1,1,114,0,0.792890," ","integrate(sec(d*x+c)^10*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-63 i \, a \tan\left(d x + c\right)^{10} - 70 \, a \tan\left(d x + c\right)^{9} - 315 i \, a \tan\left(d x + c\right)^{8} - 360 \, a \tan\left(d x + c\right)^{7} - 630 i \, a \tan\left(d x + c\right)^{6} - 756 \, a \tan\left(d x + c\right)^{5} - 630 i \, a \tan\left(d x + c\right)^{4} - 840 \, a \tan\left(d x + c\right)^{3} - 315 i \, a \tan\left(d x + c\right)^{2} - 630 \, a \tan\left(d x + c\right)}{630 \, d}"," ",0,"-1/630*(-63*I*a*tan(d*x + c)^10 - 70*a*tan(d*x + c)^9 - 315*I*a*tan(d*x + c)^8 - 360*a*tan(d*x + c)^7 - 630*I*a*tan(d*x + c)^6 - 756*a*tan(d*x + c)^5 - 630*I*a*tan(d*x + c)^4 - 840*a*tan(d*x + c)^3 - 315*I*a*tan(d*x + c)^2 - 630*a*tan(d*x + c))/d","A",0
2,1,92,0,1.002374," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-35 i \, a \tan\left(d x + c\right)^{8} - 40 \, a \tan\left(d x + c\right)^{7} - 140 i \, a \tan\left(d x + c\right)^{6} - 168 \, a \tan\left(d x + c\right)^{5} - 210 i \, a \tan\left(d x + c\right)^{4} - 280 \, a \tan\left(d x + c\right)^{3} - 140 i \, a \tan\left(d x + c\right)^{2} - 280 \, a \tan\left(d x + c\right)}{280 \, d}"," ",0,"-1/280*(-35*I*a*tan(d*x + c)^8 - 40*a*tan(d*x + c)^7 - 140*I*a*tan(d*x + c)^6 - 168*a*tan(d*x + c)^5 - 210*I*a*tan(d*x + c)^4 - 280*a*tan(d*x + c)^3 - 140*I*a*tan(d*x + c)^2 - 280*a*tan(d*x + c))/d","A",0
3,1,70,0,0.673742," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-5 i \, a \tan\left(d x + c\right)^{6} - 6 \, a \tan\left(d x + c\right)^{5} - 15 i \, a \tan\left(d x + c\right)^{4} - 20 \, a \tan\left(d x + c\right)^{3} - 15 i \, a \tan\left(d x + c\right)^{2} - 30 \, a \tan\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(-5*I*a*tan(d*x + c)^6 - 6*a*tan(d*x + c)^5 - 15*I*a*tan(d*x + c)^4 - 20*a*tan(d*x + c)^3 - 15*I*a*tan(d*x + c)^2 - 30*a*tan(d*x + c))/d","A",0
4,1,48,0,0.617095," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-3 i \, a \tan\left(d x + c\right)^{4} - 4 \, a \tan\left(d x + c\right)^{3} - 6 i \, a \tan\left(d x + c\right)^{2} - 12 \, a \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(-3*I*a*tan(d*x + c)^4 - 4*a*tan(d*x + c)^3 - 6*I*a*tan(d*x + c)^2 - 12*a*tan(d*x + c))/d","A",0
5,1,26,0,0.758083," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-i \, a \tan\left(d x + c\right)^{2} - 2 \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(-I*a*tan(d*x + c)^2 - 2*a*tan(d*x + c))/d","A",0
6,1,18,0,0.438872," ","integrate(a+I*a*tan(d*x+c),x, algorithm=""giac"")","a x - \frac{i \, a \log\left({\left| \cos\left(d x + c\right) \right|}\right)}{d}"," ",0,"a*x - I*a*log(abs(cos(d*x + c)))/d","A",0
7,1,23,0,0.532377," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\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
8,1,103,0,0.538105," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{{\left(12 \, a d x e^{\left(2 i \, d x + 2 i \, c\right)} + i \, a 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 \, a e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\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^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - I*a*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-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
9,1,127,0,0.763388," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{{\left(120 \, a d x e^{\left(4 i \, d x + 2 i \, c\right)} + 12 i \, a e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 12 i \, a e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 2 i \, a e^{\left(10 i \, d x + 8 i \, c\right)} - 15 i \, a e^{\left(8 i \, d x + 6 i \, c\right)} - 60 i \, a e^{\left(6 i \, d x + 4 i \, c\right)} + 30 i \, a e^{\left(2 i \, d x\right)} + 3 i \, a e^{\left(-2 i \, c\right)}\right)} e^{\left(-4 i \, d x - 2 i \, c\right)}}{384 \, d}"," ",0,"1/384*(120*a*d*x*e^(4*I*d*x + 2*I*c) + 12*I*a*e^(4*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 12*I*a*e^(4*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) - 2*I*a*e^(10*I*d*x + 8*I*c) - 15*I*a*e^(8*I*d*x + 6*I*c) - 60*I*a*e^(6*I*d*x + 4*I*c) + 30*I*a*e^(2*I*d*x) + 3*I*a*e^(-2*I*c))*e^(-4*I*d*x - 2*I*c)/d","A",0
10,1,151,0,0.721467," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{{\left(840 \, a d x e^{\left(6 i \, d x + 2 i \, c\right)} + 84 i \, a e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 84 i \, a e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 3 i \, a e^{\left(14 i \, d x + 10 i \, c\right)} - 28 i \, a e^{\left(12 i \, d x + 8 i \, c\right)} - 126 i \, a e^{\left(10 i \, d x + 6 i \, c\right)} - 420 i \, a e^{\left(8 i \, d x + 4 i \, c\right)} + 42 i \, a e^{\left(2 i \, d x - 2 i \, c\right)} + 252 i \, a e^{\left(4 i \, d x\right)} + 4 i \, a e^{\left(-4 i \, c\right)}\right)} e^{\left(-6 i \, d x - 2 i \, c\right)}}{3072 \, d}"," ",0,"1/3072*(840*a*d*x*e^(6*I*d*x + 2*I*c) + 84*I*a*e^(6*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 84*I*a*e^(6*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) - 3*I*a*e^(14*I*d*x + 10*I*c) - 28*I*a*e^(12*I*d*x + 8*I*c) - 126*I*a*e^(10*I*d*x + 6*I*c) - 420*I*a*e^(8*I*d*x + 4*I*c) + 42*I*a*e^(2*I*d*x - 2*I*c) + 252*I*a*e^(4*I*d*x) + 4*I*a*e^(-4*I*c))*e^(-6*I*d*x - 2*I*c)/d","A",0
11,1,181,0,2.251830," ","integrate(sec(d*x+c)^7*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{105 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 105 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + \frac{2 \, {\left(231 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 336 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 196 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 595 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1680 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 595 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1008 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 196 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 231 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 i \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{336 \, d}"," ",0,"1/336*(105*a*log(tan(1/2*d*x + 1/2*c) + 1) - 105*a*log(tan(1/2*d*x + 1/2*c) - 1) + 2*(231*a*tan(1/2*d*x + 1/2*c)^13 - 336*I*a*tan(1/2*d*x + 1/2*c)^12 - 196*a*tan(1/2*d*x + 1/2*c)^11 + 595*a*tan(1/2*d*x + 1/2*c)^9 - 1680*I*a*tan(1/2*d*x + 1/2*c)^8 - 595*a*tan(1/2*d*x + 1/2*c)^5 - 1008*I*a*tan(1/2*d*x + 1/2*c)^4 + 196*a*tan(1/2*d*x + 1/2*c)^3 - 231*a*tan(1/2*d*x + 1/2*c) - 48*I*a)/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","B",0
12,1,139,0,0.713638," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{15 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 15 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + \frac{2 \, {\left(25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 40 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 i \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{40 \, d}"," ",0,"1/40*(15*a*log(tan(1/2*d*x + 1/2*c) + 1) - 15*a*log(tan(1/2*d*x + 1/2*c) - 1) + 2*(25*a*tan(1/2*d*x + 1/2*c)^9 - 40*I*a*tan(1/2*d*x + 1/2*c)^8 - 10*a*tan(1/2*d*x + 1/2*c)^7 - 80*I*a*tan(1/2*d*x + 1/2*c)^4 + 10*a*tan(1/2*d*x + 1/2*c)^3 - 25*a*tan(1/2*d*x + 1/2*c) - 8*I*a)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
13,1,97,0,1.424385," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 i \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*a*log(tan(1/2*d*x + 1/2*c) + 1) - 3*a*log(tan(1/2*d*x + 1/2*c) - 1) + 2*(3*a*tan(1/2*d*x + 1/2*c)^5 - 6*I*a*tan(1/2*d*x + 1/2*c)^4 - 3*a*tan(1/2*d*x + 1/2*c) - 2*I*a)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
14,1,52,0,0.964639," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) - \frac{2 i \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"(a*log(tan(1/2*d*x + 1/2*c) + 1) - a*log(tan(1/2*d*x + 1/2*c) - 1) - 2*I*a/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
15,1,84,0,4.050863," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{4 i \, a e^{\left(i \, d x + i \, c\right)} + a \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + a \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - a \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - a \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right)}{4 \, d}"," ",0,"-1/4*(4*I*a*e^(I*d*x + I*c) + a*log(I*e^(I*d*x + I*c) + 1) + a*log(I*e^(I*d*x + I*c) - 1) - a*log(-I*e^(I*d*x + I*c) + 1) - a*log(-I*e^(I*d*x + I*c) - 1))/d","B",0
16,1,196,0,1.182047," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(9 \, a e^{\left(i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 6 \, a e^{\left(i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9 \, a e^{\left(i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 6 \, a e^{\left(i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3 \, a e^{\left(i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3 \, a e^{\left(i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 4 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 24 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 12 i \, a\right)} e^{\left(-i \, d x - i \, c\right)}}{48 \, d}"," ",0,"-1/48*(9*a*e^(I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 6*a*e^(I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) - 9*a*e^(I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 6*a*e^(I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3*a*e^(I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 3*a*e^(I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 4*I*a*e^(4*I*d*x + 4*I*c) + 24*I*a*e^(2*I*d*x + 2*I*c) - 12*I*a)*e^(-I*d*x - I*c)/d","B",0
17,1,220,0,1.042901," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(135 \, a e^{\left(3 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 90 \, a e^{\left(3 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 135 \, a e^{\left(3 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 90 \, a e^{\left(3 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 45 \, a e^{\left(3 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 45 \, a e^{\left(3 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 12 i \, a e^{\left(8 i \, d x + 6 i \, c\right)} + 80 i \, a e^{\left(6 i \, d x + 4 i \, c\right)} + 360 i \, a e^{\left(4 i \, d x + 2 i \, c\right)} - 240 i \, a e^{\left(2 i \, d x\right)} - 20 i \, a e^{\left(-2 i \, c\right)}\right)} e^{\left(-3 i \, d x - i \, c\right)}}{960 \, d}"," ",0,"-1/960*(135*a*e^(3*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 90*a*e^(3*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) - 135*a*e^(3*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 90*a*e^(3*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 45*a*e^(3*I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 45*a*e^(3*I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 12*I*a*e^(8*I*d*x + 6*I*c) + 80*I*a*e^(6*I*d*x + 4*I*c) + 360*I*a*e^(4*I*d*x + 2*I*c) - 240*I*a*e^(2*I*d*x) - 20*I*a*e^(-2*I*c))*e^(-3*I*d*x - I*c)/d","B",0
18,1,244,0,1.253486," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(1015 \, a e^{\left(5 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 700 \, a e^{\left(5 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1015 \, a e^{\left(5 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 700 \, a e^{\left(5 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 315 \, a e^{\left(5 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 315 \, a e^{\left(5 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 20 i \, a e^{\left(12 i \, d x + 8 i \, c\right)} + 168 i \, a e^{\left(10 i \, d x + 6 i \, c\right)} + 700 i \, a e^{\left(8 i \, d x + 4 i \, c\right)} + 2800 i \, a e^{\left(6 i \, d x + 2 i \, c\right)} - 280 i \, a e^{\left(2 i \, d x - 2 i \, c\right)} - 2100 i \, a e^{\left(4 i \, d x\right)} - 28 i \, a e^{\left(-4 i \, c\right)}\right)} e^{\left(-5 i \, d x - i \, c\right)}}{8960 \, d}"," ",0,"-1/8960*(1015*a*e^(5*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 700*a*e^(5*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) - 1015*a*e^(5*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 700*a*e^(5*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 315*a*e^(5*I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 315*a*e^(5*I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 20*I*a*e^(12*I*d*x + 8*I*c) + 168*I*a*e^(10*I*d*x + 6*I*c) + 700*I*a*e^(8*I*d*x + 4*I*c) + 2800*I*a*e^(6*I*d*x + 2*I*c) - 280*I*a*e^(2*I*d*x - 2*I*c) - 2100*I*a*e^(4*I*d*x) - 28*I*a*e^(-4*I*c))*e^(-5*I*d*x - I*c)/d","B",0
19,1,108,0,0.997268," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{28 \, a^{2} \tan\left(d x + c\right)^{9} - 63 i \, a^{2} \tan\left(d x + c\right)^{8} + 72 \, a^{2} \tan\left(d x + c\right)^{7} - 252 i \, a^{2} \tan\left(d x + c\right)^{6} - 378 i \, a^{2} \tan\left(d x + c\right)^{4} - 168 \, a^{2} \tan\left(d x + c\right)^{3} - 252 i \, a^{2} \tan\left(d x + c\right)^{2} - 252 \, a^{2} \tan\left(d x + c\right)}{252 \, d}"," ",0,"-1/252*(28*a^2*tan(d*x + c)^9 - 63*I*a^2*tan(d*x + c)^8 + 72*a^2*tan(d*x + c)^7 - 252*I*a^2*tan(d*x + c)^6 - 378*I*a^2*tan(d*x + c)^4 - 168*a^2*tan(d*x + c)^3 - 252*I*a^2*tan(d*x + c)^2 - 252*a^2*tan(d*x + c))/d","A",0
20,1,95,0,1.450540," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{15 \, a^{2} \tan\left(d x + c\right)^{7} - 35 i \, a^{2} \tan\left(d x + c\right)^{6} + 21 \, a^{2} \tan\left(d x + c\right)^{5} - 105 i \, a^{2} \tan\left(d x + c\right)^{4} - 35 \, a^{2} \tan\left(d x + c\right)^{3} - 105 i \, a^{2} \tan\left(d x + c\right)^{2} - 105 \, a^{2} \tan\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(15*a^2*tan(d*x + c)^7 - 35*I*a^2*tan(d*x + c)^6 + 21*a^2*tan(d*x + c)^5 - 105*I*a^2*tan(d*x + c)^4 - 35*a^2*tan(d*x + c)^3 - 105*I*a^2*tan(d*x + c)^2 - 105*a^2*tan(d*x + c))/d","A",0
21,1,56,0,0.951856," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, a^{2} \tan\left(d x + c\right)^{5} - 5 i \, a^{2} \tan\left(d x + c\right)^{4} - 10 i \, a^{2} \tan\left(d x + c\right)^{2} - 10 \, a^{2} \tan\left(d x + c\right)}{10 \, d}"," ",0,"-1/10*(2*a^2*tan(d*x + c)^5 - 5*I*a^2*tan(d*x + c)^4 - 10*I*a^2*tan(d*x + c)^2 - 10*a^2*tan(d*x + c))/d","A",0
22,1,42,0,1.096730," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{a^{2} \tan\left(d x + c\right)^{3} - 3 i \, a^{2} \tan\left(d x + c\right)^{2} - 3 \, a^{2} \tan\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(a^2*tan(d*x + c)^3 - 3*I*a^2*tan(d*x + c)^2 - 3*a^2*tan(d*x + c))/d","A",0
23,1,65,0,0.566843," ","integrate((a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{-2 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 2 i \, a^{2} \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)} + d}"," ",0,"(-2*I*a^2*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 2*I*a^2*log(e^(2*I*d*x + 2*I*c) + 1) - 2*I*a^2)/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
24,1,17,0,0.956901," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\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
25,1,257,0,1.170093," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{8 \, a^{2} d x e^{\left(4 i \, d x + 2 i \, c\right)} + 16 \, a^{2} d x e^{\left(2 i \, d x\right)} + 8 \, a^{2} d x e^{\left(-2 i \, c\right)} - i \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 2 i \, a^{2} e^{\left(2 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - i \, a^{2} e^{\left(-2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + i \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 2 i \, a^{2} e^{\left(2 i \, d x\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + i \, a^{2} e^{\left(-2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 2 i \, a^{2} e^{\left(8 i \, d x + 6 i \, c\right)} - 12 i \, a^{2} e^{\left(6 i \, d x + 4 i \, c\right)} - 18 i \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} - 8 i \, a^{2} e^{\left(2 i \, d x\right)}}{32 \, {\left(d e^{\left(4 i \, d x + 2 i \, c\right)} + 2 \, d e^{\left(2 i \, d x\right)} + d e^{\left(-2 i \, c\right)}\right)}}"," ",0,"1/32*(8*a^2*d*x*e^(4*I*d*x + 2*I*c) + 16*a^2*d*x*e^(2*I*d*x) + 8*a^2*d*x*e^(-2*I*c) - I*a^2*e^(4*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 2*I*a^2*e^(2*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) - I*a^2*e^(-2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + I*a^2*e^(4*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 2*I*a^2*e^(2*I*d*x)*log(e^(2*I*d*x) + e^(-2*I*c)) + I*a^2*e^(-2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) - 2*I*a^2*e^(8*I*d*x + 6*I*c) - 12*I*a^2*e^(6*I*d*x + 4*I*c) - 18*I*a^2*e^(4*I*d*x + 2*I*c) - 8*I*a^2*e^(2*I*d*x))/(d*e^(4*I*d*x + 2*I*c) + 2*d*e^(2*I*d*x) + d*e^(-2*I*c))","B",0
