) + 2 \, {\left(2 \, {\left(5 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sin\left(d x + c\right)}{30 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/30*(15*a*b*cos(d*x + c) + 2*(2*(5*a^2 - b^2)*cos(d*x + c)^4 + (5*a^2 - b^2)*cos(d*x + c)^2 + 3*b^2)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
520,1,55,0,1.319585," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a b \cos\left(d x + c\right) + {\left({\left(3 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)^{3}}"," ",0,"1/3*(3*a*b*cos(d*x + c) + ((3*a^2 - b^2)*cos(d*x + c)^2 + b^2)*sin(d*x + c))/(d*cos(d*x + c)^3)","B",0
521,1,52,0,0.569959," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a b \cos\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} d x - {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*a*b*cos(d*x + c)^2 - (a^2 + b^2)*d*x - (a^2 - b^2)*cos(d*x + c)*sin(d*x + c))/d","A",0
522,1,75,0,0.553036," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a b \cos\left(d x + c\right)^{4} - {\left(3 \, a^{2} + b^{2}\right)} d x - {\left(2 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(4*a*b*cos(d*x + c)^4 - (3*a^2 + b^2)*d*x - (2*(a^2 - b^2)*cos(d*x + c)^3 + (3*a^2 + b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
523,1,163,0,0.753263," ","integrate(sec(d*x+c)^7*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{105 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{8} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{8} \log\left(-\sin\left(d x + c\right) + 1\right) + 1536 \, a b \cos\left(d x + c\right) + 14 \, {\left(15 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} + 10 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 8 \, {\left(8 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 48 \, b^{2}\right)} \sin\left(d x + c\right)}{5376 \, d \cos\left(d x + c\right)^{8}}"," ",0,"1/5376*(105*(8*a^2 - b^2)*cos(d*x + c)^8*log(sin(d*x + c) + 1) - 105*(8*a^2 - b^2)*cos(d*x + c)^8*log(-sin(d*x + c) + 1) + 1536*a*b*cos(d*x + c) + 14*(15*(8*a^2 - b^2)*cos(d*x + c)^6 + 10*(8*a^2 - b^2)*cos(d*x + c)^4 + 8*(8*a^2 - b^2)*cos(d*x + c)^2 + 48*b^2)*sin(d*x + c))/(d*cos(d*x + c)^8)","A",0
524,1,142,0,0.843729," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 192 \, a b \cos\left(d x + c\right) + 10 \, {\left(3 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, b^{2}\right)} \sin\left(d x + c\right)}{480 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/480*(15*(6*a^2 - b^2)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 15*(6*a^2 - b^2)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 192*a*b*cos(d*x + c) + 10*(3*(6*a^2 - b^2)*cos(d*x + c)^4 + 2*(6*a^2 - b^2)*cos(d*x + c)^2 + 8*b^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
525,1,120,0,0.633389," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, {\left(4 \, a^{2} - 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} - b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 32 \, a b \cos\left(d x + c\right) + 6 \, {\left({\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, 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 - b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(4*a^2 - b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 32*a*b*cos(d*x + c) + 6*((4*a^2 - b^2)*cos(d*x + c)^2 + 2*b^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
526,1,96,0,0.699063," ","integrate(sec(d*x+c)*(a+b*tan(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) + 8 \, a b \cos\left(d x + c\right) + 2 \, b^{2} \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) + 8*a*b*cos(d*x + c) + 2*b^2*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
527,1,62,0,0.752451," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a b \cos\left(d x + c\right) - 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 \, {\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(4*a*b*cos(d*x + c) - b^2*log(sin(d*x + c) + 1) + b^2*log(-sin(d*x + c) + 1) - 2*(a^2 - b^2)*sin(d*x + c))/d","A",0
528,1,53,0,0.672018," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a b \cos\left(d x + c\right)^{3} - {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(2*a*b*cos(d*x + c)^3 - ((a^2 - b^2)*cos(d*x + c)^2 + 2*a^2 + b^2)*sin(d*x + c))/d","A",0
529,1,74,0,0.723007," ","integrate(cos(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a b \cos\left(d x + c\right)^{5} - {\left(3 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, a^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(6*a*b*cos(d*x + c)^5 - (3*(a^2 - b^2)*cos(d*x + c)^4 + (4*a^2 + b^2)*cos(d*x + c)^2 + 8*a^2 + 2*b^2)*sin(d*x + c))/d","A",0
530,1,94,0,0.619171," ","integrate(cos(d*x+c)^7*(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{30 \, a b \cos\left(d x + c\right)^{7} - {\left(15 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(6 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(6 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} + 48 \, a^{2} + 8 \, b^{2}\right)} \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(30*a*b*cos(d*x + c)^7 - (15*(a^2 - b^2)*cos(d*x + c)^6 + 3*(6*a^2 + b^2)*cos(d*x + c)^4 + 4*(6*a^2 + b^2)*cos(d*x + c)^2 + 48*a^2 + 8*b^2)*sin(d*x + c))/d","A",0
531,1,150,0,0.756229," ","integrate(sec(d*x+c)^8*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{84 \, b^{3} + 105 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(16 \, {\left(3 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{9} + 8 \, {\left(3 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{5} + 35 \, a b^{2} \cos\left(d x + c\right) + 5 \, {\left(3 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{840 \, d \cos\left(d x + c\right)^{10}}"," ",0,"1/840*(84*b^3 + 105*(3*a^2*b - b^3)*cos(d*x + c)^2 + 8*(16*(3*a^3 - a*b^2)*cos(d*x + c)^9 + 8*(3*a^3 - a*b^2)*cos(d*x + c)^7 + 6*(3*a^3 - a*b^2)*cos(d*x + c)^5 + 35*a*b^2*cos(d*x + c) + 5*(3*a^3 - a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^10)","A",0
532,1,128,0,0.776023," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{105 \, b^{3} + 140 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 8 \, {\left(8 \, {\left(7 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{7} + 4 \, {\left(7 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 45 \, a b^{2} \cos\left(d x + c\right) + 3 \, {\left(7 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{840 \, d \cos\left(d x + c\right)^{8}}"," ",0,"1/840*(105*b^3 + 140*(3*a^2*b - b^3)*cos(d*x + c)^2 + 8*(8*(7*a^3 - 3*a*b^2)*cos(d*x + c)^7 + 4*(7*a^3 - 3*a*b^2)*cos(d*x + c)^5 + 45*a*b^2*cos(d*x + c) + 3*(7*a^3 - 3*a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^8)","A",0
533,1,105,0,0.646435," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, b^{3} + 15 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(5 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 9 \, a b^{2} \cos\left(d x + c\right) + {\left(5 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{60 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/60*(10*b^3 + 15*(3*a^2*b - b^3)*cos(d*x + c)^2 + 4*(2*(5*a^3 - 3*a*b^2)*cos(d*x + c)^5 + 9*a*b^2*cos(d*x + c) + (5*a^3 - 3*a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
534,1,78,0,0.819680," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{b^{3} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/4*(b^3 + 2*(3*a^2*b - b^3)*cos(d*x + c)^2 + 4*(a*b^2*cos(d*x + c) + (a^3 - a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^4)","B",0
535,1,79,0,0.765092," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} \log\left(-\cos\left(d x + c\right)\right) - {\left(a^{3} + 3 \, a b^{2}\right)} d x + {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*b^3*log(-cos(d*x + c)) - (a^3 + 3*a*b^2)*d*x + (3*a^2*b - b^3)*cos(d*x + c)^2 - (a^3 - 3*a*b^2)*cos(d*x + c)*sin(d*x + c))/d","A",0
536,1,100,0,0.689400," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4 \, b^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(a^{3} + a b^{2}\right)} d x - {\left(2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(4*b^3*cos(d*x + c)^2 + 2*(3*a^2*b - b^3)*cos(d*x + c)^4 - 3*(a^3 + a*b^2)*d*x - (2*(a^3 - 3*a*b^2)*cos(d*x + c)^3 + 3*(a^3 + a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
537,1,170,0,0.839302," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{105 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{7} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{7} \log\left(-\sin\left(d x + c\right) + 1\right) + 160 \, b^{3} + 224 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 70 \, {\left(3 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{5} + 8 \, a b^{2} \cos\left(d x + c\right) + 2 \, {\left(2 \, a^{3} - a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{1120 \, d \cos\left(d x + c\right)^{7}}"," ",0,"1/1120*(105*(2*a^3 - a*b^2)*cos(d*x + c)^7*log(sin(d*x + c) + 1) - 105*(2*a^3 - a*b^2)*cos(d*x + c)^7*log(-sin(d*x + c) + 1) + 160*b^3 + 224*(3*a^2*b - b^3)*cos(d*x + c)^2 + 70*(3*(2*a^3 - a*b^2)*cos(d*x + c)^5 + 8*a*b^2*cos(d*x + c) + 2*(2*a^3 - a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^7)","A",0
538,1,147,0,0.702075," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, {\left(4 \, a^{3} - 3 \, 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} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} \log\left(-\sin\left(d x + c\right) + 1\right) + 48 \, b^{3} + 80 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left(6 \, a b^{2} \cos\left(d x + c\right) + {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{240 \, d \cos\left(d x + c\right)^{5}}"," ",0,"1/240*(15*(4*a^3 - 3*a*b^2)*cos(d*x + c)^5*log(sin(d*x + c) + 1) - 15*(4*a^3 - 3*a*b^2)*cos(d*x + c)^5*log(-sin(d*x + c) + 1) + 48*b^3 + 80*(3*a^2*b - b^3)*cos(d*x + c)^2 + 30*(6*a*b^2*cos(d*x + c) + (4*a^3 - 3*a*b^2)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^5)","A",0
539,1,123,0,0.712210," ","integrate(sec(d*x+c)*(a+b*tan(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) + 18 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, b^{3} + 12 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}}{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) + 18*a*b^2*cos(d*x + c)*sin(d*x + c) + 4*b^3 + 12*(3*a^2*b - b^3)*cos(d*x + c)^2)/(d*cos(d*x + c)^3)","A",0
540,1,109,0,0.767493," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{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 \, b^{3} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(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*b^3 - 2*(3*a^2*b - b^3)*cos(d*x + c)^2 + 2*(a^3 - 3*a*b^2)*cos(d*x + c)*sin(d*x + c))/(d*cos(d*x + c))","A",0
541,1,77,0,1.536943," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, b^{3} \cos\left(d x + c\right) + {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{3} + 3 \, a b^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(3*b^3*cos(d*x + c) + (3*a^2*b - b^3)*cos(d*x + c)^3 - (2*a^3 + 3*a*b^2 + (a^3 - 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
542,1,102,0,0.663687," ","integrate(cos(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{5 \, b^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{5} - {\left(3 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + 8 \, a^{3} + 6 \, a b^{2} + {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{15 \, d}"," ",0,"-1/15*(5*b^3*cos(d*x + c)^3 + 3*(3*a^2*b - b^3)*cos(d*x + c)^5 - (3*(a^3 - 3*a*b^2)*cos(d*x + c)^4 + 8*a^3 + 6*a*b^2 + (4*a^3 + 3*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
543,1,123,0,0.959332," ","integrate(cos(d*x+c)^7*(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{7 \, b^{3} \cos\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{7} - {\left(5 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{4} + 16 \, a^{3} + 8 \, a b^{2} + 4 \, {\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{35 \, d}"," ",0,"-1/35*(7*b^3*cos(d*x + c)^5 + 5*(3*a^2*b - b^3)*cos(d*x + c)^7 - (5*(a^3 - 3*a*b^2)*cos(d*x + c)^6 + 3*(2*a^3 + a*b^2)*cos(d*x + c)^4 + 16*a^3 + 8*a*b^2 + 4*(2*a^3 + a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