26,1,169,0,1.106799," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{96 \, a^{2} d x e^{\left(6 i \, d x + 4 i \, c\right)} + 192 \, a^{2} d x e^{\left(4 i \, d x + 2 i \, c\right)} + 96 \, a^{2} d x e^{\left(2 i \, d x\right)} - 4 i \, a^{2} e^{\left(12 i \, d x + 10 i \, c\right)} - 32 i \, a^{2} e^{\left(10 i \, d x + 8 i \, c\right)} - 124 i \, a^{2} e^{\left(8 i \, d x + 6 i \, c\right)} - 168 i \, a^{2} e^{\left(6 i \, d x + 4 i \, c\right)} - 60 i \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} + 24 i \, a^{2} e^{\left(2 i \, d x\right)} + 12 i \, a^{2} e^{\left(-2 i \, c\right)}}{384 \, {\left(d e^{\left(6 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(4 i \, d x + 2 i \, c\right)} + d e^{\left(2 i \, d x\right)}\right)}}"," ",0,"1/384*(96*a^2*d*x*e^(6*I*d*x + 4*I*c) + 192*a^2*d*x*e^(4*I*d*x + 2*I*c) + 96*a^2*d*x*e^(2*I*d*x) - 4*I*a^2*e^(12*I*d*x + 10*I*c) - 32*I*a^2*e^(10*I*d*x + 8*I*c) - 124*I*a^2*e^(8*I*d*x + 6*I*c) - 168*I*a^2*e^(6*I*d*x + 4*I*c) - 60*I*a^2*e^(4*I*d*x + 2*I*c) + 24*I*a^2*e^(2*I*d*x) + 12*I*a^2*e^(-2*I*c))/(d*e^(6*I*d*x + 4*I*c) + 2*d*e^(4*I*d*x + 2*I*c) + d*e^(2*I*d*x))","A",0
27,1,342,0,2.031031," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{120 \, a^{2} d x e^{\left(8 i \, d x + 4 i \, c\right)} + 240 \, a^{2} d x e^{\left(6 i \, d x + 2 i \, c\right)} + 120 \, a^{2} d x e^{\left(4 i \, d x\right)} + 8 i \, a^{2} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 16 i \, a^{2} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 8 i \, a^{2} e^{\left(4 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 8 i \, a^{2} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 16 i \, a^{2} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 8 i \, a^{2} e^{\left(4 i \, d x\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - i \, a^{2} e^{\left(16 i \, d x + 12 i \, c\right)} - 10 i \, a^{2} e^{\left(14 i \, d x + 10 i \, c\right)} - 47 i \, a^{2} e^{\left(12 i \, d x + 8 i \, c\right)} - 148 i \, a^{2} e^{\left(10 i \, d x + 6 i \, c\right)} - 190 i \, a^{2} e^{\left(8 i \, d x + 4 i \, c\right)} - 56 i \, a^{2} e^{\left(6 i \, d x + 2 i \, c\right)} + 28 i \, a^{2} e^{\left(2 i \, d x - 2 i \, c\right)} + 50 i \, a^{2} e^{\left(4 i \, d x\right)} + 2 i \, a^{2} e^{\left(-4 i \, c\right)}}{512 \, {\left(d e^{\left(8 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(6 i \, d x + 2 i \, c\right)} + d e^{\left(4 i \, d x\right)}\right)}}"," ",0,"1/512*(120*a^2*d*x*e^(8*I*d*x + 4*I*c) + 240*a^2*d*x*e^(6*I*d*x + 2*I*c) + 120*a^2*d*x*e^(4*I*d*x) + 8*I*a^2*e^(8*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 16*I*a^2*e^(6*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 8*I*a^2*e^(4*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) - 8*I*a^2*e^(8*I*d*x + 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) - 16*I*a^2*e^(6*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) - 8*I*a^2*e^(4*I*d*x)*log(e^(2*I*d*x) + e^(-2*I*c)) - I*a^2*e^(16*I*d*x + 12*I*c) - 10*I*a^2*e^(14*I*d*x + 10*I*c) - 47*I*a^2*e^(12*I*d*x + 8*I*c) - 148*I*a^2*e^(10*I*d*x + 6*I*c) - 190*I*a^2*e^(8*I*d*x + 4*I*c) - 56*I*a^2*e^(6*I*d*x + 2*I*c) + 28*I*a^2*e^(2*I*d*x - 2*I*c) + 50*I*a^2*e^(4*I*d*x) + 2*I*a^2*e^(-4*I*c))/(d*e^(8*I*d*x + 4*I*c) + 2*d*e^(6*I*d*x + 2*I*c) + d*e^(4*I*d*x))","B",0
28,1,237,0,1.003273," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{105 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 105 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + \frac{2 \, {\left(135 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 445 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 960 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 445 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 135 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 i \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(105*a^2*log(tan(1/2*d*x + 1/2*c) + 1) - 105*a^2*log(tan(1/2*d*x + 1/2*c) - 1) + 2*(135*a^2*tan(1/2*d*x + 1/2*c)^11 - 480*I*a^2*tan(1/2*d*x + 1/2*c)^10 - 445*a^2*tan(1/2*d*x + 1/2*c)^9 + 480*I*a^2*tan(1/2*d*x + 1/2*c)^8 - 330*a^2*tan(1/2*d*x + 1/2*c)^7 - 960*I*a^2*tan(1/2*d*x + 1/2*c)^6 - 330*a^2*tan(1/2*d*x + 1/2*c)^5 + 960*I*a^2*tan(1/2*d*x + 1/2*c)^4 - 445*a^2*tan(1/2*d*x + 1/2*c)^3 - 96*I*a^2*tan(1/2*d*x + 1/2*c)^2 + 135*a^2*tan(1/2*d*x + 1/2*c) + 96*I*a^2)/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
29,1,173,0,0.788709," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 15 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + \frac{2 \, {\left(9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 33 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 33 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 i \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(15*a^2*log(tan(1/2*d*x + 1/2*c) + 1) - 15*a^2*log(tan(1/2*d*x + 1/2*c) - 1) + 2*(9*a^2*tan(1/2*d*x + 1/2*c)^7 - 48*I*a^2*tan(1/2*d*x + 1/2*c)^6 - 33*a^2*tan(1/2*d*x + 1/2*c)^5 + 48*I*a^2*tan(1/2*d*x + 1/2*c)^4 - 33*a^2*tan(1/2*d*x + 1/2*c)^3 - 16*I*a^2*tan(1/2*d*x + 1/2*c)^2 + 9*a^2*tan(1/2*d*x + 1/2*c) + 16*I*a^2)/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
30,1,107,0,0.766937," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 3 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) - \frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 i \, a^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(3*a^2*log(tan(1/2*d*x + 1/2*c) + 1) - 3*a^2*log(tan(1/2*d*x + 1/2*c) - 1) - 2*(a^2*tan(1/2*d*x + 1/2*c)^3 + 4*I*a^2*tan(1/2*d*x + 1/2*c)^2 + a^2*tan(1/2*d*x + 1/2*c) - 4*I*a^2)/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
31,1,56,0,1.194416," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{-2 i \, a^{2} e^{\left(i \, d x + i \, c\right)} - a^{2} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + a^{2} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right)}{d}"," ",0,"(-2*I*a^2*e^(I*d*x + I*c) - a^2*log(I*e^(I*d*x + I*c) - 1) + a^2*log(-I*e^(I*d*x + I*c) - 1))/d","A",0
32,1,531,0,1.189184," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{24 \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 48 \, a^{2} e^{\left(2 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 24 \, a^{2} e^{\left(-2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 27 \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 54 \, a^{2} e^{\left(2 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 27 \, a^{2} e^{\left(-2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 24 \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 48 \, a^{2} e^{\left(2 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 24 \, a^{2} e^{\left(-2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 27 \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 54 \, a^{2} e^{\left(2 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 27 \, a^{2} e^{\left(-2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3 \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 6 \, a^{2} e^{\left(2 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3 \, a^{2} e^{\left(-2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3 \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 6 \, a^{2} e^{\left(2 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3 \, a^{2} e^{\left(-2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 16 i \, a^{2} e^{\left(7 i \, d x + 5 i \, c\right)} + 80 i \, a^{2} e^{\left(5 i \, d x + 3 i \, c\right)} + 112 i \, a^{2} e^{\left(3 i \, d x + i \, c\right)} + 48 i \, a^{2} e^{\left(i \, d x - i \, c\right)}}{96 \, {\left(d e^{\left(4 i \, d x + 2 i \, c\right)} + 2 \, d e^{\left(2 i \, d x\right)} + d e^{\left(-2 i \, c\right)}\right)}}"," ",0,"-1/96*(24*a^2*e^(4*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 48*a^2*e^(2*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 24*a^2*e^(-2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 27*a^2*e^(4*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 54*a^2*e^(2*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 27*a^2*e^(-2*I*c)*log(I*e^(I*d*x + I*c) - 1) - 24*a^2*e^(4*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 48*a^2*e^(2*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 24*a^2*e^(-2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 27*a^2*e^(4*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 54*a^2*e^(2*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 27*a^2*e^(-2*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 3*a^2*e^(4*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 6*a^2*e^(2*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) + 3*a^2*e^(-2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 3*a^2*e^(4*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 6*a^2*e^(2*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) - 3*a^2*e^(-2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 16*I*a^2*e^(7*I*d*x + 5*I*c) + 80*I*a^2*e^(5*I*d*x + 3*I*c) + 112*I*a^2*e^(3*I*d*x + I*c) + 48*I*a^2*e^(I*d*x - I*c))/(d*e^(4*I*d*x + 2*I*c) + 2*d*e^(2*I*d*x) + d*e^(-2*I*c))","B",0
33,1,613,0,2.023381," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{45 \, a^{2} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 90 \, a^{2} e^{\left(3 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 45 \, a^{2} e^{\left(i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 40 \, a^{2} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 80 \, a^{2} e^{\left(3 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 40 \, a^{2} e^{\left(i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 45 \, a^{2} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 90 \, a^{2} e^{\left(3 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 45 \, a^{2} e^{\left(i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 40 \, a^{2} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 80 \, a^{2} e^{\left(3 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 40 \, a^{2} e^{\left(i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5 \, a^{2} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 10 \, a^{2} e^{\left(3 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 5 \, a^{2} e^{\left(i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 5 \, a^{2} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 10 \, a^{2} e^{\left(3 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 5 \, a^{2} e^{\left(i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 4 i \, a^{2} e^{\left(10 i \, d x + 8 i \, c\right)} + 28 i \, a^{2} e^{\left(8 i \, d x + 6 i \, c\right)} + 104 i \, a^{2} e^{\left(6 i \, d x + 4 i \, c\right)} + 120 i \, a^{2} e^{\left(4 i \, d x + 2 i \, c\right)} + 20 i \, a^{2} e^{\left(2 i \, d x\right)} - 20 i \, a^{2} e^{\left(-2 i \, c\right)}}{160 \, {\left(d e^{\left(5 i \, d x + 3 i \, c\right)} + 2 \, d e^{\left(3 i \, d x + i \, c\right)} + d e^{\left(i \, d x - i \, c\right)}\right)}}"," ",0,"-1/160*(45*a^2*e^(5*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 90*a^2*e^(3*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 45*a^2*e^(I*d*x - I*c)*log(I*e^(I*d*x + I*c) + 1) + 40*a^2*e^(5*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 80*a^2*e^(3*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) + 40*a^2*e^(I*d*x - I*c)*log(I*e^(I*d*x + I*c) - 1) - 45*a^2*e^(5*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 90*a^2*e^(3*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 45*a^2*e^(I*d*x - I*c)*log(-I*e^(I*d*x + I*c) + 1) - 40*a^2*e^(5*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 80*a^2*e^(3*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 40*a^2*e^(I*d*x - I*c)*log(-I*e^(I*d*x + I*c) - 1) - 5*a^2*e^(5*I*d*x + 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 10*a^2*e^(3*I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 5*a^2*e^(I*d*x - I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 5*a^2*e^(5*I*d*x + 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 10*a^2*e^(3*I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 5*a^2*e^(I*d*x - I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 4*I*a^2*e^(10*I*d*x + 8*I*c) + 28*I*a^2*e^(8*I*d*x + 6*I*c) + 104*I*a^2*e^(6*I*d*x + 4*I*c) + 120*I*a^2*e^(4*I*d*x + 2*I*c) + 20*I*a^2*e^(2*I*d*x) - 20*I*a^2*e^(-2*I*c))/(d*e^(5*I*d*x + 3*I*c) + 2*d*e^(3*I*d*x + I*c) + d*e^(I*d*x - I*c))","B",0
34,1,641,0,2.856145," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{2583 \, a^{2} e^{\left(7 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5166 \, a^{2} e^{\left(5 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2583 \, a^{2} e^{\left(3 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2121 \, a^{2} e^{\left(7 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 4242 \, a^{2} e^{\left(5 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 2121 \, a^{2} e^{\left(3 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 2583 \, a^{2} e^{\left(7 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5166 \, a^{2} e^{\left(5 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2583 \, a^{2} e^{\left(3 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2121 \, a^{2} e^{\left(7 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 4242 \, a^{2} e^{\left(5 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 2121 \, a^{2} e^{\left(3 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 462 \, a^{2} e^{\left(7 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 924 \, a^{2} e^{\left(5 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 462 \, a^{2} e^{\left(3 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 462 \, a^{2} e^{\left(7 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 924 \, a^{2} e^{\left(5 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 462 \, a^{2} e^{\left(3 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 48 i \, a^{2} e^{\left(14 i \, d x + 10 i \, c\right)} + 432 i \, a^{2} e^{\left(12 i \, d x + 8 i \, c\right)} + 1840 i \, a^{2} e^{\left(10 i \, d x + 6 i \, c\right)} + 5936 i \, a^{2} e^{\left(8 i \, d x + 4 i \, c\right)} + 6160 i \, a^{2} e^{\left(6 i \, d x + 2 i \, c\right)} - 1904 i \, a^{2} e^{\left(2 i \, d x - 2 i \, c\right)} - 112 i \, a^{2} e^{\left(4 i \, d x\right)} - 112 i \, a^{2} e^{\left(-4 i \, c\right)}}{10752 \, {\left(d e^{\left(7 i \, d x + 3 i \, c\right)} + 2 \, d e^{\left(5 i \, d x + i \, c\right)} + d e^{\left(3 i \, d x - i \, c\right)}\right)}}"," ",0,"-1/10752*(2583*a^2*e^(7*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 5166*a^2*e^(5*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 2583*a^2*e^(3*I*d*x - I*c)*log(I*e^(I*d*x + I*c) + 1) + 2121*a^2*e^(7*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 4242*a^2*e^(5*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) + 2121*a^2*e^(3*I*d*x - I*c)*log(I*e^(I*d*x + I*c) - 1) - 2583*a^2*e^(7*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 5166*a^2*e^(5*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2583*a^2*e^(3*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2121*a^2*e^(7*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 4242*a^2*e^(5*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 2121*a^2*e^(3*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) - 1) - 462*a^2*e^(7*I*d*x + 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 924*a^2*e^(5*I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 462*a^2*e^(3*I*d*x - I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 462*a^2*e^(7*I*d*x + 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 924*a^2*e^(5*I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 462*a^2*e^(3*I*d*x - I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 48*I*a^2*e^(14*I*d*x + 10*I*c) + 432*I*a^2*e^(12*I*d*x + 8*I*c) + 1840*I*a^2*e^(10*I*d*x + 6*I*c) + 5936*I*a^2*e^(8*I*d*x + 4*I*c) + 6160*I*a^2*e^(6*I*d*x + 2*I*c) - 1904*I*a^2*e^(2*I*d*x - 2*I*c) - 112*I*a^2*e^(4*I*d*x) - 112*I*a^2*e^(-4*I*c))/(d*e^(7*I*d*x + 3*I*c) + 2*d*e^(5*I*d*x + I*c) + d*e^(3*I*d*x - I*c))","B",0