544,1,183,0,0.597086," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\cos\left(d x + c\right)^{2}\right) + 3 \, b^{4} + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(a b^{3} \cos\left(d x + c\right) + {\left(3 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{12 \, b^{5} d \cos\left(d x + c\right)^{4}}"," ",0,"1/12*(6*(a^4 + 2*a^2*b^2 + b^4)*cos(d*x + c)^4*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*(a^4 + 2*a^2*b^2 + b^4)*cos(d*x + c)^4*log(cos(d*x + c)^2) + 3*b^4 + 6*(a^2*b^2 + b^4)*cos(d*x + c)^2 - 4*(a*b^3*cos(d*x + c) + (3*a^3*b + 5*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(b^5*d*cos(d*x + c)^4)","A",0
545,1,117,0,0.830323," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\cos\left(d x + c\right)^{2}\right) - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + b^{2}}{2 \, b^{3} d \cos\left(d x + c\right)^{2}}"," ",0,"1/2*((a^2 + b^2)*cos(d*x + c)^2*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^2 + b^2)*cos(d*x + c)^2*log(cos(d*x + c)^2) - 2*a*b*cos(d*x + c)*sin(d*x + c) + b^2)/(b^3*d*cos(d*x + c)^2)","B",0
546,1,59,0,0.535716," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - \log\left(\cos\left(d x + c\right)^{2}\right)}{2 \, b d}"," ",0,"1/2*(log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - log(cos(d*x + c)^2))/(b*d)","B",0
547,1,119,0,0.462913," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{b^{3} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) + {\left(a^{3} + 3 \, a b^{2}\right)} d x + {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"1/2*(b^3*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + (a^3 + 3*a*b^2)*d*x + (a^2*b + b^3)*cos(d*x + c)^2 + (a^3 + a*b^2)*cos(d*x + c)*sin(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d)","A",0
548,1,208,0,0.999778," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, b^{5} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} d x + 4 \, {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 7 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}"," ",0,"1/8*(4*b^5*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^4 + (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*d*x + 4*(a^2*b^3 + b^5)*cos(d*x + c)^2 + (2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^3 + (3*a^5 + 10*a^3*b^2 + 7*a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)","A",0
549,1,259,0,1.886687," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(a^{2} + b^{2}\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\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) + 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) - 6 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, b^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}}{12 \, b^{4} d \cos\left(d x + c\right)^{3}}"," ",0,"1/12*(6*(a^2 + b^2)^(3/2)*cos(d*x + c)^3*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 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) - 6*a*b^2*cos(d*x + c)*sin(d*x + c) + 4*b^3 + 12*(a^2*b + b^3)*cos(d*x + c)^2)/(b^4*d*cos(d*x + c)^3)","A",0
550,1,191,0,0.775754," ","integrate(sec(d*x+c)^3/(a+b*tan(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) - \sqrt{a^{2} + b^{2}} \cos\left(d x + c\right) \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 2 \, b}{2 \, b^{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) - sqrt(a^2 + b^2)*cos(d*x + c)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 2*b)/(b^2*d*cos(d*x + c))","B",0
551,1,131,0,0.616554," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{2 \, \sqrt{a^{2} + b^{2}} d}"," ",0,"1/2*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2))/(sqrt(a^2 + b^2)*d)","B",0
552,1,187,0,0.705358," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} b^{2} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"1/2*(sqrt(a^2 + b^2)*b^2*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(a^2*b + b^3)*cos(d*x + c) + 2*(a^3 + a*b^2)*sin(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d)","B",0
553,1,262,0,0.775576," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a^{2} + b^{2}} b^{4} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + 2 \, {\left(2 \, a^{5} + 7 \, a^{3} b^{2} + 5 \, a b^{4} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d}"," ",0,"1/6*(3*sqrt(a^2 + b^2)*b^4*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^3 + 6*(a^2*b^3 + b^5)*cos(d*x + c) + 2*(2*a^5 + 7*a^3*b^2 + 5*a*b^4 + (a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d)","A",0
554,1,386,0,0.857490," ","integrate(sec(d*x+c)^8/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(15 \, a^{4} b^{2} + 25 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 2 \, b^{6} - 2 \, {\left(15 \, a^{4} b^{2} + 25 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 30 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{6} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{5} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 30 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{6} + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{5} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right) + {\left(3 \, a b^{5} \cos\left(d x + c\right) - 4 \, {\left(15 \, a^{5} b + 25 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{10 \, {\left(a b^{7} d \cos\left(d x + c\right)^{6} + b^{8} d \cos\left(d x + c\right)^{5} \sin\left(d x + c\right)\right)}}"," ",0,"-1/10*(4*(15*a^4*b^2 + 25*a^2*b^4 + 8*b^6)*cos(d*x + c)^6 - 2*b^6 - 2*(15*a^4*b^2 + 25*a^2*b^4 + 8*b^6)*cos(d*x + c)^4 - (5*a^2*b^4 + 4*b^6)*cos(d*x + c)^2 + 30*((a^6 + 2*a^4*b^2 + a^2*b^4)*cos(d*x + c)^6 + (a^5*b + 2*a^3*b^3 + a*b^5)*cos(d*x + c)^5*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 30*((a^6 + 2*a^4*b^2 + a^2*b^4)*cos(d*x + c)^6 + (a^5*b + 2*a^3*b^3 + a*b^5)*cos(d*x + c)^5*sin(d*x + c))*log(cos(d*x + c)^2) + (3*a*b^5*cos(d*x + c) - 4*(15*a^5*b + 25*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^5 + 2*(5*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^3)*sin(d*x + c))/(a*b^7*d*cos(d*x + c)^6 + b^8*d*cos(d*x + c)^5*sin(d*x + c))","B",0
555,1,281,0,0.714682," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{4} - b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right) + 2 \, {\left(a b^{3} \cos\left(d x + c\right) - 2 \, {\left(3 \, a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{3 \, {\left(a b^{5} d \cos\left(d x + c\right)^{4} + b^{6} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(4*(3*a^2*b^2 + 2*b^4)*cos(d*x + c)^4 - b^4 - 2*(3*a^2*b^2 + 2*b^4)*cos(d*x + c)^2 + 6*((a^4 + a^2*b^2)*cos(d*x + c)^4 + (a^3*b + a*b^3)*cos(d*x + c)^3*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*((a^4 + a^2*b^2)*cos(d*x + c)^4 + (a^3*b + a*b^3)*cos(d*x + c)^3*sin(d*x + c))*log(cos(d*x + c)^2) + 2*(a*b^3*cos(d*x + c) - 2*(3*a^3*b + 2*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(a*b^5*d*cos(d*x + c)^4 + b^6*d*cos(d*x + c)^3*sin(d*x + c))","B",0
556,1,178,0,0.594723," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - b^{2} + {\left(a^{2} \cos\left(d x + c\right)^{2} + a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} + a b \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right)}{a b^{3} d \cos\left(d x + c\right)^{2} + b^{4} d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"-(2*b^2*cos(d*x + c)^2 - 2*a*b*cos(d*x + c)*sin(d*x + c) - b^2 + (a^2*cos(d*x + c)^2 + a*b*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^2*cos(d*x + c)^2 + a*b*cos(d*x + c)*sin(d*x + c))*log(cos(d*x + c)^2))/(a*b^3*d*cos(d*x + c)^2 + b^4*d*cos(d*x + c)*sin(d*x + c))","B",0
557,1,57,0,0.718930," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right) - a \sin\left(d x + c\right)}{{\left(a^{3} + a b^{2}\right)} d \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} d \sin\left(d x + c\right)}"," ",0,"-(b*cos(d*x + c) - a*sin(d*x + c))/((a^3 + a*b^2)*d*cos(d*x + c) + (a^2*b + b^3)*d*sin(d*x + c))","B",0
558,1,279,0,0.574550," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{2} b^{3} + 3 \, b^{5} - {\left(a^{5} + 6 \, a^{3} b^{2} - 3 \, a b^{4}\right)} d x\right)} \cos\left(d x + c\right) + 4 \, {\left(a^{2} b^{3} \cos\left(d x + c\right) + a b^{4} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a^{3} b^{2} - a b^{4} - {\left(a^{4} b + 6 \, a^{2} b^{3} - 3 \, b^{5}\right)} d x - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"1/2*((a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^3 - (a^2*b^3 + 3*b^5 - (a^5 + 6*a^3*b^2 - 3*a*b^4)*d*x)*cos(d*x + c) + 4*(a^2*b^3*cos(d*x + c) + a*b^4*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^3*b^2 - a*b^4 - (a^4*b + 6*a^2*b^3 - 3*b^5)*d*x - (a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d*sin(d*x + c))","A",0
559,1,424,0,0.684205," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{5} - 2 \, {\left(a^{6} b - 3 \, a^{4} b^{3} - 9 \, a^{2} b^{5} - 5 \, b^{7}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{6} b + 8 \, a^{4} b^{3} - 9 \, a^{2} b^{5} - 30 \, b^{7} + 6 \, {\left(a^{7} + 5 \, a^{5} b^{2} + 15 \, a^{3} b^{4} - 5 \, a b^{6}\right)} d x\right)} \cos\left(d x + c\right) + 48 \, {\left(a^{2} b^{5} \cos\left(d x + c\right) + a b^{6} \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(3 \, a^{5} b^{2} + 22 \, a^{3} b^{4} + 3 \, a b^{6} - 4 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{4} - 6 \, {\left(a^{6} b + 5 \, a^{4} b^{3} + 15 \, a^{2} b^{5} - 5 \, b^{7}\right)} d x - 6 \, {\left(a^{7} + 5 \, a^{5} b^{2} + 7 \, a^{3} b^{4} + 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"1/16*(4*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^5 - 2*(a^6*b - 3*a^4*b^3 - 9*a^2*b^5 - 5*b^7)*cos(d*x + c)^3 + (3*a^6*b + 8*a^4*b^3 - 9*a^2*b^5 - 30*b^7 + 6*(a^7 + 5*a^5*b^2 + 15*a^3*b^4 - 5*a*b^6)*d*x)*cos(d*x + c) + 48*(a^2*b^5*cos(d*x + c) + a*b^6*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (3*a^5*b^2 + 22*a^3*b^4 + 3*a*b^6 - 4*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c)^4 - 6*(a^6*b + 5*a^4*b^3 + 15*a^2*b^5 - 5*b^7)*d*x - 6*(a^7 + 5*a^5*b^2 + 7*a^3*b^4 + 3*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d*cos(d*x + c) + (a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d*sin(d*x + c))","A",0
560,1,472,0,1.063429," ","integrate(sec(d*x+c)^7/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{12 \, b^{5} - 30 \, {\left(8 \, a^{4} b + 12 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + 120 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} \cos\left(d x + c\right)^{5} + {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 15 \, {\left({\left(8 \, a^{5} + 12 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + {\left(8 \, a^{4} b + 12 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(8 \, a^{5} + 12 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + {\left(8 \, a^{4} b + 12 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 10 \, {\left(2 \, a b^{4} \cos\left(d x + c\right) + 3 \, {\left(4 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{48 \, {\left(a b^{6} d \cos\left(d x + c\right)^{5} + b^{7} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\right)}}"," ",0,"1/48*(12*b^5 - 30*(8*a^4*b + 12*a^2*b^3 + 3*b^5)*cos(d*x + c)^4 + 10*(4*a^2*b^3 + 3*b^5)*cos(d*x + c)^2 + 120*((a^4 + a^2*b^2)*cos(d*x + c)^5 + (a^3*b + a*b^3)*cos(d*x + c)^4*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 15*((8*a^5 + 12*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^5 + (8*a^4*b + 12*a^2*b^3 + 3*b^5)*cos(d*x + c)^4*sin(d*x + c))*log(sin(d*x + c) + 1) - 15*((8*a^5 + 12*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^5 + (8*a^4*b + 12*a^2*b^3 + 3*b^5)*cos(d*x + c)^4*sin(d*x + c))*log(-sin(d*x + c) + 1) - 10*(2*a*b^4*cos(d*x + c) + 3*(4*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(a*b^6*d*cos(d*x + c)^5 + b^7*d*cos(d*x + c)^4*sin(d*x + c))","B",0
561,1,355,0,1.038335," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, b^{3} + 6 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 3 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{4 \, {\left(a b^{4} d \cos\left(d x + c\right)^{3} + b^{5} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\right)}}"," ",0,"-1/4*(6*a*b^2*cos(d*x + c)*sin(d*x + c) - 2*b^3 + 6*(2*a^2*b + b^3)*cos(d*x + c)^2 - 6*(a^2*cos(d*x + c)^3 + a*b*cos(d*x + c)^2*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 3*((2*a^3 + a*b^2)*cos(d*x + c)^3 + (2*a^2*b + b^3)*cos(d*x + c)^2*sin(d*x + c))*log(sin(d*x + c) + 1) + 3*((2*a^3 + a*b^2)*cos(d*x + c)^3 + (2*a^2*b + b^3)*cos(d*x + c)^2*sin(d*x + c))*log(-sin(d*x + c) + 1))/(a*b^4*d*cos(d*x + c)^3 + b^5*d*cos(d*x + c)^2*sin(d*x + c))","B",0
562,1,293,0,0.575703," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} b + 2 \, b^{3} - {\left(a^{2} \cos\left(d x + c\right) + a b \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - {\left({\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a^2*b + 2*b^3 - (a^2*cos(d*x + c) + a*b*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - ((a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))*log(sin(d*x + c) + 1) + ((a^3 + a*b^2)*cos(d*x + c) + (a^2*b + b^3)*sin(d*x + c))*log(-sin(d*x + c) + 1))/((a^3*b^2 + a*b^4)*d*cos(d*x + c) + (a^2*b^3 + b^5)*d*sin(d*x + c))","B",0
563,1,215,0,0.668759," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} b + 2 \, b^{3} - {\left(a^{2} \cos\left(d x + c\right) + a b \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\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 \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a^2*b + 2*b^3 - (a^2*cos(d*x + c) + a*b*sin(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((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*sin(d*x + c))","B",0
564,1,302,0,0.674483," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{4} b - 2 \, a^{2} b^{3} - 4 \, b^{5} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left(a^{2} b^{2} \cos\left(d x + c\right) + a b^{3} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right)}{2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) + {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"1/2*(2*a^4*b - 2*a^2*b^3 - 4*b^5 + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(d*x + c)*sin(d*x + c) + 3*(a^2*b^2*cos(d*x + c) + a*b^3*sin(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*d*cos(d*x + c) + (a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*d*sin(d*x + c))","A",0
565,1,418,0,0.623434," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{6} b + 22 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - 16 \, b^{7} + 2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left(a^{2} b^{4} \cos\left(d x + c\right) + a b^{5} \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{7} + 11 \, a^{5} b^{2} + 16 \, a^{3} b^{4} + 7 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right) + {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} d \sin\left(d x + c\right)\right)}}"," ",0,"1/6*(4*a^6*b + 22*a^4*b^3 + 2*a^2*b^5 - 16*b^7 + 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^4 - 2*(a^6*b - 2*a^4*b^3 - 7*a^2*b^5 - 4*b^7)*cos(d*x + c)^2 + 15*(a^2*b^4*cos(d*x + c) + a*b^5*sin(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c)^3 + (2*a^7 + 11*a^5*b^2 + 16*a^3*b^4 + 7*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*d*cos(d*x + c) + (a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*d*sin(d*x + c))","A",0
566,1,476,0,2.185016," ","integrate(sec(d*x+c)^8/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, {\left(15 \, a^{4} b^{2} + 13 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{6} + b^{6} - 2 \, {\left(45 \, a^{4} b^{2} + 44 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left({\left(5 \, a^{6} + a^{4} b^{2} - 5 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{5} b + 6 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 6 \, {\left({\left(5 \, a^{6} + a^{4} b^{2} - 5 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{5} b + 6 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + {\left(5 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\cos\left(d x + c\right)^{2}\right) - 2 \, {\left(a b^{5} \cos\left(d x + c\right) + 2 \, {\left(15 \, a^{5} b - 2 \, a^{3} b^{3} - 13 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(2 \, a b^{8} d \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + b^{9} d \cos\left(d x + c\right)^{4} + {\left(a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/4*(8*(15*a^4*b^2 + 13*a^2*b^4)*cos(d*x + c)^6 + b^6 - 2*(45*a^4*b^2 + 44*a^2*b^4 + 3*b^6)*cos(d*x + c)^4 + (5*a^2*b^4 + 3*b^6)*cos(d*x + c)^2 + 6*((5*a^6 + a^4*b^2 - 5*a^2*b^4 - b^6)*cos(d*x + c)^6 + 2*(5*a^5*b + 6*a^3*b^3 + a*b^5)*cos(d*x + c)^5*sin(d*x + c) + (5*a^4*b^2 + 6*a^2*b^4 + b^6)*cos(d*x + c)^4)*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 6*((5*a^6 + a^4*b^2 - 5*a^2*b^4 - b^6)*cos(d*x + c)^6 + 2*(5*a^5*b + 6*a^3*b^3 + a*b^5)*cos(d*x + c)^5*sin(d*x + c) + (5*a^4*b^2 + 6*a^2*b^4 + b^6)*cos(d*x + c)^4)*log(cos(d*x + c)^2) - 2*(a*b^5*cos(d*x + c) + 2*(15*a^5*b - 2*a^3*b^3 - 13*a*b^5)*cos(d*x + c)^5 + 10*(a^3*b^3 + a*b^5)*cos(d*x + c)^3)*sin(d*x + c))/(2*a*b^8*d*cos(d*x + c)^5*sin(d*x + c) + b^9*d*cos(d*x + c)^4 + (a^2*b^7 - b^9)*d*cos(d*x + c)^6)","B",0
567,1,354,0,0.805559," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{24 \, a^{2} b^{2} \cos\left(d x + c\right)^{4} + b^{4} - 2 \, {\left(9 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 2 \, {\left({\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right)^{2}\right) - 4 \, {\left(a b^{3} \cos\left(d x + c\right) + 3 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(2 \, a b^{6} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + b^{7} d \cos\left(d x + c\right)^{2} + {\left(a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/2*(24*a^2*b^2*cos(d*x + c)^4 + b^4 - 2*(9*a^2*b^2 + b^4)*cos(d*x + c)^2 + 2*((3*a^4 - 2*a^2*b^2 - b^4)*cos(d*x + c)^4 + 2*(3*a^3*b + a*b^3)*cos(d*x + c)^3*sin(d*x + c) + (3*a^2*b^2 + b^4)*cos(d*x + c)^2)*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 2*((3*a^4 - 2*a^2*b^2 - b^4)*cos(d*x + c)^4 + 2*(3*a^3*b + a*b^3)*cos(d*x + c)^3*sin(d*x + c) + (3*a^2*b^2 + b^4)*cos(d*x + c)^2)*log(cos(d*x + c)^2) - 4*(a*b^3*cos(d*x + c) + 3*(a^3*b - a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(2*a*b^6*d*cos(d*x + c)^3*sin(d*x + c) + b^7*d*cos(d*x + c)^2 + (a^2*b^5 - b^7)*d*cos(d*x + c)^4)","B",0
568,1,284,0,1.079305," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b^{2} - b^{4} - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4} + {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - {\left(a^{2} b^{2} + b^{4} + {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2}\right)}{2 \, {\left({\left(a^{4} b^{3} - b^{7}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{4} + a b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} b^{5} + b^{7}\right)} d\right)}}"," ",0,"1/2*(4*a^2*b^2*cos(d*x + c)^2 - 3*a^2*b^2 - b^4 - 2*(a^3*b - a*b^3)*cos(d*x + c)*sin(d*x + c) + (a^2*b^2 + b^4 + (a^4 - b^4)*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - (a^2*b^2 + b^4 + (a^4 - b^4)*cos(d*x + c)^2 + 2*(a^3*b + a*b^3)*cos(d*x + c)*sin(d*x + c))*log(cos(d*x + c)^2))/((a^4*b^3 - b^7)*d*cos(d*x + c)^2 + 2*(a^3*b^4 + a*b^6)*d*cos(d*x + c)*sin(d*x + c) + (a^2*b^5 + b^7)*d)","B",0
569,1,142,0,0.679941," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4 \, a^{2} b \cos\left(d x + c\right)^{2} - a^{2} b + b^{3} - 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}"," ",0,"-1/2*(4*a^2*b*cos(d*x + c)^2 - a^2*b + b^3 - 2*(a^3 - a*b^2)*cos(d*x + c)*sin(d*x + c))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d)","B",0
570,1,503,0,1.122565," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, a^{4} b^{3} - 16 \, a^{2} b^{5} + b^{7} - 2 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b^{2} + 10 \, a^{3} b^{4} - 15 \, a b^{6}\right)} d x - {\left(a^{6} b - a^{4} b^{3} - 45 \, a^{2} b^{5} - 3 \, b^{7} + 2 \, {\left(a^{7} + 9 \, a^{5} b^{2} - 25 \, a^{3} b^{4} + 15 \, a b^{6}\right)} d x\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left(5 \, a^{2} b^{5} - b^{7} + {\left(5 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 2 \, {\left({\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b^{2} - 3 \, a^{3} b^{4} + 6 \, a b^{6} - {\left(a^{6} b + 10 \, a^{4} b^{3} - 15 \, a^{2} b^{5}\right)} d x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} d\right)}}"," ",0,"-1/4*(3*a^4*b^3 - 16*a^2*b^5 + b^7 - 2*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^4 - 2*(a^5*b^2 + 10*a^3*b^4 - 15*a*b^6)*d*x - (a^6*b - a^4*b^3 - 45*a^2*b^5 - 3*b^7 + 2*(a^7 + 9*a^5*b^2 - 25*a^3*b^4 + 15*a*b^6)*d*x)*cos(d*x + c)^2 - 4*(5*a^2*b^5 - b^7 + (5*a^4*b^3 - 6*a^2*b^5 + b^7)*cos(d*x + c)^2 + 2*(5*a^3*b^4 - a*b^6)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 2*((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c)^3 - 2*(a^5*b^2 - 3*a^3*b^4 + 6*a*b^6 - (a^6*b + 10*a^4*b^3 - 15*a^2*b^5)*d*x)*cos(d*x + c))*sin(d*x + c))/((a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d*cos(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*d)","B",0
571,1,671,0,0.875901," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{9 \, a^{6} b^{3} + 95 \, a^{4} b^{5} - 141 \, a^{2} b^{7} - 3 \, b^{9} - 8 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{6} + 8 \, {\left(a^{8} b - 6 \, a^{4} b^{5} - 8 \, a^{2} b^{7} - 3 \, b^{9}\right)} \cos\left(d x + c\right)^{4} - 12 \, {\left(a^{7} b^{2} + 7 \, a^{5} b^{4} + 35 \, a^{3} b^{6} - 35 \, a b^{8}\right)} d x - {\left(15 \, a^{8} b + 82 \, a^{6} b^{3} + 68 \, a^{4} b^{5} - 498 \, a^{2} b^{7} - 51 \, b^{9} + 12 \, {\left(a^{9} + 6 \, a^{7} b^{2} + 28 \, a^{5} b^{4} - 70 \, a^{3} b^{6} + 35 \, a b^{8}\right)} d x\right)} \cos\left(d x + c\right)^{2} - 48 \, {\left(7 \, a^{2} b^{7} - b^{9} + {\left(7 \, a^{4} b^{5} - 8 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(7 \, a^{3} b^{6} - a b^{8}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \log\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right) - 2 \, {\left(4 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{9} + 20 \, a^{7} b^{2} + 42 \, a^{5} b^{4} + 36 \, a^{3} b^{6} + 11 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{7} b^{2} + 53 \, a^{5} b^{4} - 15 \, a^{3} b^{6} + 159 \, a b^{8} - 12 \, {\left(a^{8} b + 7 \, a^{6} b^{3} + 35 \, a^{4} b^{5} - 35 \, a^{2} b^{7}\right)} d x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{32 \, {\left({\left(a^{12} + 4 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 5 \, a^{4} b^{8} - 4 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} d\right)}}"," ",0,"-1/32*(9*a^6*b^3 + 95*a^4*b^5 - 141*a^2*b^7 - 3*b^9 - 8*(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*cos(d*x + c)^6 + 8*(a^8*b - 6*a^4*b^5 - 8*a^2*b^7 - 3*b^9)*cos(d*x + c)^4 - 12*(a^7*b^2 + 7*a^5*b^4 + 35*a^3*b^6 - 35*a*b^8)*d*x - (15*a^8*b + 82*a^6*b^3 + 68*a^4*b^5 - 498*a^2*b^7 - 51*b^9 + 12*(a^9 + 6*a^7*b^2 + 28*a^5*b^4 - 70*a^3*b^6 + 35*a*b^8)*d*x)*cos(d*x + c)^2 - 48*(7*a^2*b^7 - b^9 + (7*a^4*b^5 - 8*a^2*b^7 + b^9)*cos(d*x + c)^2 + 2*(7*a^3*b^6 - a*b^8)*cos(d*x + c)*sin(d*x + c))*log(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2) - 2*(4*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*cos(d*x + c)^5 + 2*(3*a^9 + 20*a^7*b^2 + 42*a^5*b^4 + 36*a^3*b^6 + 11*a*b^8)*cos(d*x + c)^3 - (3*a^7*b^2 + 53*a^5*b^4 - 15*a^3*b^6 + 159*a*b^8 - 12*(a^8*b + 7*a^6*b^3 + 35*a^4*b^5 - 35*a^2*b^7)*d*x)*cos(d*x + c))*sin(d*x + c))/((a^12 + 4*a^10*b^2 + 5*a^8*b^4 - 5*a^4*b^8 - 4*a^2*b^10 - b^12)*d*cos(d*x + c)^2 + 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*d*cos(d*x + c)*sin(d*x + c) + (a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*d)","B",0
572,1,564,0,0.854681," ","integrate(sec(d*x+c)^7/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, b^{5} + 30 \, {\left(4 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{4} + 20 \, {\left(2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(4 \, a^{4} - 3 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(4 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 15 \, {\left({\left(4 \, a^{5} - a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{4} b + 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left({\left(4 \, a^{5} - a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{4} b + 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 10 \, {\left(a b^{4} \cos\left(d x + c\right) - 6 \, {\left(3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(2 \, a b^{7} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + b^{8} d \cos\left(d x + c\right)^{3} + {\left(a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"1/12*(4*b^5 + 30*(4*a^4*b + a^2*b^3 - b^5)*cos(d*x + c)^4 + 20*(2*a^2*b^3 + b^5)*cos(d*x + c)^2 + 15*((4*a^4 - 3*a^2*b^2 - b^4)*cos(d*x + c)^5 + 2*(4*a^3*b + a*b^3)*cos(d*x + c)^4*sin(d*x + c) + (4*a^2*b^2 + b^4)*cos(d*x + c)^3)*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 15*((4*a^5 - a^3*b^2 - 3*a*b^4)*cos(d*x + c)^5 + 2*(4*a^4*b + 3*a^2*b^3)*cos(d*x + c)^4*sin(d*x + c) + (4*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^3)*log(sin(d*x + c) + 1) + 15*((4*a^5 - a^3*b^2 - 3*a*b^4)*cos(d*x + c)^5 + 2*(4*a^4*b + 3*a^2*b^3)*cos(d*x + c)^4*sin(d*x + c) + (4*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^3)*log(-sin(d*x + c) + 1) - 10*(a*b^4*cos(d*x + c) - 6*(3*a^3*b^2 + 2*a*b^4)*cos(d*x + c)^3)*sin(d*x + c))/(2*a*b^7*d*cos(d*x + c)^4*sin(d*x + c) + b^8*d*cos(d*x + c)^3 + (a^2*b^6 - b^8)*d*cos(d*x + c)^5)","B",0