35,1,669,0,2.120326," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{18585 \, a^{2} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 37170 \, a^{2} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 18585 \, a^{2} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 14625 \, a^{2} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 29250 \, a^{2} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 14625 \, a^{2} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 18585 \, a^{2} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 37170 \, a^{2} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 18585 \, a^{2} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 14625 \, a^{2} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 29250 \, a^{2} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 14625 \, a^{2} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3960 \, a^{2} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 7920 \, a^{2} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3960 \, a^{2} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3960 \, a^{2} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 7920 \, a^{2} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3960 \, a^{2} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 80 i \, a^{2} e^{\left(18 i \, d x + 12 i \, c\right)} + 880 i \, a^{2} e^{\left(16 i \, d x + 10 i \, c\right)} + 4544 i \, a^{2} e^{\left(14 i \, d x + 8 i \, c\right)} + 15168 i \, a^{2} e^{\left(12 i \, d x + 6 i \, c\right)} + 45024 i \, a^{2} e^{\left(10 i \, d x + 4 i \, c\right)} + 43680 i \, a^{2} e^{\left(8 i \, d x + 2 i \, c\right)} - 18624 i \, a^{2} e^{\left(4 i \, d x - 2 i \, c\right)} - 1968 i \, a^{2} e^{\left(2 i \, d x - 4 i \, c\right)} - 6720 i \, a^{2} e^{\left(6 i \, d x\right)} - 144 i \, a^{2} e^{\left(-6 i \, c\right)}}{92160 \, {\left(d e^{\left(9 i \, d x + 3 i \, c\right)} + 2 \, d e^{\left(7 i \, d x + i \, c\right)} + d e^{\left(5 i \, d x - i \, c\right)}\right)}}"," ",0,"-1/92160*(18585*a^2*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 37170*a^2*e^(7*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 18585*a^2*e^(5*I*d*x - I*c)*log(I*e^(I*d*x + I*c) + 1) + 14625*a^2*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 29250*a^2*e^(7*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) + 14625*a^2*e^(5*I*d*x - I*c)*log(I*e^(I*d*x + I*c) - 1) - 18585*a^2*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 37170*a^2*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 18585*a^2*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) + 1) - 14625*a^2*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 29250*a^2*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 14625*a^2*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3960*a^2*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 7920*a^2*e^(7*I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 3960*a^2*e^(5*I*d*x - I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 3960*a^2*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 7920*a^2*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 3960*a^2*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 80*I*a^2*e^(18*I*d*x + 12*I*c) + 880*I*a^2*e^(16*I*d*x + 10*I*c) + 4544*I*a^2*e^(14*I*d*x + 8*I*c) + 15168*I*a^2*e^(12*I*d*x + 6*I*c) + 45024*I*a^2*e^(10*I*d*x + 4*I*c) + 43680*I*a^2*e^(8*I*d*x + 2*I*c) - 18624*I*a^2*e^(4*I*d*x - 2*I*c) - 1968*I*a^2*e^(2*I*d*x - 4*I*c) - 6720*I*a^2*e^(6*I*d*x) - 144*I*a^2*e^(-6*I*c))/(d*e^(9*I*d*x + 3*I*c) + 2*d*e^(7*I*d*x + I*c) + d*e^(5*I*d*x - I*c))","B",0
36,1,108,0,1.312091," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{21 i \, a^{3} \tan\left(d x + c\right)^{10} + 70 \, a^{3} \tan\left(d x + c\right)^{9} + 240 \, a^{3} \tan\left(d x + c\right)^{7} - 210 i \, a^{3} \tan\left(d x + c\right)^{6} + 252 \, a^{3} \tan\left(d x + c\right)^{5} - 420 i \, a^{3} \tan\left(d x + c\right)^{4} - 315 i \, a^{3} \tan\left(d x + c\right)^{2} - 210 \, a^{3} \tan\left(d x + c\right)}{210 \, d}"," ",0,"-1/210*(21*I*a^3*tan(d*x + c)^10 + 70*a^3*tan(d*x + c)^9 + 240*a^3*tan(d*x + c)^7 - 210*I*a^3*tan(d*x + c)^6 + 252*a^3*tan(d*x + c)^5 - 420*I*a^3*tan(d*x + c)^4 - 315*I*a^3*tan(d*x + c)^2 - 210*a^3*tan(d*x + c))/d","A",0
37,1,108,0,1.417187," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{21 i \, a^{3} \tan\left(d x + c\right)^{8} + 72 \, a^{3} \tan\left(d x + c\right)^{7} - 28 i \, a^{3} \tan\left(d x + c\right)^{6} + 168 \, a^{3} \tan\left(d x + c\right)^{5} - 210 i \, a^{3} \tan\left(d x + c\right)^{4} + 56 \, a^{3} \tan\left(d x + c\right)^{3} - 252 i \, a^{3} \tan\left(d x + c\right)^{2} - 168 \, a^{3} \tan\left(d x + c\right)}{168 \, d}"," ",0,"-1/168*(21*I*a^3*tan(d*x + c)^8 + 72*a^3*tan(d*x + c)^7 - 28*I*a^3*tan(d*x + c)^6 + 168*a^3*tan(d*x + c)^5 - 210*I*a^3*tan(d*x + c)^4 + 56*a^3*tan(d*x + c)^3 - 252*I*a^3*tan(d*x + c)^2 - 168*a^3*tan(d*x + c))/d","A",0
38,1,82,0,1.622297," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{5 i \, a^{3} \tan\left(d x + c\right)^{6} + 18 \, a^{3} \tan\left(d x + c\right)^{5} - 15 i \, a^{3} \tan\left(d x + c\right)^{4} + 20 \, a^{3} \tan\left(d x + c\right)^{3} - 45 i \, a^{3} \tan\left(d x + c\right)^{2} - 30 \, a^{3} \tan\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(5*I*a^3*tan(d*x + c)^6 + 18*a^3*tan(d*x + c)^5 - 15*I*a^3*tan(d*x + c)^4 + 20*a^3*tan(d*x + c)^3 - 45*I*a^3*tan(d*x + c)^2 - 30*a^3*tan(d*x + c))/d","A",0
39,1,56,0,1.149885," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{i \, a^{3} \tan\left(d x + c\right)^{4} + 4 \, a^{3} \tan\left(d x + c\right)^{3} - 6 i \, a^{3} \tan\left(d x + c\right)^{2} - 4 \, a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(I*a^3*tan(d*x + c)^4 + 4*a^3*tan(d*x + c)^3 - 6*I*a^3*tan(d*x + c)^2 - 4*a^3*tan(d*x + c))/d","B",0
40,1,117,0,0.661301," ","integrate((a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{-4 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 8 i \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} - 4 i \, a^{3} \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 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(-4*I*a^3*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 8*I*a^3*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 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) - 6*I*a^3)/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
41,1,36,0,1.941823," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\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
42,1,135,0,1.711751," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{-8 i \, a^{3} e^{\left(12 i \, d x + 8 i \, c\right)} - 48 i \, a^{3} e^{\left(10 i \, d x + 6 i \, c\right)} - 112 i \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} - 128 i \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} - 16 i \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} - 72 i \, a^{3} e^{\left(4 i \, d x\right)}}{64 \, {\left(d e^{\left(8 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 2 i \, c\right)} + 4 \, d e^{\left(2 i \, d x - 2 i \, c\right)} + 6 \, d e^{\left(4 i \, d x\right)} + d e^{\left(-4 i \, c\right)}\right)}}"," ",0,"1/64*(-8*I*a^3*e^(12*I*d*x + 8*I*c) - 48*I*a^3*e^(10*I*d*x + 6*I*c) - 112*I*a^3*e^(8*I*d*x + 4*I*c) - 128*I*a^3*e^(6*I*d*x + 2*I*c) - 16*I*a^3*e^(2*I*d*x - 2*I*c) - 72*I*a^3*e^(4*I*d*x))/(d*e^(8*I*d*x + 4*I*c) + 4*d*e^(6*I*d*x + 2*I*c) + 4*d*e^(2*I*d*x - 2*I*c) + 6*d*e^(4*I*d*x) + d*e^(-4*I*c))","B",0
43,1,457,0,2.167192," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{48 \, a^{3} d x e^{\left(8 i \, d x + 4 i \, c\right)} + 192 \, a^{3} d x e^{\left(6 i \, d x + 2 i \, c\right)} + 192 \, a^{3} d x e^{\left(2 i \, d x - 2 i \, c\right)} + 288 \, a^{3} d x e^{\left(4 i \, d x\right)} + 48 \, a^{3} d x e^{\left(-4 i \, c\right)} - 12 i \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 48 i \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 48 i \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 72 i \, a^{3} e^{\left(4 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 12 i \, a^{3} e^{\left(-4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 12 i \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 48 i \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 48 i \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 72 i \, a^{3} e^{\left(4 i \, d x\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 12 i \, a^{3} e^{\left(-4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 8 i \, a^{3} e^{\left(14 i \, d x + 10 i \, c\right)} - 68 i \, a^{3} e^{\left(12 i \, d x + 8 i \, c\right)} - 264 i \, a^{3} e^{\left(10 i \, d x + 6 i \, c\right)} - 536 i \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} - 584 i \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} - 72 i \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} - 324 i \, a^{3} e^{\left(4 i \, d x\right)}}{384 \, {\left(d e^{\left(8 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 2 i \, c\right)} + 4 \, d e^{\left(2 i \, d x - 2 i \, c\right)} + 6 \, d e^{\left(4 i \, d x\right)} + d e^{\left(-4 i \, c\right)}\right)}}"," ",0,"1/384*(48*a^3*d*x*e^(8*I*d*x + 4*I*c) + 192*a^3*d*x*e^(6*I*d*x + 2*I*c) + 192*a^3*d*x*e^(2*I*d*x - 2*I*c) + 288*a^3*d*x*e^(4*I*d*x) + 48*a^3*d*x*e^(-4*I*c) - 12*I*a^3*e^(8*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 48*I*a^3*e^(6*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 48*I*a^3*e^(2*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 72*I*a^3*e^(4*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) - 12*I*a^3*e^(-4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 12*I*a^3*e^(8*I*d*x + 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 48*I*a^3*e^(6*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 48*I*a^3*e^(2*I*d*x - 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 72*I*a^3*e^(4*I*d*x)*log(e^(2*I*d*x) + e^(-2*I*c)) + 12*I*a^3*e^(-4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) - 8*I*a^3*e^(14*I*d*x + 10*I*c) - 68*I*a^3*e^(12*I*d*x + 8*I*c) - 264*I*a^3*e^(10*I*d*x + 6*I*c) - 536*I*a^3*e^(8*I*d*x + 4*I*c) - 584*I*a^3*e^(6*I*d*x + 2*I*c) - 72*I*a^3*e^(2*I*d*x - 2*I*c) - 324*I*a^3*e^(4*I*d*x))/(d*e^(8*I*d*x + 4*I*c) + 4*d*e^(6*I*d*x + 2*I*c) + 4*d*e^(2*I*d*x - 2*I*c) + 6*d*e^(4*I*d*x) + d*e^(-4*I*c))","B",0
44,1,514,0,2.949307," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{480 \, a^{3} d x e^{\left(10 i \, d x + 6 i \, c\right)} + 1920 \, a^{3} d x e^{\left(8 i \, d x + 4 i \, c\right)} + 2880 \, a^{3} d x e^{\left(6 i \, d x + 2 i \, c\right)} + 480 \, a^{3} d x e^{\left(2 i \, d x - 2 i \, c\right)} + 1920 \, a^{3} d x e^{\left(4 i \, d x\right)} - 66 i \, a^{3} e^{\left(10 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 264 i \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 396 i \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 66 i \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 264 i \, a^{3} e^{\left(4 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 66 i \, a^{3} e^{\left(10 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 264 i \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 396 i \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 66 i \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 264 i \, a^{3} e^{\left(4 i \, d x\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 12 i \, a^{3} e^{\left(18 i \, d x + 14 i \, c\right)} - 128 i \, a^{3} e^{\left(16 i \, d x + 12 i \, c\right)} - 632 i \, a^{3} e^{\left(14 i \, d x + 10 i \, c\right)} - 1968 i \, a^{3} e^{\left(12 i \, d x + 8 i \, c\right)} - 3692 i \, a^{3} e^{\left(10 i \, d x + 6 i \, c\right)} - 3872 i \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} - 1968 i \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} + 192 i \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} - 192 i \, a^{3} e^{\left(4 i \, d x\right)} + 48 i \, a^{3} e^{\left(-4 i \, c\right)}}{3072 \, {\left(d e^{\left(10 i \, d x + 6 i \, c\right)} + 4 \, d e^{\left(8 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(6 i \, d x + 2 i \, c\right)} + d e^{\left(2 i \, d x - 2 i \, c\right)} + 4 \, d e^{\left(4 i \, d x\right)}\right)}}"," ",0,"1/3072*(480*a^3*d*x*e^(10*I*d*x + 6*I*c) + 1920*a^3*d*x*e^(8*I*d*x + 4*I*c) + 2880*a^3*d*x*e^(6*I*d*x + 2*I*c) + 480*a^3*d*x*e^(2*I*d*x - 2*I*c) + 1920*a^3*d*x*e^(4*I*d*x) - 66*I*a^3*e^(10*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 264*I*a^3*e^(8*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 396*I*a^3*e^(6*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 66*I*a^3*e^(2*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 264*I*a^3*e^(4*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) + 66*I*a^3*e^(10*I*d*x + 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 264*I*a^3*e^(8*I*d*x + 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 396*I*a^3*e^(6*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 66*I*a^3*e^(2*I*d*x - 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 264*I*a^3*e^(4*I*d*x)*log(e^(2*I*d*x) + e^(-2*I*c)) - 12*I*a^3*e^(18*I*d*x + 14*I*c) - 128*I*a^3*e^(16*I*d*x + 12*I*c) - 632*I*a^3*e^(14*I*d*x + 10*I*c) - 1968*I*a^3*e^(12*I*d*x + 8*I*c) - 3692*I*a^3*e^(10*I*d*x + 6*I*c) - 3872*I*a^3*e^(8*I*d*x + 4*I*c) - 1968*I*a^3*e^(6*I*d*x + 2*I*c) + 192*I*a^3*e^(2*I*d*x - 2*I*c) - 192*I*a^3*e^(4*I*d*x) + 48*I*a^3*e^(-4*I*c))/(d*e^(10*I*d*x + 6*I*c) + 4*d*e^(8*I*d*x + 4*I*c) + 6*d*e^(6*I*d*x + 2*I*c) + d*e^(2*I*d*x - 2*I*c) + 4*d*e^(4*I*d*x))","B",0
45,1,189,0,1.079822," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{105 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 105 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + \frac{2 \, {\left(15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 390 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 400 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 390 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 320 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 136 i \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(105*a^3*log(tan(1/2*d*x + 1/2*c) + 1) - 105*a^3*log(tan(1/2*d*x + 1/2*c) - 1) + 2*(15*a^3*tan(1/2*d*x + 1/2*c)^9 - 360*I*a^3*tan(1/2*d*x + 1/2*c)^8 - 390*a^3*tan(1/2*d*x + 1/2*c)^7 + 960*I*a^3*tan(1/2*d*x + 1/2*c)^6 - 400*I*a^3*tan(1/2*d*x + 1/2*c)^4 + 390*a^3*tan(1/2*d*x + 1/2*c)^3 + 320*I*a^3*tan(1/2*d*x + 1/2*c)^2 - 15*a^3*tan(1/2*d*x + 1/2*c) - 136*I*a^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
46,1,125,0,1.138563," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 15 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) - \frac{2 \, {\left(9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 18 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 48 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 22 i \, a^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(15*a^3*log(tan(1/2*d*x + 1/2*c) + 1) - 15*a^3*log(tan(1/2*d*x + 1/2*c) - 1) - 2*(9*a^3*tan(1/2*d*x + 1/2*c)^5 + 18*I*a^3*tan(1/2*d*x + 1/2*c)^4 - 48*I*a^3*tan(1/2*d*x + 1/2*c)^2 - 9*a^3*tan(1/2*d*x + 1/2*c) + 22*I*a^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","A",0