573,1,513,0,0.714252," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} b^{3} + 4 \, b^{5} + 6 \, {\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + 18 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left({\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 6 \, {\left({\left(a^{5} - a b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(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) + 6 \, {\left({\left(a^{5} - a b^{4}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(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)}{4 \, {\left({\left(a^{4} b^{4} - b^{8}\right)} d \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(4*a^2*b^3 + 4*b^5 + 6*(2*a^4*b + a^2*b^3 - b^5)*cos(d*x + c)^2 + 18*(a^3*b^2 + a*b^4)*cos(d*x + c)*sin(d*x + c) + 3*((2*a^4 - a^2*b^2 - b^4)*cos(d*x + c)^3 + 2*(2*a^3*b + a*b^3)*cos(d*x + c)^2*sin(d*x + c) + (2*a^2*b^2 + b^4)*cos(d*x + c))*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 6*((a^5 - a*b^4)*cos(d*x + c)^3 + 2*(a^4*b + a^2*b^3)*cos(d*x + c)^2*sin(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c))*log(sin(d*x + c) + 1) + 6*((a^5 - a*b^4)*cos(d*x + c)^3 + 2*(a^4*b + a^2*b^3)*cos(d*x + c)^2*sin(d*x + c) + (a^3*b^2 + a*b^4)*cos(d*x + c))*log(-sin(d*x + c) + 1))/((a^4*b^4 - b^8)*d*cos(d*x + c)^3 + 2*(a^3*b^5 + a*b^7)*d*cos(d*x + c)^2*sin(d*x + c) + (a^2*b^6 + b^8)*d*cos(d*x + c))","B",0
574,1,294,0,0.501560," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} d\right)}}"," ",0,"1/4*((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)*sqrt(a^2 + b^2)*log(-(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 + 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) - 2*(a^2*b + b^3)*cos(d*x + c) + 2*(a^3 + a*b^2)*sin(d*x + c))/((a^6 + a^4*b^2 - a^2*b^4 - b^6)*d*cos(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*d*cos(d*x + c)*sin(d*x + c) + (a^4*b^2 + 2*a^2*b^4 + b^6)*d)","B",0
575,1,352,0,0.832962," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} b^{2} - b^{4} + {\left(2 \, a^{4} - 3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(4 \, a^{4} b + 5 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} + 2 \, a^{6} b^{2} - 2 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d \cos\left(d x + c\right) \sin\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)}}"," ",0,"-1/4*((2*a^2*b^2 - b^4 + (2*a^4 - 3*a^2*b^2 + b^4)*cos(d*x + c)^2 + 2*(2*a^3*b - a*b^3)*cos(d*x + c)*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(4*a^4*b + 5*a^2*b^3 + b^5)*cos(d*x + c) + 6*(a^3*b^2 + a*b^4)*sin(d*x + c))/((a^8 + 2*a^6*b^2 - 2*a^2*b^6 - b^8)*d*cos(d*x + c)^2 + 2*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d)","B",0
576,1,480,0,0.793363," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} b^{4} - b^{6} + {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(4 \, a^{6} b - 10 \, a^{4} b^{3} - 17 \, a^{2} b^{5} - 3 \, b^{7}\right)} \cos\left(d x + c\right) + 2 \, {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} - 13 \, a b^{6} + 2 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{10} + 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} - 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b + 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} + 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} d\right)}}"," ",0,"1/4*(4*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)^3 - 3*(4*a^2*b^4 - b^6 + (4*a^4*b^2 - 5*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(4*a^3*b^3 - a*b^5)*cos(d*x + c)*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(4*a^6*b - 10*a^4*b^3 - 17*a^2*b^5 - 3*b^7)*cos(d*x + c) + 2*(2*a^5*b^2 - 11*a^3*b^4 - 13*a*b^6 + 2*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^10 + 3*a^8*b^2 + 2*a^6*b^4 - 2*a^4*b^6 - 3*a^2*b^8 - b^10)*d*cos(d*x + c)^2 + 2*(a^9*b + 4*a^7*b^3 + 6*a^5*b^5 + 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) + (a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*d)","B",0
577,1,619,0,0.843836," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \cos\left(d x + c\right)^{5} - 4 \, {\left(2 \, a^{8} b + a^{6} b^{3} - 9 \, a^{4} b^{5} - 13 \, a^{2} b^{7} - 5 \, b^{9}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(6 \, a^{2} b^{6} - b^{8} + {\left(6 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cos\left(d x + c\right) - a \sin\left(d x + c\right)\right)}}{2 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + b^{2}}\right) + 2 \, {\left(8 \, a^{8} b + 64 \, a^{6} b^{3} - 16 \, a^{4} b^{5} - 87 \, a^{2} b^{7} - 15 \, b^{9}\right)} \cos\left(d x + c\right) + 2 \, {\left(4 \, a^{7} b^{2} + 32 \, a^{5} b^{4} - 53 \, a^{3} b^{6} - 81 \, a b^{8} + 2 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{9} + 15 \, a^{7} b^{2} + 33 \, a^{5} b^{4} + 29 \, a^{3} b^{6} + 9 \, a b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{12} + 4 \, a^{10} b^{2} + 5 \, a^{8} b^{4} - 5 \, a^{4} b^{8} - 4 \, a^{2} b^{10} - b^{12}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{11} b + 5 \, a^{9} b^{3} + 10 \, a^{7} b^{5} + 10 \, a^{5} b^{7} + 5 \, a^{3} b^{9} + a b^{11}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{10} b^{2} + 5 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 10 \, a^{4} b^{8} + 5 \, a^{2} b^{10} + b^{12}\right)} d\right)}}"," ",0,"1/12*(4*(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*cos(d*x + c)^5 - 4*(2*a^8*b + a^6*b^3 - 9*a^4*b^5 - 13*a^2*b^7 - 5*b^9)*cos(d*x + c)^3 - 15*(6*a^2*b^6 - b^8 + (6*a^4*b^4 - 7*a^2*b^6 + b^8)*cos(d*x + c)^2 + 2*(6*a^3*b^5 - a*b^7)*cos(d*x + c)*sin(d*x + c))*sqrt(a^2 + b^2)*log((2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 - b^2 - 2*sqrt(a^2 + b^2)*(b*cos(d*x + c) - a*sin(d*x + c)))/(2*a*b*cos(d*x + c)*sin(d*x + c) + (a^2 - b^2)*cos(d*x + c)^2 + b^2)) + 2*(8*a^8*b + 64*a^6*b^3 - 16*a^4*b^5 - 87*a^2*b^7 - 15*b^9)*cos(d*x + c) + 2*(4*a^7*b^2 + 32*a^5*b^4 - 53*a^3*b^6 - 81*a*b^8 + 2*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8)*cos(d*x + c)^4 + 2*(2*a^9 + 15*a^7*b^2 + 33*a^5*b^4 + 29*a^3*b^6 + 9*a*b^8)*cos(d*x + c)^2)*sin(d*x + c))/((a^12 + 4*a^10*b^2 + 5*a^8*b^4 - 5*a^4*b^8 - 4*a^2*b^10 - b^12)*d*cos(d*x + c)^2 + 2*(a^11*b + 5*a^9*b^3 + 10*a^7*b^5 + 10*a^5*b^7 + 5*a^3*b^9 + a*b^11)*d*cos(d*x + c)*sin(d*x + c) + (a^10*b^2 + 5*a^8*b^4 + 10*a^6*b^6 + 10*a^4*b^8 + 5*a^2*b^10 + b^12)*d)","B",0
578,0,0,0,0.691711," ","integrate((d*sec(f*x+e))^(7/2)*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b d^{3} \sec\left(f x + e\right)^{3} \tan\left(f x + e\right) + a d^{3} \sec\left(f x + e\right)^{3}\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b*d^3*sec(f*x + e)^3*tan(f*x + e) + a*d^3*sec(f*x + e)^3)*sqrt(d*sec(f*x + e)), x)","F",0
579,0,0,0,0.725067," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right) + a d^{2} \sec\left(f x + e\right)^{2}\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b*d^2*sec(f*x + e)^2*tan(f*x + e) + a*d^2*sec(f*x + e)^2)*sqrt(d*sec(f*x + e)), x)","F",0
580,0,0,0,0.648073," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b d \sec\left(f x + e\right) \tan\left(f x + e\right) + a d \sec\left(f x + e\right)\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b*d*sec(f*x + e)*tan(f*x + e) + a*d*sec(f*x + e))*sqrt(d*sec(f*x + e)), x)","F",0
581,0,0,0,0.614191," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a), x)","F",0
582,0,0,0,1.435869," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)/(d*sec(f*x + e)), x)","F",0
583,0,0,0,0.567929," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}}{d^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)/(d^2*sec(f*x + e)^2), x)","F",0
584,0,0,0,0.977787," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}}{d^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)/(d^3*sec(f*x + e)^3), x)","F",0
585,0,0,0,2.469532," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}}{d^{4} \sec\left(f x + e\right)^{4}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)/(d^4*sec(f*x + e)^4), x)","F",0
586,0,0,0,1.049304," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right)^{2} + 2 \, a b d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right) + a^{2} d^{2} \sec\left(f x + e\right)^{2}\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^2*d^2*sec(f*x + e)^2*tan(f*x + e)^2 + 2*a*b*d^2*sec(f*x + e)^2*tan(f*x + e) + a^2*d^2*sec(f*x + e)^2)*sqrt(d*sec(f*x + e)), x)","F",0
587,0,0,0,0.597825," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d \sec\left(f x + e\right) \tan\left(f x + e\right)^{2} + 2 \, a b d \sec\left(f x + e\right) \tan\left(f x + e\right) + a^{2} d \sec\left(f x + e\right)\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^2*d*sec(f*x + e)*tan(f*x + e)^2 + 2*a*b*d*sec(f*x + e)*tan(f*x + e) + a^2*d*sec(f*x + e))*sqrt(d*sec(f*x + e)), x)","F",0
588,0,0,0,0.554993," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*sqrt(d*sec(f*x + e)), x)","F",0
589,0,0,0,0.833408," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \sqrt{d \sec\left(f x + e\right)}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*sqrt(d*sec(f*x + e))/(d*sec(f*x + e)), x)","F",0
590,0,0,0,0.575809," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*sqrt(d*sec(f*x + e))/(d^2*sec(f*x + e)^2), x)","F",0
591,0,0,0,0.699910," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*sqrt(d*sec(f*x + e))/(d^3*sec(f*x + e)^3), x)","F",0
592,0,0,0,0.442191," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{4} \sec\left(f x + e\right)^{4}}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*sqrt(d*sec(f*x + e))/(d^4*sec(f*x + e)^4), x)","F",0
593,0,0,0,0.602716," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{5} \sec\left(f x + e\right)^{5}}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*sqrt(d*sec(f*x + e))/(d^5*sec(f*x + e)^5), x)","F",0
594,0,0,0,0.785428," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b d^{2} \sec\left(f x + e\right)^{2} \tan\left(f x + e\right) + a^{3} d^{2} \sec\left(f x + e\right)^{2}\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^3*d^2*sec(f*x + e)^2*tan(f*x + e)^3 + 3*a*b^2*d^2*sec(f*x + e)^2*tan(f*x + e)^2 + 3*a^2*b*d^2*sec(f*x + e)^2*tan(f*x + e) + a^3*d^2*sec(f*x + e)^2)*sqrt(d*sec(f*x + e)), x)","F",0
595,0,0,0,1.276726," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} d \sec\left(f x + e\right) \tan\left(f x + e\right)^{3} + 3 \, a b^{2} d \sec\left(f x + e\right) \tan\left(f x + e\right)^{2} + 3 \, a^{2} b d \sec\left(f x + e\right) \tan\left(f x + e\right) + a^{3} d \sec\left(f x + e\right)\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^3*d*sec(f*x + e)*tan(f*x + e)^3 + 3*a*b^2*d*sec(f*x + e)*tan(f*x + e)^2 + 3*a^2*b*d*sec(f*x + e)*tan(f*x + e) + a^3*d*sec(f*x + e))*sqrt(d*sec(f*x + e)), x)","F",0
596,0,0,0,0.584509," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*sqrt(d*sec(f*x + e)), x)","F",0
597,0,0,0,0.766846," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \sec\left(f x + e\right)}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*sqrt(d*sec(f*x + e))/(d*sec(f*x + e)), x)","F",0
598,0,0,0,0.572425," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*sqrt(d*sec(f*x + e))/(d^2*sec(f*x + e)^2), x)","F",0
599,0,0,0,0.653832," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{3} \sec\left(f x + e\right)^{3}}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*sqrt(d*sec(f*x + e))/(d^3*sec(f*x + e)^3), x)","F",0
600,0,0,0,2.376215," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{4} \sec\left(f x + e\right)^{4}}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*sqrt(d*sec(f*x + e))/(d^4*sec(f*x + e)^4), x)","F",0
601,0,0,0,0.767070," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{5} \sec\left(f x + e\right)^{5}}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*sqrt(d*sec(f*x + e))/(d^5*sec(f*x + e)^5), x)","F",0
602,0,0,0,1.072550," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \sqrt{d \sec\left(f x + e\right)}}{d^{6} \sec\left(f x + e\right)^{6}}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*sqrt(d*sec(f*x + e))/(d^6*sec(f*x + e)^6), x)","F",0
603,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
611,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
613,-2,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
614,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,0,0,0,0.989546," ","integrate((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b d \sec\left(f x + e\right) \tan\left(f x + e\right) + a d \sec\left(f x + e\right)\right)} \left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((b*d*sec(f*x + e)*tan(f*x + e) + a*d*sec(f*x + e))*(d*sec(f*x + e))^(2/3), x)","F",0
625,0,0,0,0.950429," ","integrate((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}, x\right)"," ",0,"integral((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a), x)","F",0
626,0,0,0,0.816665," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} {\left(b \tan\left(f x + e\right) + a\right)}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((d*sec(f*x + e))^(2/3)*(b*tan(f*x + e) + a)/(d*sec(f*x + e)), x)","F",0
627,0,0,0,0.578663," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}}{d^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a)/(d^2*sec(f*x + e)^2), x)","F",0
628,0,0,0,0.495257," ","integrate((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d \sec\left(f x + e\right) \tan\left(f x + e\right)^{2} + 2 \, a b d \sec\left(f x + e\right) \tan\left(f x + e\right) + a^{2} d \sec\left(f x + e\right)\right)} \left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((b^2*d*sec(f*x + e)*tan(f*x + e)^2 + 2*a*b*d*sec(f*x + e)*tan(f*x + e) + a^2*d*sec(f*x + e))*(d*sec(f*x + e))^(2/3), x)","F",0
629,0,0,0,0.456502," ","integrate((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*(d*sec(f*x + e))^(1/3), x)","F",0
630,0,0,0,0.469056," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}}}{d \sec\left(f x + e\right)}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*(d*sec(f*x + e))^(2/3)/(d*sec(f*x + e)), x)","F",0
631,0,0,0,0.499231," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}{d^{2} \sec\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*(d*sec(f*x + e))^(1/3)/(d^2*sec(f*x + e)^2), x)","F",0
632,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,-1,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,0,0,0,0.599789," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \left(d \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*(d*sec(f*x + e))^m, x)","F",0
641,0,0,0,0.585426," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \left(d \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*(d*sec(f*x + e))^m, x)","F",0
642,0,0,0,0.484267," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(f x + e\right) + a\right)} \left(d \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)*(d*sec(f*x + e))^m, x)","F",0
643,0,0,0,0.589903," ","integrate((d*sec(f*x+e))^m/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{m}}{b \tan\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*sec(f*x + e))^m/(b*tan(f*x + e) + a), x)","F",0
644,0,0,0,0.659902," ","integrate((d*sec(f*x+e))^m/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \sec\left(f x + e\right)\right)^{m}}{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*sec(f*x + e))^m/(b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2), x)","F",0
645,0,0,0,0.647983," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \sec\left(f x + e\right)\right)^{m} {\left(b \tan\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*sec(f*x + e))^m*(b*tan(f*x + e) + a)^n, x)","F",0
646,1,420,0,0.746712," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4} - {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} n^{2} + 3 \, {\left(a^{3} b^{2} + 5 \, a b^{4}\right)} n\right)} \cos\left(d x + c\right)^{5} + 4 \, {\left(2 \, a b^{4} n^{3} + 3 \, {\left(a^{3} b^{2} + 3 \, a b^{4}\right)} n^{2} + {\left(3 \, a^{3} b^{2} + 7 \, a b^{4}\right)} n\right)} \cos\left(d x + c\right)^{3} + {\left(a b^{4} n^{4} + 6 \, a b^{4} n^{3} + 11 \, a b^{4} n^{2} + 6 \, a b^{4} n\right)} \cos\left(d x + c\right) + {\left(b^{5} n^{4} + 10 \, b^{5} n^{3} + 35 \, b^{5} n^{2} + 50 \, b^{5} n + 24 \, b^{5} + 8 \, {\left(8 \, b^{5} - {\left(3 \, a^{2} b^{3} - b^{5}\right)} n^{2} - 3 \, {\left(a^{4} b + 3 \, a^{2} b^{3} - 2 \, b^{5}\right)} n\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(8 \, b^{5} - {\left(a^{2} b^{3} - b^{5}\right)} n^{3} - {\left(3 \, a^{2} b^{3} - 7 \, b^{5}\right)} n^{2} - 2 \, {\left(a^{2} b^{3} - 7 \, b^{5}\right)} n\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{n}}{{\left(b^{5} d n^{5} + 15 \, b^{5} d n^{4} + 85 \, b^{5} d n^{3} + 225 \, b^{5} d n^{2} + 274 \, b^{5} d n + 120 \, b^{5} d\right)} \cos\left(d x + c\right)^{5}}"," ",0,"(8*(3*a^5 + 10*a^3*b^2 + 15*a*b^4 - (a^3*b^2 - 3*a*b^4)*n^2 + 3*(a^3*b^2 + 5*a*b^4)*n)*cos(d*x + c)^5 + 4*(2*a*b^4*n^3 + 3*(a^3*b^2 + 3*a*b^4)*n^2 + (3*a^3*b^2 + 7*a*b^4)*n)*cos(d*x + c)^3 + (a*b^4*n^4 + 6*a*b^4*n^3 + 11*a*b^4*n^2 + 6*a*b^4*n)*cos(d*x + c) + (b^5*n^4 + 10*b^5*n^3 + 35*b^5*n^2 + 50*b^5*n + 24*b^5 + 8*(8*b^5 - (3*a^2*b^3 - b^5)*n^2 - 3*(a^4*b + 3*a^2*b^3 - 2*b^5)*n)*cos(d*x + c)^4 + 4*(8*b^5 - (a^2*b^3 - b^5)*n^3 - (3*a^2*b^3 - 7*b^5)*n^2 - 2*(a^2*b^3 - 7*b^5)*n)*cos(d*x + c)^2)*sin(d*x + c))*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^n/((b^5*d*n^5 + 15*b^5*d*n^4 + 85*b^5*d*n^3 + 225*b^5*d*n^2 + 274*b^5*d*n + 120*b^5*d)*cos(d*x + c)^5)","B",0
647,1,176,0,0.890713," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(2 \, a b^{2} n + a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(a b^{2} n^{2} + a b^{2} n\right)} \cos\left(d x + c\right) + {\left(b^{3} n^{2} + 3 \, b^{3} n + 2 \, b^{3} + 2 \, {\left(2 \, b^{3} - {\left(a^{2} b - b^{3}\right)} n\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{n}}{{\left(b^{3} d n^{3} + 6 \, b^{3} d n^{2} + 11 \, b^{3} d n + 6 \, b^{3} d\right)} \cos\left(d x + c\right)^{3}}"," ",0,"(2*(2*a*b^2*n + a^3 + 3*a*b^2)*cos(d*x + c)^3 + (a*b^2*n^2 + a*b^2*n)*cos(d*x + c) + (b^3*n^2 + 3*b^3*n + 2*b^3 + 2*(2*b^3 - (a^2*b - b^3)*n)*cos(d*x + c)^2)*sin(d*x + c))*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^n/((b^3*d*n^3 + 6*b^3*d*n^2 + 11*b^3*d*n + 6*b^3*d)*cos(d*x + c)^3)","A",0
648,1,64,0,0.452456," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","\frac{{\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)} \left(\frac{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}{\cos\left(d x + c\right)}\right)^{n}}{{\left(b d n + b d\right)} \cos\left(d x + c\right)}"," ",0,"(a*cos(d*x + c) + b*sin(d*x + c))*((a*cos(d*x + c) + b*sin(d*x + c))/cos(d*x + c))^n/((b*d*n + b*d)*cos(d*x + c))","B",0
649,0,0,0,0.500910," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*cos(d*x + c)^2, x)","F",0
650,0,0,0,0.567186," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*cos(d*x + c)^4, x)","F",0
651,0,0,0,0.704255," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*sec(d*x + c)^3, x)","F",0
652,0,0,0,0.430786," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right), x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*sec(d*x + c), x)","F",0
653,0,0,0,0.427921," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right), x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*cos(d*x + c), x)","F",0
654,0,0,0,0.535609," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*tan(d*x + c) + a)^n*cos(d*x + c)^3, x)","F",0
655,0,0,0,0.503678," ","integrate((e*cos(d*x+c))^(7/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(\sqrt{\frac{1}{2}} {\left(-3 i \, a e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} - 16 i \, a e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, a e^{3}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 42 \, d e^{\left(i \, d x + i \, c\right)} {\rm integral}\left(-\frac{10 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e^{3} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{21 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}, x\right)\right)} e^{\left(-i \, d x - i \, c\right)}}{42 \, d}"," ",0,"1/42*(sqrt(1/2)*(-3*I*a*e^3*e^(4*I*d*x + 4*I*c) - 16*I*a*e^3*e^(2*I*d*x + 2*I*c) + 7*I*a*e^3)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c) + 42*d*e^(I*d*x + I*c)*integral(-10/21*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e^3*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^(2*I*d*x + 2*I*c) + d), x))*e^(-I*d*x - I*c)/d","F",0
656,0,0,0,0.471361," ","integrate((e*cos(d*x+c))^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(-i \, a e^{2} e^{\left(3 i \, d x + 3 i \, c\right)} + i \, a e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 7 i \, a e^{2} e^{\left(i \, d x + i \, c\right)} - 5 i \, a e^{2}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 5 \, {\left(d e^{\left(i \, d x + i \, c\right)} - d\right)} {\rm integral}\left(\frac{\sqrt{\frac{1}{2}} {\left(-6 i \, a e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 12 i \, a e^{2} e^{\left(i \, d x + i \, c\right)} - 6 i \, a e^{2}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{5 \, {\left(d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, d e^{\left(i \, d x + i \, c\right)} + d\right)}}, x\right)}{5 \, {\left(d e^{\left(i \, d x + i \, c\right)} - d\right)}}"," ",0,"1/5*(sqrt(1/2)*(-I*a*e^2*e^(3*I*d*x + 3*I*c) + I*a*e^2*e^(2*I*d*x + 2*I*c) - 7*I*a*e^2*e^(I*d*x + I*c) - 5*I*a*e^2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c) + 5*(d*e^(I*d*x + I*c) - d)*integral(1/5*sqrt(1/2)*(-6*I*a*e^2*e^(2*I*d*x + 2*I*c) - 12*I*a*e^2*e^(I*d*x + I*c) - 6*I*a*e^2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(3*I*d*x + 3*I*c) + 2*d*e^(2*I*d*x + 2*I*c) - 2*d*e^(I*d*x + I*c) + d), x))/(d*e^(I*d*x + I*c) - d)","F",0
657,0,0,0,0.443192," ","integrate((e*cos(d*x+c))^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + 3 \, d {\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}, x\right)}{3 \, d}"," ",0,"1/3*(-2*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e*e^(1/2*I*d*x + 1/2*I*c) + 3*d*integral(-2/3*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^(2*I*d*x + 2*I*c) + d), x))/d","F",0
658,0,0,0,0.460794," ","integrate((e*cos(d*x+c))^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","\frac{-4 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + {\left(d e^{\left(i \, d x + i \, c\right)} - d\right)} {\rm integral}\left(\frac{\sqrt{\frac{1}{2}} {\left(-2 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a e^{\left(i \, d x + i \, c\right)} - 2 i \, a\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, d e^{\left(3 i \, d x + 3 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, d e^{\left(i \, d x + i \, c\right)} + d}, x\right)}{d e^{\left(i \, d x + i \, c\right)} - d}"," ",0,"(-4*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e^(1/2*I*d*x + 1/2*I*c) + (d*e^(I*d*x + I*c) - d)*integral(sqrt(1/2)*(-2*I*a*e^(2*I*d*x + 2*I*c) - 4*I*a*e^(I*d*x + I*c) - 2*I*a)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^(4*I*d*x + 4*I*c) - 2*d*e^(3*I*d*x + 3*I*c) + 2*d*e^(2*I*d*x + 2*I*c) - 2*d*e^(I*d*x + I*c) + d), x))/(d*e^(I*d*x + I*c) - d)","F",0
659,0,0,0,0.508276," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{4 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} + {\left(d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e\right)} {\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e}, x\right)}{d e e^{\left(2 i \, d x + 2 i \, c\right)} + d e}"," ",0,"(4*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e^(1/2*I*d*x + 1/2*I*c) + (d*e*e^(2*I*d*x + 2*I*c) + d*e)*integral(-2*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e^(-1/2*I*d*x - 1/2*I*c)/(d*e*e^(2*I*d*x + 2*I*c) + d*e), x))/(d*e*e^(2*I*d*x + 2*I*c) + d*e)","F",0