47,1,234,0,3.831021," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{63 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 33 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 63 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 33 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 128 i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)} - 192 i \, a^{3} e^{\left(i \, d x + i \, c\right)} + 63 \, a^{3} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 33 \, a^{3} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 63 \, a^{3} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 33 \, a^{3} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right)}{32 \, {\left(d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/32*(63*a^3*e^(2*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) - 33*a^3*e^(2*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) - 63*a^3*e^(2*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) + 33*a^3*e^(2*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 128*I*a^3*e^(3*I*d*x + 3*I*c) - 192*I*a^3*e^(I*d*x + I*c) + 63*a^3*log(I*e^(I*d*x + I*c) + 1) - 33*a^3*log(I*e^(I*d*x + I*c) - 1) - 63*a^3*log(-I*e^(I*d*x + I*c) + 1) + 33*a^3*log(-I*e^(I*d*x + I*c) - 1))/(d*e^(2*I*d*x + 2*I*c) + d)","B",0
48,1,901,0,3.989925," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{108 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 432 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 432 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 648 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 108 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 111 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 444 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 444 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 666 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 111 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 108 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 432 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 432 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 648 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 108 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 111 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 444 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 444 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 666 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 111 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 12 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 12 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 18 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 12 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 12 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 18 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 128 i \, a^{3} e^{\left(11 i \, d x + 7 i \, c\right)} + 512 i \, a^{3} e^{\left(9 i \, d x + 5 i \, c\right)} + 768 i \, a^{3} e^{\left(7 i \, d x + 3 i \, c\right)} + 512 i \, a^{3} e^{\left(5 i \, d x + i \, c\right)} + 128 i \, a^{3} e^{\left(3 i \, d x - i \, c\right)}}{384 \, {\left(d e^{\left(8 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 2 i \, c\right)} + 4 \, d e^{\left(2 i \, d x - 2 i \, c\right)} + 6 \, d e^{\left(4 i \, d x\right)} + d e^{\left(-4 i \, c\right)}\right)}}"," ",0,"-1/384*(108*a^3*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 432*a^3*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 432*a^3*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 648*a^3*e^(4*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 108*a^3*e^(-4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 111*a^3*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 444*a^3*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 444*a^3*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 666*a^3*e^(4*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 111*a^3*e^(-4*I*c)*log(I*e^(I*d*x + I*c) - 1) - 108*a^3*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 432*a^3*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 432*a^3*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 648*a^3*e^(4*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 108*a^3*e^(-4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 111*a^3*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 444*a^3*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 444*a^3*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 666*a^3*e^(4*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 111*a^3*e^(-4*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 3*a^3*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 12*a^3*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 12*a^3*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 18*a^3*e^(4*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) + 3*a^3*e^(-4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 3*a^3*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 12*a^3*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 12*a^3*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 18*a^3*e^(4*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) - 3*a^3*e^(-4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 128*I*a^3*e^(11*I*d*x + 7*I*c) + 512*I*a^3*e^(9*I*d*x + 5*I*c) + 768*I*a^3*e^(7*I*d*x + 3*I*c) + 512*I*a^3*e^(5*I*d*x + I*c) + 128*I*a^3*e^(3*I*d*x - I*c))/(d*e^(8*I*d*x + 4*I*c) + 4*d*e^(6*I*d*x + 2*I*c) + 4*d*e^(2*I*d*x - 2*I*c) + 6*d*e^(4*I*d*x) + d*e^(-4*I*c))","B",0
49,1,929,0,4.783800," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{1785 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 7140 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 7140 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 10710 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1785 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1530 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 6120 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 6120 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 9180 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1530 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1785 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 7140 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 7140 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 10710 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1785 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1530 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 6120 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 6120 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9180 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1530 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 255 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1020 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1020 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1530 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 255 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 255 \, a^{3} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1020 \, a^{3} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1020 \, a^{3} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1530 \, a^{3} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 255 \, a^{3} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 384 i \, a^{3} e^{\left(13 i \, d x + 9 i \, c\right)} - 2816 i \, a^{3} e^{\left(11 i \, d x + 7 i \, c\right)} - 9344 i \, a^{3} e^{\left(9 i \, d x + 5 i \, c\right)} - 16896 i \, a^{3} e^{\left(7 i \, d x + 3 i \, c\right)} - 17024 i \, a^{3} e^{\left(5 i \, d x + i \, c\right)} - 8960 i \, a^{3} e^{\left(3 i \, d x - i \, c\right)} - 1920 i \, a^{3} e^{\left(i \, d x - 3 i \, c\right)}}{7680 \, {\left(d e^{\left(8 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 2 i \, c\right)} + 4 \, d e^{\left(2 i \, d x - 2 i \, c\right)} + 6 \, d e^{\left(4 i \, d x\right)} + d e^{\left(-4 i \, c\right)}\right)}}"," ",0,"1/7680*(1785*a^3*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 7140*a^3*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 7140*a^3*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 10710*a^3*e^(4*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 1785*a^3*e^(-4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1530*a^3*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 6120*a^3*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 6120*a^3*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 9180*a^3*e^(4*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 1530*a^3*e^(-4*I*c)*log(I*e^(I*d*x + I*c) - 1) - 1785*a^3*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 7140*a^3*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 7140*a^3*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 10710*a^3*e^(4*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 1785*a^3*e^(-4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1530*a^3*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 6120*a^3*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 6120*a^3*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 9180*a^3*e^(4*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 1530*a^3*e^(-4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 255*a^3*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 1020*a^3*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 1020*a^3*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 1530*a^3*e^(4*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 255*a^3*e^(-4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 255*a^3*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 1020*a^3*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 1020*a^3*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 1530*a^3*e^(4*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 255*a^3*e^(-4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 384*I*a^3*e^(13*I*d*x + 9*I*c) - 2816*I*a^3*e^(11*I*d*x + 7*I*c) - 9344*I*a^3*e^(9*I*d*x + 5*I*c) - 16896*I*a^3*e^(7*I*d*x + 3*I*c) - 17024*I*a^3*e^(5*I*d*x + I*c) - 8960*I*a^3*e^(3*I*d*x - I*c) - 1920*I*a^3*e^(I*d*x - 3*I*c))/(d*e^(8*I*d*x + 4*I*c) + 4*d*e^(6*I*d*x + 2*I*c) + 4*d*e^(2*I*d*x - 2*I*c) + 6*d*e^(4*I*d*x) + d*e^(-4*I*c))","B",0
50,1,465,0,3.741413," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{19635 \, a^{3} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 39270 \, a^{3} e^{\left(3 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 19635 \, a^{3} e^{\left(i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 19635 \, a^{3} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 39270 \, a^{3} e^{\left(3 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 19635 \, a^{3} e^{\left(i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 19635 \, a^{3} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 39270 \, a^{3} e^{\left(3 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 19635 \, a^{3} e^{\left(i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 19635 \, a^{3} e^{\left(5 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 39270 \, a^{3} e^{\left(3 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 19635 \, a^{3} e^{\left(i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 640 i \, a^{3} e^{\left(12 i \, d x + 10 i \, c\right)} - 4864 i \, a^{3} e^{\left(10 i \, d x + 8 i \, c\right)} - 16768 i \, a^{3} e^{\left(8 i \, d x + 6 i \, c\right)} - 39424 i \, a^{3} e^{\left(6 i \, d x + 4 i \, c\right)} - 40320 i \, a^{3} e^{\left(4 i \, d x + 2 i \, c\right)} - 8960 i \, a^{3} e^{\left(2 i \, d x\right)} + 4480 i \, a^{3} e^{\left(-2 i \, c\right)}}{71680 \, {\left(d e^{\left(5 i \, d x + 3 i \, c\right)} + 2 \, d e^{\left(3 i \, d x + i \, c\right)} + d e^{\left(i \, d x - i \, c\right)}\right)}}"," ",0,"1/71680*(19635*a^3*e^(5*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 39270*a^3*e^(3*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 19635*a^3*e^(I*d*x - I*c)*log(I*e^(I*d*x + I*c) + 1) + 19635*a^3*e^(5*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 39270*a^3*e^(3*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) + 19635*a^3*e^(I*d*x - I*c)*log(I*e^(I*d*x + I*c) - 1) - 19635*a^3*e^(5*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 39270*a^3*e^(3*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 19635*a^3*e^(I*d*x - I*c)*log(-I*e^(I*d*x + I*c) + 1) - 19635*a^3*e^(5*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 39270*a^3*e^(3*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 19635*a^3*e^(I*d*x - I*c)*log(-I*e^(I*d*x + I*c) - 1) - 640*I*a^3*e^(12*I*d*x + 10*I*c) - 4864*I*a^3*e^(10*I*d*x + 8*I*c) - 16768*I*a^3*e^(8*I*d*x + 6*I*c) - 39424*I*a^3*e^(6*I*d*x + 4*I*c) - 40320*I*a^3*e^(4*I*d*x + 2*I*c) - 8960*I*a^3*e^(2*I*d*x) + 4480*I*a^3*e^(-2*I*c))/(d*e^(5*I*d*x + 3*I*c) + 2*d*e^(3*I*d*x + I*c) + d*e^(I*d*x - I*c))","B",0
51,1,1039,0,3.918004," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{119511 \, a^{3} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 478044 \, a^{3} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 717066 \, a^{3} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 478044 \, a^{3} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 119511 \, a^{3} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 128898 \, a^{3} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 515592 \, a^{3} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 773388 \, a^{3} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 515592 \, a^{3} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 128898 \, a^{3} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 119511 \, a^{3} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 478044 \, a^{3} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 717066 \, a^{3} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 478044 \, a^{3} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 119511 \, a^{3} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 128898 \, a^{3} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 515592 \, a^{3} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 773388 \, a^{3} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 515592 \, a^{3} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 128898 \, a^{3} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 9387 \, a^{3} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 37548 \, a^{3} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 56322 \, a^{3} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 37548 \, a^{3} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 9387 \, a^{3} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 9387 \, a^{3} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 37548 \, a^{3} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 56322 \, a^{3} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 37548 \, a^{3} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 9387 \, a^{3} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 896 i \, a^{3} e^{\left(20 i \, d x + 14 i \, c\right)} - 10496 i \, a^{3} e^{\left(18 i \, d x + 12 i \, c\right)} - 57216 i \, a^{3} e^{\left(16 i \, d x + 10 i \, c\right)} - 195584 i \, a^{3} e^{\left(14 i \, d x + 8 i \, c\right)} - 509696 i \, a^{3} e^{\left(12 i \, d x + 6 i \, c\right)} - 861696 i \, a^{3} e^{\left(10 i \, d x + 4 i \, c\right)} - 768768 i \, a^{3} e^{\left(8 i \, d x + 2 i \, c\right)} + 88704 i \, a^{3} e^{\left(4 i \, d x - 2 i \, c\right)} + 59136 i \, a^{3} e^{\left(2 i \, d x - 4 i \, c\right)} - 236544 i \, a^{3} e^{\left(6 i \, d x\right)} + 2688 i \, a^{3} e^{\left(-6 i \, c\right)}}{516096 \, {\left(d e^{\left(11 i \, d x + 5 i \, c\right)} + 4 \, d e^{\left(9 i \, d x + 3 i \, c\right)} + 6 \, d e^{\left(7 i \, d x + i \, c\right)} + 4 \, d e^{\left(5 i \, d x - i \, c\right)} + d e^{\left(3 i \, d x - 3 i \, c\right)}\right)}}"," ",0,"1/516096*(119511*a^3*e^(11*I*d*x + 5*I*c)*log(I*e^(I*d*x + I*c) + 1) + 478044*a^3*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 717066*a^3*e^(7*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 478044*a^3*e^(5*I*d*x - I*c)*log(I*e^(I*d*x + I*c) + 1) + 119511*a^3*e^(3*I*d*x - 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 128898*a^3*e^(11*I*d*x + 5*I*c)*log(I*e^(I*d*x + I*c) - 1) + 515592*a^3*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 773388*a^3*e^(7*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) + 515592*a^3*e^(5*I*d*x - I*c)*log(I*e^(I*d*x + I*c) - 1) + 128898*a^3*e^(3*I*d*x - 3*I*c)*log(I*e^(I*d*x + I*c) - 1) - 119511*a^3*e^(11*I*d*x + 5*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 478044*a^3*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 717066*a^3*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 478044*a^3*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) + 1) - 119511*a^3*e^(3*I*d*x - 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 128898*a^3*e^(11*I*d*x + 5*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 515592*a^3*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 773388*a^3*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 515592*a^3*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) - 1) - 128898*a^3*e^(3*I*d*x - 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 9387*a^3*e^(11*I*d*x + 5*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 37548*a^3*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 56322*a^3*e^(7*I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 37548*a^3*e^(5*I*d*x - I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 9387*a^3*e^(3*I*d*x - 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 9387*a^3*e^(11*I*d*x + 5*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 37548*a^3*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 56322*a^3*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 37548*a^3*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 9387*a^3*e^(3*I*d*x - 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 896*I*a^3*e^(20*I*d*x + 14*I*c) - 10496*I*a^3*e^(18*I*d*x + 12*I*c) - 57216*I*a^3*e^(16*I*d*x + 10*I*c) - 195584*I*a^3*e^(14*I*d*x + 8*I*c) - 509696*I*a^3*e^(12*I*d*x + 6*I*c) - 861696*I*a^3*e^(10*I*d*x + 4*I*c) - 768768*I*a^3*e^(8*I*d*x + 2*I*c) + 88704*I*a^3*e^(4*I*d*x - 2*I*c) + 59136*I*a^3*e^(2*I*d*x - 4*I*c) - 236544*I*a^3*e^(6*I*d*x) + 2688*I*a^3*e^(-6*I*c))/(d*e^(11*I*d*x + 5*I*c) + 4*d*e^(9*I*d*x + 3*I*c) + 6*d*e^(7*I*d*x + I*c) + 4*d*e^(5*I*d*x - I*c) + d*e^(3*I*d*x - 3*I*c))","B",0
52,1,237,0,1.315363," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{315 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 315 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) - \frac{2 \, {\left(75 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 960 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1175 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 4800 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1890 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 4480 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1890 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1920 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1175 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1728 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 75 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 448 i \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(315*a^4*log(tan(1/2*d*x + 1/2*c) + 1) - 315*a^4*log(tan(1/2*d*x + 1/2*c) - 1) - 2*(75*a^4*tan(1/2*d*x + 1/2*c)^11 + 960*I*a^4*tan(1/2*d*x + 1/2*c)^10 + 1175*a^4*tan(1/2*d*x + 1/2*c)^9 - 4800*I*a^4*tan(1/2*d*x + 1/2*c)^8 - 1890*a^4*tan(1/2*d*x + 1/2*c)^7 + 4480*I*a^4*tan(1/2*d*x + 1/2*c)^6 - 1890*a^4*tan(1/2*d*x + 1/2*c)^5 - 1920*I*a^4*tan(1/2*d*x + 1/2*c)^4 + 1175*a^4*tan(1/2*d*x + 1/2*c)^3 + 1728*I*a^4*tan(1/2*d*x + 1/2*c)^2 + 75*a^4*tan(1/2*d*x + 1/2*c) - 448*I*a^4)/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","A",0
53,1,173,0,1.621965," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{105 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 105 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) - \frac{2 \, {\left(81 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 105 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 480 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 544 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 81 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 160 i \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(105*a^4*log(tan(1/2*d*x + 1/2*c) + 1) - 105*a^4*log(tan(1/2*d*x + 1/2*c) - 1) - 2*(81*a^4*tan(1/2*d*x + 1/2*c)^7 + 96*I*a^4*tan(1/2*d*x + 1/2*c)^6 - 105*a^4*tan(1/2*d*x + 1/2*c)^5 - 480*I*a^4*tan(1/2*d*x + 1/2*c)^4 - 105*a^4*tan(1/2*d*x + 1/2*c)^3 + 544*I*a^4*tan(1/2*d*x + 1/2*c)^2 + 81*a^4*tan(1/2*d*x + 1/2*c) - 160*I*a^4)/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","A",0
54,1,372,0,3.623305," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{235 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 470 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 10 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 235 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 470 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 10 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 256 i \, a^{4} e^{\left(5 i \, d x + 5 i \, c\right)} - 800 i \, a^{4} e^{\left(3 i \, d x + 3 i \, c\right)} - 480 i \, a^{4} e^{\left(i \, d x + i \, c\right)} + 235 \, a^{4} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5 \, a^{4} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 235 \, a^{4} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5 \, a^{4} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right)}{32 \, {\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,"1/32*(235*a^4*e^(4*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 470*a^4*e^(2*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) - 5*a^4*e^(4*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) - 10*a^4*e^(2*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) - 235*a^4*e^(4*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 470*a^4*e^(2*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) + 5*a^4*e^(4*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 10*a^4*e^(2*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 256*I*a^4*e^(5*I*d*x + 5*I*c) - 800*I*a^4*e^(3*I*d*x + 3*I*c) - 480*I*a^4*e^(I*d*x + I*c) + 235*a^4*log(I*e^(I*d*x + I*c) + 1) - 5*a^4*log(I*e^(I*d*x + I*c) - 1) - 235*a^4*log(-I*e^(I*d*x + I*c) + 1) + 5*a^4*log(-I*e^(I*d*x + I*c) - 1))/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
55,1,1299,0,3.388476," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{1110 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 6660 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 16650 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 16650 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 6660 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 22200 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1110 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1875 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 11250 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 28125 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 28125 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 11250 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 37500 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1875 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1110 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 6660 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 16650 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 16650 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 6660 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 22200 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1110 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1875 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 11250 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 28125 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 28125 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 11250 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 37500 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1875 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 18 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 45 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 45 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 18 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 60 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 18 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 45 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 45 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 18 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 60 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 512 i \, a^{4} e^{\left(15 i \, d x + 9 i \, c\right)} - 1536 i \, a^{4} e^{\left(13 i \, d x + 7 i \, c\right)} + 1536 i \, a^{4} e^{\left(11 i \, d x + 5 i \, c\right)} + 12800 i \, a^{4} e^{\left(9 i \, d x + 3 i \, c\right)} + 23040 i \, a^{4} e^{\left(7 i \, d x + i \, c\right)} + 19968 i \, a^{4} e^{\left(5 i \, d x - i \, c\right)} + 8704 i \, a^{4} e^{\left(3 i \, d x - 3 i \, c\right)} + 1536 i \, a^{4} e^{\left(i \, d x - 5 i \, c\right)}}{768 \, {\left(d e^{\left(12 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 4 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 2 i \, c\right)} + 15 \, d e^{\left(4 i \, d x - 2 i \, c\right)} + 6 \, d e^{\left(2 i \, d x - 4 i \, c\right)} + 20 \, d e^{\left(6 i \, d x\right)} + d e^{\left(-6 i \, c\right)}\right)}}"," ",0,"1/768*(1110*a^4*e^(12*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 6660*a^4*e^(10*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 16650*a^4*e^(8*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 16650*a^4*e^(4*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 6660*a^4*e^(2*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 22200*a^4*e^(6*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 1110*a^4*e^(-6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1875*a^4*e^(12*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 11250*a^4*e^(10*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 28125*a^4*e^(8*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 28125*a^4*e^(4*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 11250*a^4*e^(2*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 37500*a^4*e^(6*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 1875*a^4*e^(-6*I*c)*log(I*e^(I*d*x + I*c) - 1) - 1110*a^4*e^(12*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 6660*a^4*e^(10*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 16650*a^4*e^(8*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 16650*a^4*e^(4*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 6660*a^4*e^(2*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 22200*a^4*e^(6*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 1110*a^4*e^(-6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1875*a^4*e^(12*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 11250*a^4*e^(10*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 28125*a^4*e^(8*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 28125*a^4*e^(4*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 11250*a^4*e^(2*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 37500*a^4*e^(6*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 1875*a^4*e^(-6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3*a^4*e^(12*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 18*a^4*e^(10*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 45*a^4*e^(8*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 45*a^4*e^(4*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 18*a^4*e^(2*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 60*a^4*e^(6*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 3*a^4*e^(-6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 3*a^4*e^(12*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 18*a^4*e^(10*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 45*a^4*e^(8*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 45*a^4*e^(4*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 18*a^4*e^(2*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 60*a^4*e^(6*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 3*a^4*e^(-6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 512*I*a^4*e^(15*I*d*x + 9*I*c) - 1536*I*a^4*e^(13*I*d*x + 7*I*c) + 1536*I*a^4*e^(11*I*d*x + 5*I*c) + 12800*I*a^4*e^(9*I*d*x + 3*I*c) + 23040*I*a^4*e^(7*I*d*x + I*c) + 19968*I*a^4*e^(5*I*d*x - I*c) + 8704*I*a^4*e^(3*I*d*x - 3*I*c) + 1536*I*a^4*e^(I*d*x - 5*I*c))/(d*e^(12*I*d*x + 6*I*c) + 6*d*e^(10*I*d*x + 4*I*c) + 15*d*e^(8*I*d*x + 2*I*c) + 15*d*e^(4*I*d*x - 2*I*c) + 6*d*e^(2*I*d*x - 4*I*c) + 20*d*e^(6*I*d*x) + d*e^(-6*I*c))","B",0
56,1,915,0,4.033442," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{9075 \, a^{4} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 36300 \, a^{4} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 36300 \, a^{4} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 54450 \, a^{4} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9075 \, a^{4} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9000 \, a^{4} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 36000 \, a^{4} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 36000 \, a^{4} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 54000 \, a^{4} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 9000 \, a^{4} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9075 \, a^{4} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 36300 \, a^{4} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 36300 \, a^{4} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 54450 \, a^{4} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9075 \, a^{4} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9000 \, a^{4} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 36000 \, a^{4} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 36000 \, a^{4} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 54000 \, a^{4} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9000 \, a^{4} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 75 \, a^{4} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 300 \, a^{4} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 300 \, a^{4} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 450 \, a^{4} e^{\left(4 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 75 \, a^{4} e^{\left(-4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 75 \, a^{4} e^{\left(8 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 300 \, a^{4} e^{\left(6 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 300 \, a^{4} e^{\left(2 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 450 \, a^{4} e^{\left(4 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 75 \, a^{4} e^{\left(-4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 768 i \, a^{4} e^{\left(13 i \, d x + 9 i \, c\right)} - 4352 i \, a^{4} e^{\left(11 i \, d x + 7 i \, c\right)} - 9728 i \, a^{4} e^{\left(9 i \, d x + 5 i \, c\right)} - 10752 i \, a^{4} e^{\left(7 i \, d x + 3 i \, c\right)} - 5888 i \, a^{4} e^{\left(5 i \, d x + i \, c\right)} - 1280 i \, a^{4} e^{\left(3 i \, d x - i \, c\right)}}{7680 \, {\left(d e^{\left(8 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 2 i \, c\right)} + 4 \, d e^{\left(2 i \, d x - 2 i \, c\right)} + 6 \, d e^{\left(4 i \, d x\right)} + d e^{\left(-4 i \, c\right)}\right)}}"," ",0,"1/7680*(9075*a^4*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 36300*a^4*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 36300*a^4*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 54450*a^4*e^(4*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 9075*a^4*e^(-4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 9000*a^4*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 36000*a^4*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 36000*a^4*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 54000*a^4*e^(4*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 9000*a^4*e^(-4*I*c)*log(I*e^(I*d*x + I*c) - 1) - 9075*a^4*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 36300*a^4*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 36300*a^4*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 54450*a^4*e^(4*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 9075*a^4*e^(-4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 9000*a^4*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 36000*a^4*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 36000*a^4*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 54000*a^4*e^(4*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 9000*a^4*e^(-4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 75*a^4*e^(8*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 300*a^4*e^(6*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 300*a^4*e^(2*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 450*a^4*e^(4*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 75*a^4*e^(-4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 75*a^4*e^(8*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 300*a^4*e^(6*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 300*a^4*e^(2*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 450*a^4*e^(4*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 75*a^4*e^(-4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 768*I*a^4*e^(13*I*d*x + 9*I*c) - 4352*I*a^4*e^(11*I*d*x + 7*I*c) - 9728*I*a^4*e^(9*I*d*x + 5*I*c) - 10752*I*a^4*e^(7*I*d*x + 3*I*c) - 5888*I*a^4*e^(5*I*d*x + I*c) - 1280*I*a^4*e^(3*I*d*x - I*c))/(d*e^(8*I*d*x + 4*I*c) + 4*d*e^(6*I*d*x + 2*I*c) + 4*d*e^(2*I*d*x - 2*I*c) + 6*d*e^(4*I*d*x) + d*e^(-4*I*c))","B",0
57,1,1327,0,4.411771," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{89950 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 539700 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1349250 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1349250 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 539700 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1799000 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 89950 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 86065 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 516390 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1290975 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1290975 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 516390 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1721300 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 86065 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 89950 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 539700 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1349250 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1349250 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 539700 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1799000 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 89950 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 86065 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 516390 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1290975 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1290975 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 516390 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1721300 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 86065 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3885 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23310 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 58275 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 58275 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23310 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 77700 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3885 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3885 \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23310 \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 58275 \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 58275 \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23310 \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 77700 \, a^{4} e^{\left(6 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3885 \, a^{4} e^{\left(-6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2560 i \, a^{4} e^{\left(19 i \, d x + 13 i \, c\right)} - 26112 i \, a^{4} e^{\left(17 i \, d x + 11 i \, c\right)} - 120832 i \, a^{4} e^{\left(15 i \, d x + 9 i \, c\right)} - 337920 i \, a^{4} e^{\left(13 i \, d x + 7 i \, c\right)} - 629760 i \, a^{4} e^{\left(11 i \, d x + 5 i \, c\right)} - 803840 i \, a^{4} e^{\left(9 i \, d x + 3 i \, c\right)} - 694272 i \, a^{4} e^{\left(7 i \, d x + i \, c\right)} - 387072 i \, a^{4} e^{\left(5 i \, d x - i \, c\right)} - 125440 i \, a^{4} e^{\left(3 i \, d x - 3 i \, c\right)} - 17920 i \, a^{4} e^{\left(i \, d x - 5 i \, c\right)}}{143360 \, {\left(d e^{\left(12 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 4 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 2 i \, c\right)} + 15 \, d e^{\left(4 i \, d x - 2 i \, c\right)} + 6 \, d e^{\left(2 i \, d x - 4 i \, c\right)} + 20 \, d e^{\left(6 i \, d x\right)} + d e^{\left(-6 i \, c\right)}\right)}}"," ",0,"1/143360*(89950*a^4*e^(12*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 539700*a^4*e^(10*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1349250*a^4*e^(8*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1349250*a^4*e^(4*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 539700*a^4*e^(2*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1799000*a^4*e^(6*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 89950*a^4*e^(-6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 86065*a^4*e^(12*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 516390*a^4*e^(10*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1290975*a^4*e^(8*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1290975*a^4*e^(4*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 516390*a^4*e^(2*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1721300*a^4*e^(6*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 86065*a^4*e^(-6*I*c)*log(I*e^(I*d*x + I*c) - 1) - 89950*a^4*e^(12*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 539700*a^4*e^(10*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1349250*a^4*e^(8*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1349250*a^4*e^(4*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 539700*a^4*e^(2*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1799000*a^4*e^(6*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 89950*a^4*e^(-6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 86065*a^4*e^(12*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 516390*a^4*e^(10*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1290975*a^4*e^(8*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1290975*a^4*e^(4*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 516390*a^4*e^(2*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1721300*a^4*e^(6*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 86065*a^4*e^(-6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3885*a^4*e^(12*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 23310*a^4*e^(10*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 58275*a^4*e^(8*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 58275*a^4*e^(4*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 23310*a^4*e^(2*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 77700*a^4*e^(6*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 3885*a^4*e^(-6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 3885*a^4*e^(12*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 23310*a^4*e^(10*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 58275*a^4*e^(8*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 58275*a^4*e^(4*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 23310*a^4*e^(2*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 77700*a^4*e^(6*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 3885*a^4*e^(-6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 2560*I*a^4*e^(19*I*d*x + 13*I*c) - 26112*I*a^4*e^(17*I*d*x + 11*I*c) - 120832*I*a^4*e^(15*I*d*x + 9*I*c) - 337920*I*a^4*e^(13*I*d*x + 7*I*c) - 629760*I*a^4*e^(11*I*d*x + 5*I*c) - 803840*I*a^4*e^(9*I*d*x + 3*I*c) - 694272*I*a^4*e^(7*I*d*x + I*c) - 387072*I*a^4*e^(5*I*d*x - I*c) - 125440*I*a^4*e^(3*I*d*x - 3*I*c) - 17920*I*a^4*e^(I*d*x - 5*I*c))/(d*e^(12*I*d*x + 6*I*c) + 6*d*e^(10*I*d*x + 4*I*c) + 15*d*e^(8*I*d*x + 2*I*c) + 15*d*e^(4*I*d*x - 2*I*c) + 6*d*e^(2*I*d*x - 4*I*c) + 20*d*e^(6*I*d*x) + d*e^(-6*I*c))","B",0
58,1,1409,0,5.140841," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{435267 \, a^{4} e^{\left(13 i \, d x + 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2611602 \, a^{4} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 6529005 \, a^{4} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 8705340 \, a^{4} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 6529005 \, a^{4} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2611602 \, a^{4} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 435267 \, a^{4} e^{\left(i \, d x - 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 427896 \, a^{4} e^{\left(13 i \, d x + 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 2567376 \, a^{4} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 6418440 \, a^{4} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 8557920 \, a^{4} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 6418440 \, a^{4} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 2567376 \, a^{4} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 427896 \, a^{4} e^{\left(i \, d x - 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 435267 \, a^{4} e^{\left(13 i \, d x + 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2611602 \, a^{4} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 6529005 \, a^{4} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 8705340 \, a^{4} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 6529005 \, a^{4} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2611602 \, a^{4} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 435267 \, a^{4} e^{\left(i \, d x - 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 427896 \, a^{4} e^{\left(13 i \, d x + 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 2567376 \, a^{4} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 6418440 \, a^{4} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 8557920 \, a^{4} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 6418440 \, a^{4} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 2567376 \, a^{4} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 427896 \, a^{4} e^{\left(i \, d x - 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7371 \, a^{4} e^{\left(13 i \, d x + 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 44226 \, a^{4} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 110565 \, a^{4} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 147420 \, a^{4} e^{\left(7 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 110565 \, a^{4} e^{\left(5 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 44226 \, a^{4} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 7371 \, a^{4} e^{\left(i \, d x - 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 7371 \, a^{4} e^{\left(13 i \, d x + 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 44226 \, a^{4} e^{\left(11 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 110565 \, a^{4} e^{\left(9 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 147420 \, a^{4} e^{\left(7 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 110565 \, a^{4} e^{\left(5 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 44226 \, a^{4} e^{\left(3 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 7371 \, a^{4} e^{\left(i \, d x - 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1792 i \, a^{4} e^{\left(22 i \, d x + 16 i \, c\right)} - 22272 i \, a^{4} e^{\left(20 i \, d x + 14 i \, c\right)} - 128256 i \, a^{4} e^{\left(18 i \, d x + 12 i \, c\right)} - 455936 i \, a^{4} e^{\left(16 i \, d x + 10 i \, c\right)} - 1144320 i \, a^{4} e^{\left(14 i \, d x + 8 i \, c\right)} - 2102784 i \, a^{4} e^{\left(12 i \, d x + 6 i \, c\right)} - 2742784 i \, a^{4} e^{\left(10 i \, d x + 4 i \, c\right)} - 2382336 i \, a^{4} e^{\left(8 i \, d x + 2 i \, c\right)} - 295680 i \, a^{4} e^{\left(4 i \, d x - 2 i \, c\right)} + 16128 i \, a^{4} e^{\left(2 i \, d x - 4 i \, c\right)} - 1241856 i \, a^{4} e^{\left(6 i \, d x\right)} + 16128 i \, a^{4} e^{\left(-6 i \, c\right)}}{516096 \, {\left(d e^{\left(13 i \, d x + 7 i \, c\right)} + 6 \, d e^{\left(11 i \, d x + 5 i \, c\right)} + 15 \, d e^{\left(9 i \, d x + 3 i \, c\right)} + 20 \, d e^{\left(7 i \, d x + i \, c\right)} + 15 \, d e^{\left(5 i \, d x - i \, c\right)} + 6 \, d e^{\left(3 i \, d x - 3 i \, c\right)} + d e^{\left(i \, d x - 5 i \, c\right)}\right)}}"," ",0,"1/516096*(435267*a^4*e^(13*I*d*x + 7*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2611602*a^4*e^(11*I*d*x + 5*I*c)*log(I*e^(I*d*x + I*c) + 1) + 6529005*a^4*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 8705340*a^4*e^(7*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 6529005*a^4*e^(5*I*d*x - I*c)*log(I*e^(I*d*x + I*c) + 1) + 2611602*a^4*e^(3*I*d*x - 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 435267*a^4*e^(I*d*x - 5*I*c)*log(I*e^(I*d*x + I*c) + 1) + 427896*a^4*e^(13*I*d*x + 7*I*c)*log(I*e^(I*d*x + I*c) - 1) + 2567376*a^4*e^(11*I*d*x + 5*I*c)*log(I*e^(I*d*x + I*c) - 1) + 6418440*a^4*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 8557920*a^4*e^(7*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) + 6418440*a^4*e^(5*I*d*x - I*c)*log(I*e^(I*d*x + I*c) - 1) + 2567376*a^4*e^(3*I*d*x - 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 427896*a^4*e^(I*d*x - 5*I*c)*log(I*e^(I*d*x + I*c) - 1) - 435267*a^4*e^(13*I*d*x + 7*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2611602*a^4*e^(11*I*d*x + 5*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 6529005*a^4*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 8705340*a^4*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 6529005*a^4*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2611602*a^4*e^(3*I*d*x - 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 435267*a^4*e^(I*d*x - 5*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 427896*a^4*e^(13*I*d*x + 7*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 2567376*a^4*e^(11*I*d*x + 5*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 6418440*a^4*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 8557920*a^4*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 6418440*a^4*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) - 1) - 2567376*a^4*e^(3*I*d*x - 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 427896*a^4*e^(I*d*x - 5*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 7371*a^4*e^(13*I*d*x + 7*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 44226*a^4*e^(11*I*d*x + 5*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 110565*a^4*e^(9*I*d*x + 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 147420*a^4*e^(7*I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 110565*a^4*e^(5*I*d*x - I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 44226*a^4*e^(3*I*d*x - 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 7371*a^4*e^(I*d*x - 5*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 7371*a^4*e^(13*I*d*x + 7*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 44226*a^4*e^(11*I*d*x + 5*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 110565*a^4*e^(9*I*d*x + 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 147420*a^4*e^(7*I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 110565*a^4*e^(5*I*d*x - I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 44226*a^4*e^(3*I*d*x - 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 7371*a^4*e^(I*d*x - 5*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 1792*I*a^4*e^(22*I*d*x + 16*I*c) - 22272*I*a^4*e^(20*I*d*x + 14*I*c) - 128256*I*a^4*e^(18*I*d*x + 12*I*c) - 455936*I*a^4*e^(16*I*d*x + 10*I*c) - 1144320*I*a^4*e^(14*I*d*x + 8*I*c) - 2102784*I*a^4*e^(12*I*d*x + 6*I*c) - 2742784*I*a^4*e^(10*I*d*x + 4*I*c) - 2382336*I*a^4*e^(8*I*d*x + 2*I*c) - 295680*I*a^4*e^(4*I*d*x - 2*I*c) + 16128*I*a^4*e^(2*I*d*x - 4*I*c) - 1241856*I*a^4*e^(6*I*d*x) + 16128*I*a^4*e^(-6*I*c))/(d*e^(13*I*d*x + 7*I*c) + 6*d*e^(11*I*d*x + 5*I*c) + 15*d*e^(9*I*d*x + 3*I*c) + 20*d*e^(7*I*d*x + I*c) + 15*d*e^(5*I*d*x - I*c) + 6*d*e^(3*I*d*x - 3*I*c) + d*e^(I*d*x - 5*I*c))","B",0