660,0,0,0,0.499080," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(-12 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 4 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 3 \, {\left(d e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)} {\rm integral}\left(\frac{2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}}, x\right)}{3 \, {\left(d e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)}}"," ",0,"1/3*(sqrt(1/2)*(-12*I*a*e^(4*I*d*x + 4*I*c) - 4*I*a*e^(2*I*d*x + 2*I*c))*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c) + 3*(d*e^2*e^(4*I*d*x + 4*I*c) + 2*d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)*integral(2*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e^(1/2*I*d*x + 1/2*I*c)/(d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2), x))/(d*e^2*e^(4*I*d*x + 4*I*c) + 2*d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)","F",0
661,0,0,0,0.556384," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(-20 i \, a e^{\left(5 i \, d x + 5 i \, c\right)} + 48 i \, a e^{\left(3 i \, d x + 3 i \, c\right)} + 20 i \, a e^{\left(i \, d x + i \, c\right)}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 15 \, {\left(d e^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3}\right)} {\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, {\left(d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3}\right)}}, x\right)}{15 \, {\left(d e^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3}\right)}}"," ",0,"1/15*(sqrt(1/2)*(-20*I*a*e^(5*I*d*x + 5*I*c) + 48*I*a*e^(3*I*d*x + 3*I*c) + 20*I*a*e^(I*d*x + I*c))*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c) + 15*(d*e^3*e^(6*I*d*x + 6*I*c) + 3*d*e^3*e^(4*I*d*x + 4*I*c) + 3*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3)*integral(-2/3*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e^(-1/2*I*d*x - 1/2*I*c)/(d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3), x))/(d*e^3*e^(6*I*d*x + 6*I*c) + 3*d*e^3*e^(4*I*d*x + 4*I*c) + 3*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3)","F",0
662,0,0,0,0.457896," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(-84 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} - 308 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 92 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 28 i \, a e^{\left(2 i \, d x + 2 i \, c\right)}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 35 \, {\left(d e^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{4}\right)} {\rm integral}\left(\frac{6 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} a e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{4}\right)}}, x\right)}{35 \, {\left(d e^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{4}\right)}}"," ",0,"1/35*(sqrt(1/2)*(-84*I*a*e^(8*I*d*x + 8*I*c) - 308*I*a*e^(6*I*d*x + 6*I*c) - 92*I*a*e^(4*I*d*x + 4*I*c) - 28*I*a*e^(2*I*d*x + 2*I*c))*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c) + 35*(d*e^4*e^(8*I*d*x + 8*I*c) + 4*d*e^4*e^(6*I*d*x + 6*I*c) + 6*d*e^4*e^(4*I*d*x + 4*I*c) + 4*d*e^4*e^(2*I*d*x + 2*I*c) + d*e^4)*integral(6/5*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*a*e^(1/2*I*d*x + 1/2*I*c)/(d*e^4*e^(2*I*d*x + 2*I*c) + d*e^4), x))/(d*e^4*e^(8*I*d*x + 8*I*c) + 4*d*e^4*e^(6*I*d*x + 6*I*c) + 6*d*e^4*e^(4*I*d*x + 4*I*c) + 4*d*e^4*e^(2*I*d*x + 2*I*c) + d*e^4)","F",0
663,0,0,0,0.533786," ","integrate((e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(1680 \, a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} {\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{3} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{7 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}, x\right) + \sqrt{\frac{1}{2}} {\left(-15 i \, e^{3} e^{\left(10 i \, d x + 10 i \, c\right)} - 185 i \, e^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 430 i \, e^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 162 i \, e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 49 i \, e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, e^{3}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)} e^{\left(-7 i \, d x - 7 i \, c\right)}}{1680 \, a^{2} d}"," ",0,"1/1680*(1680*a^2*d*e^(7*I*d*x + 7*I*c)*integral(-2/7*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^3*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d), x) + sqrt(1/2)*(-15*I*e^3*e^(10*I*d*x + 10*I*c) - 185*I*e^3*e^(8*I*d*x + 8*I*c) + 430*I*e^3*e^(6*I*d*x + 6*I*c) + 162*I*e^3*e^(4*I*d*x + 4*I*c) + 49*I*e^3*e^(2*I*d*x + 2*I*c) + 7*I*e^3)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c))*e^(-7*I*d*x - 7*I*c)/(a^2*d)","F",0
664,0,0,0,0.478480," ","integrate((e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(-13 i \, e^{2} e^{\left(9 i \, d x + 9 i \, c\right)} + 13 i \, e^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 286 i \, e^{2} e^{\left(7 i \, d x + 7 i \, c\right)} - 386 i \, e^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 88 i \, e^{2} e^{\left(5 i \, d x + 5 i \, c\right)} - 88 i \, e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 30 i \, e^{2} e^{\left(3 i \, d x + 3 i \, c\right)} - 30 i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, e^{2} e^{\left(i \, d x + i \, c\right)} - 5 i \, e^{2}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 520 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{\frac{1}{2}} {\left(-42 i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 84 i \, e^{2} e^{\left(i \, d x + i \, c\right)} - 42 i \, e^{2}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{65 \, {\left(a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, a^{2} d e^{\left(i \, d x + i \, c\right)} + a^{2} d\right)}}, x\right)}{520 \, {\left(a^{2} d e^{\left(7 i \, d x + 7 i \, c\right)} - a^{2} d e^{\left(6 i \, d x + 6 i \, c\right)}\right)}}"," ",0,"1/520*(sqrt(1/2)*(-13*I*e^2*e^(9*I*d*x + 9*I*c) + 13*I*e^2*e^(8*I*d*x + 8*I*c) - 286*I*e^2*e^(7*I*d*x + 7*I*c) - 386*I*e^2*e^(6*I*d*x + 6*I*c) + 88*I*e^2*e^(5*I*d*x + 5*I*c) - 88*I*e^2*e^(4*I*d*x + 4*I*c) + 30*I*e^2*e^(3*I*d*x + 3*I*c) - 30*I*e^2*e^(2*I*d*x + 2*I*c) + 5*I*e^2*e^(I*d*x + I*c) - 5*I*e^2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c) + 520*(a^2*d*e^(7*I*d*x + 7*I*c) - a^2*d*e^(6*I*d*x + 6*I*c))*integral(1/65*sqrt(1/2)*(-42*I*e^2*e^(2*I*d*x + 2*I*c) - 84*I*e^2*e^(I*d*x + I*c) - 42*I*e^2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e^(4*I*d*x + 4*I*c) - 2*a^2*d*e^(3*I*d*x + 3*I*c) + 2*a^2*d*e^(2*I*d*x + 2*I*c) - 2*a^2*d*e^(I*d*x + I*c) + a^2*d), x))/(a^2*d*e^(7*I*d*x + 7*I*c) - a^2*d*e^(6*I*d*x + 6*I*c))","F",0
665,0,0,0,0.514766," ","integrate((e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(132 \, a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} {\rm integral}\left(-\frac{10 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{33 \, {\left(a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d\right)}}, x\right) + \sqrt{\frac{1}{2}} {\left(-11 i \, e e^{\left(6 i \, d x + 6 i \, c\right)} + 41 i \, e e^{\left(4 i \, d x + 4 i \, c\right)} + 15 i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, e\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)} e^{\left(-5 i \, d x - 5 i \, c\right)}}{132 \, a^{2} d}"," ",0,"1/132*(132*a^2*d*e^(5*I*d*x + 5*I*c)*integral(-10/33*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e^(2*I*d*x + 2*I*c) + a^2*d), x) + sqrt(1/2)*(-11*I*e*e^(6*I*d*x + 6*I*c) + 41*I*e*e^(4*I*d*x + 4*I*c) + 15*I*e*e^(2*I*d*x + 2*I*c) + 3*I*e)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c))*e^(-5*I*d*x - 5*I*c)/(a^2*d)","F",0
666,0,0,0,0.473080," ","integrate((e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} {\left(-9 i \, e^{\left(5 i \, d x + 5 i \, c\right)} - 15 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + 4 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i \, e^{\left(i \, d x + i \, c\right)} - i\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 18 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)} {\rm integral}\left(\frac{\sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} {\left(-2 i \, e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, e^{\left(i \, d x + i \, c\right)} - 2 i\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, {\left(a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)} - 2 \, a^{2} d e^{\left(3 i \, d x + 3 i \, c\right)} + 2 \, a^{2} d e^{\left(2 i \, d x + 2 i \, c\right)} - 2 \, a^{2} d e^{\left(i \, d x + i \, c\right)} + a^{2} d\right)}}, x\right)}{18 \, {\left(a^{2} d e^{\left(5 i \, d x + 5 i \, c\right)} - a^{2} d e^{\left(4 i \, d x + 4 i \, c\right)}\right)}}"," ",0,"1/18*(sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*(-9*I*e^(5*I*d*x + 5*I*c) - 15*I*e^(4*I*d*x + 4*I*c) + 4*I*e^(3*I*d*x + 3*I*c) - 4*I*e^(2*I*d*x + 2*I*c) + I*e^(I*d*x + I*c) - I)*e^(-1/2*I*d*x - 1/2*I*c) + 18*(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))*integral(1/3*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*(-2*I*e^(2*I*d*x + 2*I*c) - 4*I*e^(I*d*x + I*c) - 2*I)*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e^(4*I*d*x + 4*I*c) - 2*a^2*d*e^(3*I*d*x + 3*I*c) + 2*a^2*d*e^(2*I*d*x + 2*I*c) - 2*a^2*d*e^(I*d*x + I*c) + a^2*d), x))/(a^2*d*e^(5*I*d*x + 5*I*c) - a^2*d*e^(4*I*d*x + 4*I*c))","F",0
667,0,0,0,0.536956," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(7 \, a^{2} d e e^{\left(3 i \, d x + 3 i \, c\right)} {\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{7 \, {\left(a^{2} d e e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e\right)}}, x\right) + \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} {\left(3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)} e^{\left(-3 i \, d x - 3 i \, c\right)}}{7 \, a^{2} d e}"," ",0,"1/7*(7*a^2*d*e*e^(3*I*d*x + 3*I*c)*integral(-2/7*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e*e^(2*I*d*x + 2*I*c) + a^2*d*e), x) + sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*(3*I*e^(2*I*d*x + 2*I*c) + I)*e^(-1/2*I*d*x - 1/2*I*c))*e^(-3*I*d*x - 3*I*c)/(a^2*d*e)","F",0
668,0,0,0,0.421189," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(5 \, a^{2} d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} {\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(a^{2} d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{2}\right)}}, x\right) + \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} {\left(4 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 2 i\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{5 \, a^{2} d e^{2}}"," ",0,"1/5*(5*a^2*d*e^2*e^(2*I*d*x + 2*I*c)*integral(-2/5*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d*e^2*e^(2*I*d*x + 2*I*c) + a^2*d*e^2), x) + sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*(4*I*e^(2*I*d*x + 2*I*c) + 2*I)*e^(-1/2*I*d*x - 1/2*I*c))*e^(-2*I*d*x - 2*I*c)/(a^2*d*e^2)","F",0
669,0,0,0,0.517514," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} d e^{3} e^{\left(i \, d x + i \, c\right)} {\rm integral}\left(\frac{2 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, {\left(a^{2} d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{3}\right)}}, x\right) + 4 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)} e^{\left(-i \, d x - i \, c\right)}}{3 \, a^{2} d e^{3}}"," ",0,"1/3*(3*a^2*d*e^3*e^(I*d*x + I*c)*integral(2/3*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e^3*e^(2*I*d*x + 2*I*c) + a^2*d*e^3), x) + 4*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c))*e^(-I*d*x - I*c)/(a^2*d*e^3)","F",0
670,0,0,0,0.462974," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} {\left(12 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + 8 i\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + {\left(a^{2} d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{4}\right)} {\rm integral}\left(-\frac{6 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{a^{2} d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{4}}, x\right)}{a^{2} d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{4}}"," ",0,"(sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*(12*I*e^(2*I*d*x + 2*I*c) + 8*I)*e^(-1/2*I*d*x - 1/2*I*c) + (a^2*d*e^4*e^(2*I*d*x + 2*I*c) + a^2*d*e^4)*integral(-6*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d*e^4*e^(2*I*d*x + 2*I*c) + a^2*d*e^4), x))/(a^2*d*e^4*e^(2*I*d*x + 2*I*c) + a^2*d*e^4)","F",0
671,0,0,0,0.456198," ","integrate(1/(e*cos(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} {\left(-20 i \, e^{\left(3 i \, d x + 3 i \, c\right)} - 28 i \, e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 3 \, {\left(a^{2} d e^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} d e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{5}\right)} {\rm integral}\left(-\frac{10 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, {\left(a^{2} d e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{5}\right)}}, x\right)}{3 \, {\left(a^{2} d e^{5} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a^{2} d e^{5} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{5}\right)}}"," ",0,"1/3*(sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*(-20*I*e^(3*I*d*x + 3*I*c) - 28*I*e^(I*d*x + I*c))*e^(-1/2*I*d*x - 1/2*I*c) + 3*(a^2*d*e^5*e^(4*I*d*x + 4*I*c) + 2*a^2*d*e^5*e^(2*I*d*x + 2*I*c) + a^2*d*e^5)*integral(-10/3*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(-1/2*I*d*x - 1/2*I*c)/(a^2*d*e^5*e^(2*I*d*x + 2*I*c) + a^2*d*e^5), x))/(a^2*d*e^5*e^(4*I*d*x + 4*I*c) + 2*a^2*d*e^5*e^(2*I*d*x + 2*I*c) + a^2*d*e^5)","F",0
672,0,0,0,0.618628," ","integrate(1/(e*cos(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} {\left(-84 i \, e^{\left(6 i \, d x + 6 i \, c\right)} - 224 i \, e^{\left(4 i \, d x + 4 i \, c\right)} - 188 i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + 15 \, {\left(a^{2} d e^{6} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{6} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{2} d e^{6} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{6}\right)} {\rm integral}\left(\frac{14 i \, \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{5 \, {\left(a^{2} d e^{6} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{6}\right)}}, x\right)}{15 \, {\left(a^{2} d e^{6} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, a^{2} d e^{6} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, a^{2} d e^{6} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} d e^{6}\right)}}"," ",0,"1/15*(sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*(-84*I*e^(6*I*d*x + 6*I*c) - 224*I*e^(4*I*d*x + 4*I*c) - 188*I*e^(2*I*d*x + 2*I*c))*e^(-1/2*I*d*x - 1/2*I*c) + 15*(a^2*d*e^6*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^6*e^(4*I*d*x + 4*I*c) + 3*a^2*d*e^6*e^(2*I*d*x + 2*I*c) + a^2*d*e^6)*integral(14/5*I*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*e^(1/2*I*d*x + 1/2*I*c)/(a^2*d*e^6*e^(2*I*d*x + 2*I*c) + a^2*d*e^6), x))/(a^2*d*e^6*e^(6*I*d*x + 6*I*c) + 3*a^2*d*e^6*e^(4*I*d*x + 4*I*c) + 3*a^2*d*e^6*e^(2*I*d*x + 2*I*c) + a^2*d*e^6)","F",0
673,1,100,0,0.699263," ","integrate((e*cos(d*x+c))^(7/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} {\left(-5 i \, e^{3} e^{\left(6 i \, d x + 6 i \, c\right)} - 35 i \, e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 105 i \, e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 7 i \, e^{3}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{5}{2} i \, d x - \frac{5}{2} i \, c\right)}}{140 \, d}"," ",0,"1/140*sqrt(2)*sqrt(1/2)*(-5*I*e^3*e^(6*I*d*x + 6*I*c) - 35*I*e^3*e^(4*I*d*x + 4*I*c) + 105*I*e^3*e^(2*I*d*x + 2*I*c) + 7*I*e^3)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-5/2*I*d*x - 5/2*I*c)/d","A",0
674,1,86,0,0.477396," ","integrate((e*cos(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} {\left(-3 i \, e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 30 i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, e^{2}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{3}{2} i \, d x - \frac{3}{2} i \, c\right)}}{30 \, d}"," ",0,"1/30*sqrt(2)*sqrt(1/2)*(-3*I*e^2*e^(4*I*d*x + 4*I*c) - 30*I*e^2*e^(2*I*d*x + 2*I*c) + 5*I*e^2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-3/2*I*d*x - 3/2*I*c)/d","A",0
675,1,68,0,0.414692," ","integrate((e*cos(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} {\left(-i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, e\right)} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{3 \, d}"," ",0,"1/3*sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*(-I*e*e^(2*I*d*x + 2*I*c) + 3*I*e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/d","A",0
676,1,52,0,0.411174," ","integrate((e*cos(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 i \, \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)}}{d}"," ",0,"-2*I*sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c)/d","A",0
677,1,313,0,0.484798," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{4 i \, a}{d^{2} e}} \log\left(\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + \frac{1}{2} i \, d e \sqrt{\frac{4 i \, a}{d^{2} e}}\right) + \frac{1}{2} \, \sqrt{\frac{4 i \, a}{d^{2} e}} \log\left(\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} - \frac{1}{2} i \, d e \sqrt{\frac{4 i \, a}{d^{2} e}}\right) - \frac{1}{2} \, \sqrt{-\frac{4 i \, a}{d^{2} e}} \log\left(\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} + \frac{1}{2} i \, d e \sqrt{-\frac{4 i \, a}{d^{2} e}}\right) + \frac{1}{2} \, \sqrt{-\frac{4 i \, a}{d^{2} e}} \log\left(\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} - \frac{1}{2} i \, d e \sqrt{-\frac{4 i \, a}{d^{2} e}}\right)"," ",0,"-1/2*sqrt(4*I*a/(d^2*e))*log(sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c) + 1/2*I*d*e*sqrt(4*I*a/(d^2*e))) + 1/2*sqrt(4*I*a/(d^2*e))*log(sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c) - 1/2*I*d*e*sqrt(4*I*a/(d^2*e))) - 1/2*sqrt(-4*I*a/(d^2*e))*log(sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c) + 1/2*I*d*e*sqrt(-4*I*a/(d^2*e))) + 1/2*sqrt(-4*I*a/(d^2*e))*log(sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c) - 1/2*I*d*e*sqrt(-4*I*a/(d^2*e)))","A",0
678,1,470,0,0.555684," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{4 i \, \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{1}{2} i \, d x + \frac{1}{2} i \, c\right)} - {\left(d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)} \sqrt{\frac{i \, a}{d^{2} e^{3}}} \log\left(d e^{2} \sqrt{\frac{i \, a}{d^{2} e^{3}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + {\left(d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)} \sqrt{\frac{i \, a}{d^{2} e^{3}}} \log\left(-d e^{2} \sqrt{\frac{i \, a}{d^{2} e^{3}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + {\left(d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)} \sqrt{-\frac{i \, a}{d^{2} e^{3}}} \log\left(d e^{2} \sqrt{-\frac{i \, a}{d^{2} e^{3}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) - {\left(d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)} \sqrt{-\frac{i \, a}{d^{2} e^{3}}} \log\left(-d e^{2} \sqrt{-\frac{i \, a}{d^{2} e^{3}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)}{2 \, {\left(d e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{2}\right)}}"," ",0,"1/2*(4*I*sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(1/2*I*d*x + 1/2*I*c) - (d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)*sqrt(I*a/(d^2*e^3))*log(d*e^2*sqrt(I*a/(d^2*e^3)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + (d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)*sqrt(I*a/(d^2*e^3))*log(-d*e^2*sqrt(I*a/(d^2*e^3)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + (d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)*sqrt(-I*a/(d^2*e^3))*log(d*e^2*sqrt(-I*a/(d^2*e^3)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) - (d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)*sqrt(-I*a/(d^2*e^3))*log(-d*e^2*sqrt(-I*a/(d^2*e^3)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)))/(d*e^2*e^(2*I*d*x + 2*I*c) + d*e^2)","A",0
679,1,569,0,0.714008," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-3 i \, e^{\left(4 i \, d x + 4 i \, c\right)} + i \, e^{\left(2 i \, d x + 2 i \, c\right)}\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} - {\left(d e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3}\right)} \sqrt{\frac{9 i \, a}{16 \, d^{2} e^{5}}} \log\left(\frac{4}{3} i \, d e^{3} \sqrt{\frac{9 i \, a}{16 \, d^{2} e^{5}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + {\left(d e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3}\right)} \sqrt{\frac{9 i \, a}{16 \, d^{2} e^{5}}} \log\left(-\frac{4}{3} i \, d e^{3} \sqrt{\frac{9 i \, a}{16 \, d^{2} e^{5}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) - {\left(d e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3}\right)} \sqrt{-\frac{9 i \, a}{16 \, d^{2} e^{5}}} \log\left(\frac{4}{3} i \, d e^{3} \sqrt{-\frac{9 i \, a}{16 \, d^{2} e^{5}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + {\left(d e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3}\right)} \sqrt{-\frac{9 i \, a}{16 \, d^{2} e^{5}}} \log\left(-\frac{4}{3} i \, d e^{3} \sqrt{-\frac{9 i \, a}{16 \, d^{2} e^{5}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)}{2 \, {\left(d e^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{3}\right)}}"," ",0,"1/2*(sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-3*I*e^(4*I*d*x + 4*I*c) + I*e^(2*I*d*x + 2*I*c))*e^(-1/2*I*d*x - 1/2*I*c) - (d*e^3*e^(4*I*d*x + 4*I*c) + 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3)*sqrt(9/16*I*a/(d^2*e^5))*log(4/3*I*d*e^3*sqrt(9/16*I*a/(d^2*e^5)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + (d*e^3*e^(4*I*d*x + 4*I*c) + 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3)*sqrt(9/16*I*a/(d^2*e^5))*log(-4/3*I*d*e^3*sqrt(9/16*I*a/(d^2*e^5)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) - (d*e^3*e^(4*I*d*x + 4*I*c) + 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3)*sqrt(-9/16*I*a/(d^2*e^5))*log(4/3*I*d*e^3*sqrt(-9/16*I*a/(d^2*e^5)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + (d*e^3*e^(4*I*d*x + 4*I*c) + 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3)*sqrt(-9/16*I*a/(d^2*e^5))*log(-4/3*I*d*e^3*sqrt(-9/16*I*a/(d^2*e^5)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)))/(d*e^3*e^(4*I*d*x + 4*I*c) + 2*d*e^3*e^(2*I*d*x + 2*I*c) + d*e^3)","A",0
680,1,657,0,0.476763," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-5 i \, e^{\left(5 i \, d x + 5 i \, c\right)} + 42 i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 15 i \, e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} - 6 \, {\left(d e^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{4}\right)} \sqrt{\frac{25 i \, a}{64 \, d^{2} e^{7}}} \log\left(\frac{8}{5} \, d e^{4} \sqrt{\frac{25 i \, a}{64 \, d^{2} e^{7}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + 6 \, {\left(d e^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{4}\right)} \sqrt{\frac{25 i \, a}{64 \, d^{2} e^{7}}} \log\left(-\frac{8}{5} \, d e^{4} \sqrt{\frac{25 i \, a}{64 \, d^{2} e^{7}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + 6 \, {\left(d e^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{4}\right)} \sqrt{-\frac{25 i \, a}{64 \, d^{2} e^{7}}} \log\left(\frac{8}{5} \, d e^{4} \sqrt{-\frac{25 i \, a}{64 \, d^{2} e^{7}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) - 6 \, {\left(d e^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{4}\right)} \sqrt{-\frac{25 i \, a}{64 \, d^{2} e^{7}}} \log\left(-\frac{8}{5} \, d e^{4} \sqrt{-\frac{25 i \, a}{64 \, d^{2} e^{7}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)}{12 \, {\left(d e^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + d e^{4}\right)}}"," ",0,"1/12*(sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-5*I*e^(5*I*d*x + 5*I*c) + 42*I*e^(3*I*d*x + 3*I*c) + 15*I*e^(I*d*x + I*c))*e^(-1/2*I*d*x - 1/2*I*c) - 6*(d*e^4*e^(6*I*d*x + 6*I*c) + 3*d*e^4*e^(4*I*d*x + 4*I*c) + 3*d*e^4*e^(2*I*d*x + 2*I*c) + d*e^4)*sqrt(25/64*I*a/(d^2*e^7))*log(8/5*d*e^4*sqrt(25/64*I*a/(d^2*e^7)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + 6*(d*e^4*e^(6*I*d*x + 6*I*c) + 3*d*e^4*e^(4*I*d*x + 4*I*c) + 3*d*e^4*e^(2*I*d*x + 2*I*c) + d*e^4)*sqrt(25/64*I*a/(d^2*e^7))*log(-8/5*d*e^4*sqrt(25/64*I*a/(d^2*e^7)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + 6*(d*e^4*e^(6*I*d*x + 6*I*c) + 3*d*e^4*e^(4*I*d*x + 4*I*c) + 3*d*e^4*e^(2*I*d*x + 2*I*c) + d*e^4)*sqrt(-25/64*I*a/(d^2*e^7))*log(8/5*d*e^4*sqrt(-25/64*I*a/(d^2*e^7)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) - 6*(d*e^4*e^(6*I*d*x + 6*I*c) + 3*d*e^4*e^(4*I*d*x + 4*I*c) + 3*d*e^4*e^(2*I*d*x + 2*I*c) + d*e^4)*sqrt(-25/64*I*a/(d^2*e^7))*log(-8/5*d*e^4*sqrt(-25/64*I*a/(d^2*e^7)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)))/(d*e^4*e^(6*I*d*x + 6*I*c) + 3*d*e^4*e^(4*I*d*x + 4*I*c) + 3*d*e^4*e^(2*I*d*x + 2*I*c) + d*e^4)","A",0