59,1,160,0,2.584392," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{-165 i \, a^{5} \tan\left(d x + c\right)^{12} - 900 \, a^{5} \tan\left(d x + c\right)^{11} + 1386 i \, a^{5} \tan\left(d x + c\right)^{10} - 1100 \, a^{5} \tan\left(d x + c\right)^{9} + 5445 i \, a^{5} \tan\left(d x + c\right)^{8} + 3960 \, a^{5} \tan\left(d x + c\right)^{7} + 4620 i \, a^{5} \tan\left(d x + c\right)^{6} + 8712 \, a^{5} \tan\left(d x + c\right)^{5} - 2475 i \, a^{5} \tan\left(d x + c\right)^{4} + 4620 \, a^{5} \tan\left(d x + c\right)^{3} - 4950 i \, a^{5} \tan\left(d x + c\right)^{2} - 1980 \, a^{5} \tan\left(d x + c\right)}{1980 \, d}"," ",0,"-1/1980*(-165*I*a^5*tan(d*x + c)^12 - 900*a^5*tan(d*x + c)^11 + 1386*I*a^5*tan(d*x + c)^10 - 1100*a^5*tan(d*x + c)^9 + 5445*I*a^5*tan(d*x + c)^8 + 3960*a^5*tan(d*x + c)^7 + 4620*I*a^5*tan(d*x + c)^6 + 8712*a^5*tan(d*x + c)^5 - 2475*I*a^5*tan(d*x + c)^4 + 4620*a^5*tan(d*x + c)^3 - 4950*I*a^5*tan(d*x + c)^2 - 1980*a^5*tan(d*x + c))/d","A",0
60,1,108,0,2.227387," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{-9 i \, a^{5} \tan\left(d x + c\right)^{10} - 50 \, a^{5} \tan\left(d x + c\right)^{9} + 90 i \, a^{5} \tan\left(d x + c\right)^{8} + 210 i \, a^{5} \tan\left(d x + c\right)^{6} + 252 \, a^{5} \tan\left(d x + c\right)^{5} + 240 \, a^{5} \tan\left(d x + c\right)^{3} - 225 i \, a^{5} \tan\left(d x + c\right)^{2} - 90 \, a^{5} \tan\left(d x + c\right)}{90 \, d}"," ",0,"-1/90*(-9*I*a^5*tan(d*x + c)^10 - 50*a^5*tan(d*x + c)^9 + 90*I*a^5*tan(d*x + c)^8 + 210*I*a^5*tan(d*x + c)^6 + 252*a^5*tan(d*x + c)^5 + 240*a^5*tan(d*x + c)^3 - 225*I*a^5*tan(d*x + c)^2 - 90*a^5*tan(d*x + c))/d","A",0
61,1,108,0,2.445704," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{-7 i \, a^{5} \tan\left(d x + c\right)^{8} - 40 \, a^{5} \tan\left(d x + c\right)^{7} + 84 i \, a^{5} \tan\left(d x + c\right)^{6} + 56 \, a^{5} \tan\left(d x + c\right)^{5} + 70 i \, a^{5} \tan\left(d x + c\right)^{4} + 168 \, a^{5} \tan\left(d x + c\right)^{3} - 140 i \, a^{5} \tan\left(d x + c\right)^{2} - 56 \, a^{5} \tan\left(d x + c\right)}{56 \, d}"," ",0,"-1/56*(-7*I*a^5*tan(d*x + c)^8 - 40*a^5*tan(d*x + c)^7 + 84*I*a^5*tan(d*x + c)^6 + 56*a^5*tan(d*x + c)^5 + 70*I*a^5*tan(d*x + c)^4 + 168*a^5*tan(d*x + c)^3 - 140*I*a^5*tan(d*x + c)^2 - 56*a^5*tan(d*x + c))/d","B",0
62,1,82,0,1.924848," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{-i \, a^{5} \tan\left(d x + c\right)^{6} - 6 \, a^{5} \tan\left(d x + c\right)^{5} + 15 i \, a^{5} \tan\left(d x + c\right)^{4} + 20 \, a^{5} \tan\left(d x + c\right)^{3} - 15 i \, a^{5} \tan\left(d x + c\right)^{2} - 6 \, a^{5} \tan\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(-I*a^5*tan(d*x + c)^6 - 6*a^5*tan(d*x + c)^5 + 15*I*a^5*tan(d*x + c)^4 + 20*a^5*tan(d*x + c)^3 - 15*I*a^5*tan(d*x + c)^2 - 6*a^5*tan(d*x + c))/d","B",0
63,1,222,0,0.773372," ","integrate((a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{-48 i \, a^{5} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 192 i \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 288 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 192 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 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)} - 48 i \, a^{5} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 100 i \, a^{5}}{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*(-48*I*a^5*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 192*I*a^5*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 288*I*a^5*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 192*I*a^5*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 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) - 48*I*a^5*log(e^(2*I*d*x + 2*I*c) + 1) - 100*I*a^5)/(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
64,1,145,0,2.600142," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{12 i \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 24 i \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 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)} + 12 i \, a^{5} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 10 i \, a^{5}}{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,"(12*I*a^5*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 24*I*a^5*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 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) + 12*I*a^5*log(e^(2*I*d*x + 2*I*c) + 1) + 10*I*a^5)/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","A",0
65,1,450,0,3.474067," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{-384 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 3072 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 10752 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 21504 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 21504 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 10752 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 3072 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 26880 i \, a^{5} e^{\left(8 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 384 i \, a^{5} e^{\left(-8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 192 i \, a^{5} e^{\left(20 i \, d x + 12 i \, c\right)} - 1152 i \, a^{5} e^{\left(18 i \, d x + 10 i \, c\right)} - 2304 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} + 8064 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} + 16128 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} + 9216 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} + 2880 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} + 384 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} + 16128 i \, a^{5} e^{\left(8 i \, d x\right)}}{384 \, {\left(d e^{\left(16 i \, d x + 8 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 4 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 2 i \, c\right)} + 56 \, d e^{\left(6 i \, d x - 2 i \, c\right)} + 28 \, d e^{\left(4 i \, d x - 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x - 6 i \, c\right)} + 70 \, d e^{\left(8 i \, d x\right)} + d e^{\left(-8 i \, c\right)}\right)}}"," ",0,"1/384*(-384*I*a^5*e^(16*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 3072*I*a^5*e^(14*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 10752*I*a^5*e^(12*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 21504*I*a^5*e^(10*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 21504*I*a^5*e^(6*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 10752*I*a^5*e^(4*I*d*x - 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 3072*I*a^5*e^(2*I*d*x - 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 26880*I*a^5*e^(8*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) - 384*I*a^5*e^(-8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 192*I*a^5*e^(20*I*d*x + 12*I*c) - 1152*I*a^5*e^(18*I*d*x + 10*I*c) - 2304*I*a^5*e^(16*I*d*x + 8*I*c) + 8064*I*a^5*e^(12*I*d*x + 4*I*c) + 16128*I*a^5*e^(10*I*d*x + 2*I*c) + 9216*I*a^5*e^(6*I*d*x - 2*I*c) + 2880*I*a^5*e^(4*I*d*x - 4*I*c) + 384*I*a^5*e^(2*I*d*x - 6*I*c) + 16128*I*a^5*e^(8*I*d*x))/(d*e^(16*I*d*x + 8*I*c) + 8*d*e^(14*I*d*x + 6*I*c) + 28*d*e^(12*I*d*x + 4*I*c) + 56*d*e^(10*I*d*x + 2*I*c) + 56*d*e^(6*I*d*x - 2*I*c) + 28*d*e^(4*I*d*x - 4*I*c) + 8*d*e^(2*I*d*x - 6*I*c) + 70*d*e^(8*I*d*x) + d*e^(-8*I*c))","B",0
66,1,187,0,3.512642," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{-32 i \, a^{5} e^{\left(18 i \, d x + 12 i \, c\right)} - 240 i \, a^{5} e^{\left(16 i \, d x + 10 i \, c\right)} - 768 i \, a^{5} e^{\left(14 i \, d x + 8 i \, c\right)} - 1360 i \, a^{5} e^{\left(12 i \, d x + 6 i \, c\right)} - 1440 i \, a^{5} e^{\left(10 i \, d x + 4 i \, c\right)} - 912 i \, a^{5} e^{\left(8 i \, d x + 2 i \, c\right)} - 48 i \, a^{5} e^{\left(4 i \, d x - 2 i \, c\right)} - 320 i \, a^{5} e^{\left(6 i \, d x\right)}}{384 \, {\left(d e^{\left(12 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 4 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 2 i \, c\right)} + 15 \, d e^{\left(4 i \, d x - 2 i \, c\right)} + 6 \, d e^{\left(2 i \, d x - 4 i \, c\right)} + 20 \, d e^{\left(6 i \, d x\right)} + d e^{\left(-6 i \, c\right)}\right)}}"," ",0,"1/384*(-32*I*a^5*e^(18*I*d*x + 12*I*c) - 240*I*a^5*e^(16*I*d*x + 10*I*c) - 768*I*a^5*e^(14*I*d*x + 8*I*c) - 1360*I*a^5*e^(12*I*d*x + 6*I*c) - 1440*I*a^5*e^(10*I*d*x + 4*I*c) - 912*I*a^5*e^(8*I*d*x + 2*I*c) - 48*I*a^5*e^(4*I*d*x - 2*I*c) - 320*I*a^5*e^(6*I*d*x))/(d*e^(12*I*d*x + 6*I*c) + 6*d*e^(10*I*d*x + 4*I*c) + 15*d*e^(8*I*d*x + 2*I*c) + 15*d*e^(4*I*d*x - 2*I*c) + 6*d*e^(2*I*d*x - 4*I*c) + 20*d*e^(6*I*d*x) + d*e^(-6*I*c))","B",0
67,1,267,0,4.716057," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{-24 i \, a^{5} e^{\left(24 i \, d x + 16 i \, c\right)} - 288 i \, a^{5} e^{\left(22 i \, d x + 14 i \, c\right)} - 1584 i \, a^{5} e^{\left(20 i \, d x + 12 i \, c\right)} - 5280 i \, a^{5} e^{\left(18 i \, d x + 10 i \, c\right)} - 11856 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} - 18816 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} - 21504 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} - 17664 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} - 3936 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} - 912 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} - 96 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} - 10200 i \, a^{5} e^{\left(8 i \, d x\right)}}{1536 \, {\left(d e^{\left(16 i \, d x + 8 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 4 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 2 i \, c\right)} + 56 \, d e^{\left(6 i \, d x - 2 i \, c\right)} + 28 \, d e^{\left(4 i \, d x - 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x - 6 i \, c\right)} + 70 \, d e^{\left(8 i \, d x\right)} + d e^{\left(-8 i \, c\right)}\right)}}"," ",0,"1/1536*(-24*I*a^5*e^(24*I*d*x + 16*I*c) - 288*I*a^5*e^(22*I*d*x + 14*I*c) - 1584*I*a^5*e^(20*I*d*x + 12*I*c) - 5280*I*a^5*e^(18*I*d*x + 10*I*c) - 11856*I*a^5*e^(16*I*d*x + 8*I*c) - 18816*I*a^5*e^(14*I*d*x + 6*I*c) - 21504*I*a^5*e^(12*I*d*x + 4*I*c) - 17664*I*a^5*e^(10*I*d*x + 2*I*c) - 3936*I*a^5*e^(6*I*d*x - 2*I*c) - 912*I*a^5*e^(4*I*d*x - 4*I*c) - 96*I*a^5*e^(2*I*d*x - 6*I*c) - 10200*I*a^5*e^(8*I*d*x))/(d*e^(16*I*d*x + 8*I*c) + 8*d*e^(14*I*d*x + 6*I*c) + 28*d*e^(12*I*d*x + 4*I*c) + 56*d*e^(10*I*d*x + 2*I*c) + 56*d*e^(6*I*d*x - 2*I*c) + 28*d*e^(4*I*d*x - 4*I*c) + 8*d*e^(2*I*d*x - 6*I*c) + 70*d*e^(8*I*d*x) + d*e^(-8*I*c))","B",0
68,1,857,0,6.403058," ","integrate(cos(d*x+c)^10*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{960 \, a^{5} d x e^{\left(16 i \, d x + 8 i \, c\right)} + 7680 \, a^{5} d x e^{\left(14 i \, d x + 6 i \, c\right)} + 26880 \, a^{5} d x e^{\left(12 i \, d x + 4 i \, c\right)} + 53760 \, a^{5} d x e^{\left(10 i \, d x + 2 i \, c\right)} + 53760 \, a^{5} d x e^{\left(6 i \, d x - 2 i \, c\right)} + 26880 \, a^{5} d x e^{\left(4 i \, d x - 4 i \, c\right)} + 7680 \, a^{5} d x e^{\left(2 i \, d x - 6 i \, c\right)} + 67200 \, a^{5} d x e^{\left(8 i \, d x\right)} + 960 \, a^{5} d x e^{\left(-8 i \, c\right)} - 390 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 3120 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 10920 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 21840 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 21840 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 10920 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 3120 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 27300 i \, a^{5} e^{\left(8 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 390 i \, a^{5} e^{\left(-8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 390 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 3120 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 10920 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 21840 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 21840 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 10920 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 3120 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 27300 i \, a^{5} e^{\left(8 i \, d x\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 390 i \, a^{5} e^{\left(-8 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 96 i \, a^{5} e^{\left(26 i \, d x + 18 i \, c\right)} - 1368 i \, a^{5} e^{\left(24 i \, d x + 16 i \, c\right)} - 9088 i \, a^{5} e^{\left(22 i \, d x + 14 i \, c\right)} - 37376 i \, a^{5} e^{\left(20 i \, d x + 12 i \, c\right)} - 106720 i \, a^{5} e^{\left(18 i \, d x + 10 i \, c\right)} - 223376 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} - 349888 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} - 409568 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} - 352096 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} - 88000 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} - 21600 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} - 2400 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} - 215000 i \, a^{5} e^{\left(8 i \, d x\right)}}{30720 \, {\left(d e^{\left(16 i \, d x + 8 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 4 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 2 i \, c\right)} + 56 \, d e^{\left(6 i \, d x - 2 i \, c\right)} + 28 \, d e^{\left(4 i \, d x - 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x - 6 i \, c\right)} + 70 \, d e^{\left(8 i \, d x\right)} + d e^{\left(-8 i \, c\right)}\right)}}"," ",0,"1/30720*(960*a^5*d*x*e^(16*I*d*x + 8*I*c) + 7680*a^5*d*x*e^(14*I*d*x + 6*I*c) + 26880*a^5*d*x*e^(12*I*d*x + 4*I*c) + 53760*a^5*d*x*e^(10*I*d*x + 2*I*c) + 53760*a^5*d*x*e^(6*I*d*x - 2*I*c) + 26880*a^5*d*x*e^(4*I*d*x - 4*I*c) + 7680*a^5*d*x*e^(2*I*d*x - 6*I*c) + 67200*a^5*d*x*e^(8*I*d*x) + 960*a^5*d*x*e^(-8*I*c) - 390*I*a^5*e^(16*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 3120*I*a^5*e^(14*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 10920*I*a^5*e^(12*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 21840*I*a^5*e^(10*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 21840*I*a^5*e^(6*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 10920*I*a^5*e^(4*I*d*x - 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 3120*I*a^5*e^(2*I*d*x - 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 27300*I*a^5*e^(8*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) - 390*I*a^5*e^(-8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 390*I*a^5*e^(16*I*d*x + 8*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 3120*I*a^5*e^(14*I*d*x + 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 10920*I*a^5*e^(12*I*d*x + 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 21840*I*a^5*e^(10*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 21840*I*a^5*e^(6*I*d*x - 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 10920*I*a^5*e^(4*I*d*x - 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 3120*I*a^5*e^(2*I*d*x - 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 27300*I*a^5*e^(8*I*d*x)*log(e^(2*I*d*x) + e^(-2*I*c)) + 390*I*a^5*e^(-8*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) - 96*I*a^5*e^(26*I*d*x + 18*I*c) - 1368*I*a^5*e^(24*I*d*x + 16*I*c) - 9088*I*a^5*e^(22*I*d*x + 14*I*c) - 37376*I*a^5*e^(20*I*d*x + 12*I*c) - 106720*I*a^5*e^(18*I*d*x + 10*I*c) - 223376*I*a^5*e^(16*I*d*x + 8*I*c) - 349888*I*a^5*e^(14*I*d*x + 6*I*c) - 409568*I*a^5*e^(12*I*d*x + 4*I*c) - 352096*I*a^5*e^(10*I*d*x + 2*I*c) - 88000*I*a^5*e^(6*I*d*x - 2*I*c) - 21600*I*a^5*e^(4*I*d*x - 4*I*c) - 2400*I*a^5*e^(2*I*d*x - 6*I*c) - 215000*I*a^5*e^(8*I*d*x))/(d*e^(16*I*d*x + 8*I*c) + 8*d*e^(14*I*d*x + 6*I*c) + 28*d*e^(12*I*d*x + 4*I*c) + 56*d*e^(10*I*d*x + 2*I*c) + 56*d*e^(6*I*d*x - 2*I*c) + 28*d*e^(4*I*d*x - 4*I*c) + 8*d*e^(2*I*d*x - 6*I*c) + 70*d*e^(8*I*d*x) + d*e^(-8*I*c))","B",0