681,1,103,0,0.489865," ","integrate((e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} {\left(-7 i \, e^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 105 i \, e^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 35 i \, e^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 5 i \, e^{2}\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{7}{2} i \, d x - \frac{7}{2} i \, c\right)}}{140 \, a d}"," ",0,"1/140*sqrt(2)*sqrt(1/2)*(-7*I*e^2*e^(6*I*d*x + 6*I*c) - 105*I*e^2*e^(4*I*d*x + 4*I*c) + 35*I*e^2*e^(2*I*d*x + 2*I*c) + 5*I*e^2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-7/2*I*d*x - 7/2*I*c)/(a*d)","A",0
682,1,83,0,0.545621," ","integrate((e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} {\left(-5 i \, e e^{\left(4 i \, d x + 4 i \, c\right)} + 30 i \, e e^{\left(2 i \, d x + 2 i \, c\right)} + 3 i \, e\right)} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{5}{2} i \, d x - \frac{5}{2} i \, c\right)}}{30 \, a d}"," ",0,"1/30*sqrt(2)*sqrt(1/2)*(-5*I*e*e^(4*I*d*x + 4*I*c) + 30*I*e*e^(2*I*d*x + 2*I*c) + 3*I*e)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-5/2*I*d*x - 5/2*I*c)/(a*d)","A",0
683,1,68,0,0.515727," ","integrate((e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-3 i \, e^{\left(2 i \, d x + 2 i \, c\right)} + i\right)} e^{\left(-\frac{3}{2} i \, d x - \frac{3}{2} i \, c\right)}}{3 \, a d}"," ",0,"1/3*sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-3*I*e^(2*I*d*x + 2*I*c) + I)*e^(-3/2*I*d*x - 3/2*I*c)/(a*d)","A",0
684,1,58,0,0.582305," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 i \, \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}}{a d e}"," ",0,"2*I*sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)/(a*d*e)","B",0
685,1,341,0,0.441908," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{4 i}{a d^{2} e^{3}}} \log\left(\frac{1}{2} \, a d e^{2} \sqrt{\frac{4 i}{a d^{2} e^{3}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + \frac{1}{2} \, \sqrt{\frac{4 i}{a d^{2} e^{3}}} \log\left(-\frac{1}{2} \, a d e^{2} \sqrt{\frac{4 i}{a d^{2} e^{3}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + \frac{1}{2} \, \sqrt{-\frac{4 i}{a d^{2} e^{3}}} \log\left(\frac{1}{2} \, a d e^{2} \sqrt{-\frac{4 i}{a d^{2} e^{3}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) - \frac{1}{2} \, \sqrt{-\frac{4 i}{a d^{2} e^{3}}} \log\left(-\frac{1}{2} \, a d e^{2} \sqrt{-\frac{4 i}{a d^{2} e^{3}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)"," ",0,"-1/2*sqrt(4*I/(a*d^2*e^3))*log(1/2*a*d*e^2*sqrt(4*I/(a*d^2*e^3)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + 1/2*sqrt(4*I/(a*d^2*e^3))*log(-1/2*a*d*e^2*sqrt(4*I/(a*d^2*e^3)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + 1/2*sqrt(-4*I/(a*d^2*e^3))*log(1/2*a*d*e^2*sqrt(-4*I/(a*d^2*e^3)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) - 1/2*sqrt(-4*I/(a*d^2*e^3))*log(-1/2*a*d*e^2*sqrt(-4*I/(a*d^2*e^3)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c))","A",0
686,1,502,0,0.465755," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{-4 i \, \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(\frac{3}{2} i \, d x + \frac{3}{2} i \, c\right)} - {\left(a d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{3}\right)} \sqrt{\frac{i}{a d^{2} e^{5}}} \log\left(i \, a d e^{3} \sqrt{\frac{i}{a d^{2} e^{5}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + {\left(a d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{3}\right)} \sqrt{\frac{i}{a d^{2} e^{5}}} \log\left(-i \, a d e^{3} \sqrt{\frac{i}{a d^{2} e^{5}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) - {\left(a d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{3}\right)} \sqrt{-\frac{i}{a d^{2} e^{5}}} \log\left(i \, a d e^{3} \sqrt{-\frac{i}{a d^{2} e^{5}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + {\left(a d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{3}\right)} \sqrt{-\frac{i}{a d^{2} e^{5}}} \log\left(-i \, a d e^{3} \sqrt{-\frac{i}{a d^{2} e^{5}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)}{2 \, {\left(a d e^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{3}\right)}}"," ",0,"1/2*(-4*I*sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(3/2*I*d*x + 3/2*I*c) - (a*d*e^3*e^(2*I*d*x + 2*I*c) + a*d*e^3)*sqrt(I/(a*d^2*e^5))*log(I*a*d*e^3*sqrt(I/(a*d^2*e^5)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + (a*d*e^3*e^(2*I*d*x + 2*I*c) + a*d*e^3)*sqrt(I/(a*d^2*e^5))*log(-I*a*d*e^3*sqrt(I/(a*d^2*e^5)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) - (a*d*e^3*e^(2*I*d*x + 2*I*c) + a*d*e^3)*sqrt(-I/(a*d^2*e^5))*log(I*a*d*e^3*sqrt(-I/(a*d^2*e^5)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + (a*d*e^3*e^(2*I*d*x + 2*I*c) + a*d*e^3)*sqrt(-I/(a*d^2*e^5))*log(-I*a*d*e^3*sqrt(-I/(a*d^2*e^5)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)))/(a*d*e^3*e^(2*I*d*x + 2*I*c) + a*d*e^3)","A",0
687,1,604,0,0.551786," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(-i \, e^{\left(3 i \, d x + 3 i \, c\right)} + 3 i \, e^{\left(i \, d x + i \, c\right)}\right)} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)} - {\left(a d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{4}\right)} \sqrt{\frac{9 i}{16 \, a d^{2} e^{7}}} \log\left(\frac{4}{3} \, a d e^{4} \sqrt{\frac{9 i}{16 \, a d^{2} e^{7}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + {\left(a d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{4}\right)} \sqrt{\frac{9 i}{16 \, a d^{2} e^{7}}} \log\left(-\frac{4}{3} \, a d e^{4} \sqrt{\frac{9 i}{16 \, a d^{2} e^{7}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) + {\left(a d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{4}\right)} \sqrt{-\frac{9 i}{16 \, a d^{2} e^{7}}} \log\left(\frac{4}{3} \, a d e^{4} \sqrt{-\frac{9 i}{16 \, a d^{2} e^{7}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right) - {\left(a d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{4}\right)} \sqrt{-\frac{9 i}{16 \, a d^{2} e^{7}}} \log\left(-\frac{4}{3} \, a d e^{4} \sqrt{-\frac{9 i}{16 \, a d^{2} e^{7}}} + \sqrt{2} \sqrt{\frac{1}{2}} \sqrt{e e^{\left(2 i \, d x + 2 i \, c\right)} + e} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(-\frac{1}{2} i \, d x - \frac{1}{2} i \, c\right)}\right)}{2 \, {\left(a d e^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, a d e^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + a d e^{4}\right)}}"," ",0,"1/2*(sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(-I*e^(3*I*d*x + 3*I*c) + 3*I*e^(I*d*x + I*c))*e^(-1/2*I*d*x - 1/2*I*c) - (a*d*e^4*e^(4*I*d*x + 4*I*c) + 2*a*d*e^4*e^(2*I*d*x + 2*I*c) + a*d*e^4)*sqrt(9/16*I/(a*d^2*e^7))*log(4/3*a*d*e^4*sqrt(9/16*I/(a*d^2*e^7)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + (a*d*e^4*e^(4*I*d*x + 4*I*c) + 2*a*d*e^4*e^(2*I*d*x + 2*I*c) + a*d*e^4)*sqrt(9/16*I/(a*d^2*e^7))*log(-4/3*a*d*e^4*sqrt(9/16*I/(a*d^2*e^7)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) + (a*d*e^4*e^(4*I*d*x + 4*I*c) + 2*a*d*e^4*e^(2*I*d*x + 2*I*c) + a*d*e^4)*sqrt(-9/16*I/(a*d^2*e^7))*log(4/3*a*d*e^4*sqrt(-9/16*I/(a*d^2*e^7)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)) - (a*d*e^4*e^(4*I*d*x + 4*I*c) + 2*a*d*e^4*e^(2*I*d*x + 2*I*c) + a*d*e^4)*sqrt(-9/16*I/(a*d^2*e^7))*log(-4/3*a*d*e^4*sqrt(-9/16*I/(a*d^2*e^7)) + sqrt(2)*sqrt(1/2)*sqrt(e*e^(2*I*d*x + 2*I*c) + e)*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(-1/2*I*d*x - 1/2*I*c)))/(a*d*e^4*e^(4*I*d*x + 4*I*c) + 2*a*d*e^4*e^(2*I*d*x + 2*I*c) + a*d*e^4)","A",0
688,0,0,0,0.530431," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)^{n} e^{\left(i \, d m x + i \, c m + m \log\left(a e\right) - m \log\left(\frac{2 \, a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}\right)\right)}, x\right)"," ",0,"integral((2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))^n*e^(I*d*m*x + I*c*m + m*log(a*e) - m*log(2*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1))), x)","F",0
689,0,0,0,0.490178," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{4 \, \left(\frac{1}{2} \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} e^{\left(-i \, d x - i \, c\right)}\right)^{m} a^{2} e^{\left(4 i \, d x + 4 i \, c\right)}}{e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(4*(1/2*(e*e^(2*I*d*x + 2*I*c) + e)*e^(-I*d*x - I*c))^m*a^2*e^(4*I*d*x + 4*I*c)/(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1), x)","F",0
690,0,0,0,0.483694," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \left(\frac{1}{2} \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} e^{\left(-i \, d x - i \, c\right)}\right)^{m} a e^{\left(2 i \, d x + 2 i \, c\right)}}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}, x\right)"," ",0,"integral(2*(1/2*(e*e^(2*I*d*x + 2*I*c) + e)*e^(-I*d*x - I*c))^m*a*e^(2*I*d*x + 2*I*c)/(e^(2*I*d*x + 2*I*c) + 1), x)","F",0
691,0,0,0,0.480911," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{1}{2} \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} e^{\left(-i \, d x - i \, c\right)}\right)^{m} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-2 i \, d x - 2 i \, c\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*(1/2*(e*e^(2*I*d*x + 2*I*c) + e)*e^(-I*d*x - I*c))^m*(e^(2*I*d*x + 2*I*c) + 1)*e^(-2*I*d*x - 2*I*c)/a, x)","F",0
692,0,0,0,0.609692," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{1}{2} \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} e^{\left(-i \, d x - i \, c\right)}\right)^{m} {\left(e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-4 i \, d x - 4 i \, c\right)}}{4 \, a^{2}}, x\right)"," ",0,"integral(1/4*(1/2*(e*e^(2*I*d*x + 2*I*c) + e)*e^(-I*d*x - I*c))^m*(e^(4*I*d*x + 4*I*c) + 2*e^(2*I*d*x + 2*I*c) + 1)*e^(-4*I*d*x - 4*I*c)/a^2, x)","F",0
693,0,0,0,0.555028," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{2} \left(\frac{1}{2} \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} e^{\left(-i \, d x - i \, c\right)}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} e^{\left(i \, d x + i \, c\right)}, x\right)"," ",0,"integral(sqrt(2)*(1/2*(e*e^(2*I*d*x + 2*I*c) + e)*e^(-I*d*x - I*c))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*e^(I*d*x + I*c), x)","F",0
694,0,0,0,0.459381," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2} \left(\frac{1}{2} \, {\left(e e^{\left(2 i \, d x + 2 i \, c\right)} + e\right)} e^{\left(-i \, d x - i \, c\right)}\right)^{m} \sqrt{\frac{a}{e^{\left(2 i \, d x + 2 i \, c\right)} + 1}} {\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right)} e^{\left(-i \, d x - i \, c\right)}}{2 \, a}, x\right)"," ",0,"integral(1/2*sqrt(2)*(1/2*(e*e^(2*I*d*x + 2*I*c) + e)*e^(-I*d*x - I*c))^m*sqrt(a/(e^(2*I*d*x + 2*I*c) + 1))*(e^(2*I*d*x + 2*I*c) + 1)*e^(-I*d*x - I*c)/a, x)","F",0
695,0,0,0,0.445610," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \tan\left(f x + e\right)^{3} + 3 \, a b^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{2} b \tan\left(f x + e\right) + a^{3}\right)} \left(d \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b^3*tan(f*x + e)^3 + 3*a*b^2*tan(f*x + e)^2 + 3*a^2*b*tan(f*x + e) + a^3)*(d*cos(f*x + e))^m, x)","F",0
696,0,0,0,0.440610," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}\right)} \left(d \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2)*(d*cos(f*x + e))^m, x)","F",0
697,0,0,0,0.479896," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \tan\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*tan(f*x + e) + a)*(d*cos(f*x + e))^m, x)","F",0
698,0,0,0,0.451029," ","integrate((d*cos(f*x+e))^m/(a+b*tan(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \cos\left(f x + e\right)\right)^{m}}{b \tan\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*cos(f*x + e))^m/(b*tan(f*x + e) + a), x)","F",0
699,0,0,0,0.490050," ","integrate((d*cos(f*x+e))^m/(a+b*tan(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d \cos\left(f x + e\right)\right)^{m}}{b^{2} \tan\left(f x + e\right)^{2} + 2 \, a b \tan\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*cos(f*x + e))^m/(b^2*tan(f*x + e)^2 + 2*a*b*tan(f*x + e) + a^2), x)","F",0
700,0,0,0,0.539640," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cos\left(f x + e\right)\right)^{m} {\left(b \tan\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*cos(f*x + e))^m*(b*tan(f*x + e) + a)^n, x)","F",0