69,1,914,0,7.736000," ","integrate(cos(d*x+c)^12*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{13440 \, a^{5} d x e^{\left(18 i \, d x + 10 i \, c\right)} + 107520 \, a^{5} d x e^{\left(16 i \, d x + 8 i \, c\right)} + 376320 \, a^{5} d x e^{\left(14 i \, d x + 6 i \, c\right)} + 752640 \, a^{5} d x e^{\left(12 i \, d x + 4 i \, c\right)} + 940800 \, a^{5} d x e^{\left(10 i \, d x + 2 i \, c\right)} + 376320 \, a^{5} d x e^{\left(6 i \, d x - 2 i \, c\right)} + 107520 \, a^{5} d x e^{\left(4 i \, d x - 4 i \, c\right)} + 13440 \, a^{5} d x e^{\left(2 i \, d x - 6 i \, c\right)} + 752640 \, a^{5} d x e^{\left(8 i \, d x\right)} - 4710 i \, a^{5} e^{\left(18 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 37680 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 131880 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 263760 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 329700 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 131880 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 37680 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 4710 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 263760 i \, a^{5} e^{\left(8 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 4710 i \, a^{5} e^{\left(18 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 37680 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 131880 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 263760 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 329700 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 131880 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 37680 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 4710 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 263760 i \, a^{5} e^{\left(8 i \, d x\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 160 i \, a^{5} e^{\left(30 i \, d x + 22 i \, c\right)} - 2624 i \, a^{5} e^{\left(28 i \, d x + 20 i \, c\right)} - 20272 i \, a^{5} e^{\left(26 i \, d x + 18 i \, c\right)} - 98112 i \, a^{5} e^{\left(24 i \, d x + 16 i \, c\right)} - 333984 i \, a^{5} e^{\left(22 i \, d x + 14 i \, c\right)} - 853440 i \, a^{5} e^{\left(20 i \, d x + 12 i \, c\right)} - 1691424 i \, a^{5} e^{\left(18 i \, d x + 10 i \, c\right)} - 2609472 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} - 3076512 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} - 2680384 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} - 1640240 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} - 124320 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} + 6720 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} + 7680 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} - 642880 i \, a^{5} e^{\left(8 i \, d x\right)} + 960 i \, a^{5} e^{\left(-8 i \, c\right)}}{245760 \, {\left(d e^{\left(18 i \, d x + 10 i \, c\right)} + 8 \, d e^{\left(16 i \, d x + 8 i \, c\right)} + 28 \, d e^{\left(14 i \, d x + 6 i \, c\right)} + 56 \, d e^{\left(12 i \, d x + 4 i \, c\right)} + 70 \, d e^{\left(10 i \, d x + 2 i \, c\right)} + 28 \, d e^{\left(6 i \, d x - 2 i \, c\right)} + 8 \, d e^{\left(4 i \, d x - 4 i \, c\right)} + d e^{\left(2 i \, d x - 6 i \, c\right)} + 56 \, d e^{\left(8 i \, d x\right)}\right)}}"," ",0,"1/245760*(13440*a^5*d*x*e^(18*I*d*x + 10*I*c) + 107520*a^5*d*x*e^(16*I*d*x + 8*I*c) + 376320*a^5*d*x*e^(14*I*d*x + 6*I*c) + 752640*a^5*d*x*e^(12*I*d*x + 4*I*c) + 940800*a^5*d*x*e^(10*I*d*x + 2*I*c) + 376320*a^5*d*x*e^(6*I*d*x - 2*I*c) + 107520*a^5*d*x*e^(4*I*d*x - 4*I*c) + 13440*a^5*d*x*e^(2*I*d*x - 6*I*c) + 752640*a^5*d*x*e^(8*I*d*x) - 4710*I*a^5*e^(18*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 37680*I*a^5*e^(16*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 131880*I*a^5*e^(14*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 263760*I*a^5*e^(12*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 329700*I*a^5*e^(10*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 131880*I*a^5*e^(6*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 37680*I*a^5*e^(4*I*d*x - 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 4710*I*a^5*e^(2*I*d*x - 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 263760*I*a^5*e^(8*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) + 4710*I*a^5*e^(18*I*d*x + 10*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 37680*I*a^5*e^(16*I*d*x + 8*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 131880*I*a^5*e^(14*I*d*x + 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 263760*I*a^5*e^(12*I*d*x + 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 329700*I*a^5*e^(10*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 131880*I*a^5*e^(6*I*d*x - 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 37680*I*a^5*e^(4*I*d*x - 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 4710*I*a^5*e^(2*I*d*x - 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 263760*I*a^5*e^(8*I*d*x)*log(e^(2*I*d*x) + e^(-2*I*c)) - 160*I*a^5*e^(30*I*d*x + 22*I*c) - 2624*I*a^5*e^(28*I*d*x + 20*I*c) - 20272*I*a^5*e^(26*I*d*x + 18*I*c) - 98112*I*a^5*e^(24*I*d*x + 16*I*c) - 333984*I*a^5*e^(22*I*d*x + 14*I*c) - 853440*I*a^5*e^(20*I*d*x + 12*I*c) - 1691424*I*a^5*e^(18*I*d*x + 10*I*c) - 2609472*I*a^5*e^(16*I*d*x + 8*I*c) - 3076512*I*a^5*e^(14*I*d*x + 6*I*c) - 2680384*I*a^5*e^(12*I*d*x + 4*I*c) - 1640240*I*a^5*e^(10*I*d*x + 2*I*c) - 124320*I*a^5*e^(6*I*d*x - 2*I*c) + 6720*I*a^5*e^(4*I*d*x - 4*I*c) + 7680*I*a^5*e^(2*I*d*x - 6*I*c) - 642880*I*a^5*e^(8*I*d*x) + 960*I*a^5*e^(-8*I*c))/(d*e^(18*I*d*x + 10*I*c) + 8*d*e^(16*I*d*x + 8*I*c) + 28*d*e^(14*I*d*x + 6*I*c) + 56*d*e^(12*I*d*x + 4*I*c) + 70*d*e^(10*I*d*x + 2*I*c) + 28*d*e^(6*I*d*x - 2*I*c) + 8*d*e^(4*I*d*x - 4*I*c) + d*e^(2*I*d*x - 6*I*c) + 56*d*e^(8*I*d*x))","B",0
70,1,189,0,2.088901," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{315 \, a^{5} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 315 \, a^{5} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) - \frac{2 \, {\left(275 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 200 i \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 750 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1600 i \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3280 i \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 750 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2240 i \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 275 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 488 i \, a^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{40 \, d}"," ",0,"1/40*(315*a^5*log(tan(1/2*d*x + 1/2*c) + 1) - 315*a^5*log(tan(1/2*d*x + 1/2*c) - 1) - 2*(275*a^5*tan(1/2*d*x + 1/2*c)^9 + 200*I*a^5*tan(1/2*d*x + 1/2*c)^8 - 750*a^5*tan(1/2*d*x + 1/2*c)^7 - 1600*I*a^5*tan(1/2*d*x + 1/2*c)^6 + 3280*I*a^5*tan(1/2*d*x + 1/2*c)^4 + 750*a^5*tan(1/2*d*x + 1/2*c)^3 - 2240*I*a^5*tan(1/2*d*x + 1/2*c)^2 - 275*a^5*tan(1/2*d*x + 1/2*c) + 488*I*a^5)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","A",0
71,1,510,0,3.486452," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\frac{8295 \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 24885 \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 24885 \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 18585 \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 55755 \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 55755 \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 8295 \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 24885 \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 24885 \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 18585 \, a^{5} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 55755 \, a^{5} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 55755 \, a^{5} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 24576 i \, a^{5} e^{\left(7 i \, d x + 7 i \, c\right)} - 118272 i \, a^{5} e^{\left(5 i \, d x + 5 i \, c\right)} - 143360 i \, a^{5} e^{\left(3 i \, d x + 3 i \, c\right)} - 53760 i \, a^{5} e^{\left(i \, d x + i \, c\right)} + 8295 \, a^{5} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 18585 \, a^{5} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 8295 \, a^{5} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 18585 \, a^{5} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right)}{1536 \, {\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,"1/1536*(8295*a^5*e^(6*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 24885*a^5*e^(4*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 24885*a^5*e^(2*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) - 18585*a^5*e^(6*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) - 55755*a^5*e^(4*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) - 55755*a^5*e^(2*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) - 8295*a^5*e^(6*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 24885*a^5*e^(4*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 24885*a^5*e^(2*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) + 18585*a^5*e^(6*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 55755*a^5*e^(4*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 55755*a^5*e^(2*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 24576*I*a^5*e^(7*I*d*x + 7*I*c) - 118272*I*a^5*e^(5*I*d*x + 5*I*c) - 143360*I*a^5*e^(3*I*d*x + 3*I*c) - 53760*I*a^5*e^(I*d*x + I*c) + 8295*a^5*log(I*e^(I*d*x + I*c) + 1) - 18585*a^5*log(I*e^(I*d*x + I*c) - 1) - 8295*a^5*log(-I*e^(I*d*x + I*c) + 1) + 18585*a^5*log(-I*e^(I*d*x + 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)","B",0
72,1,1683,0,3.226378," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{39225 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 313800 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1098300 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2196600 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2196600 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1098300 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 313800 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2745750 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 39225 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 8520 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 68160 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 238560 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 477120 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 477120 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 238560 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 68160 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 596400 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 8520 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 39225 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 313800 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1098300 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2196600 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2196600 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1098300 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 313800 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2745750 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 39225 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 8520 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 68160 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 238560 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 477120 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 477120 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 238560 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 68160 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 596400 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 8520 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 15 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 120 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 420 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 840 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 840 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 420 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 120 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1050 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 15 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 15 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 120 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 420 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 840 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 840 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 420 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 120 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1050 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 15 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 8192 i \, a^{5} e^{\left(19 i \, d x + 11 i \, c\right)} + 16384 i \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} - 176128 i \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} - 1003520 i \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} - 2437120 i \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} - 3411968 i \, a^{5} e^{\left(9 i \, d x + i \, c\right)} - 2953216 i \, a^{5} e^{\left(7 i \, d x - i \, c\right)} - 1568768 i \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} - 471040 i \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)} - 61440 i \, a^{5} e^{\left(i \, d x - 7 i \, c\right)}}{6144 \, {\left(d e^{\left(16 i \, d x + 8 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 4 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 2 i \, c\right)} + 56 \, d e^{\left(6 i \, d x - 2 i \, c\right)} + 28 \, d e^{\left(4 i \, d x - 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x - 6 i \, c\right)} + 70 \, d e^{\left(8 i \, d x\right)} + d e^{\left(-8 i \, c\right)}\right)}}"," ",0,"-1/6144*(39225*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 313800*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1098300*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2196600*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2196600*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1098300*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 313800*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2745750*a^5*e^(8*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 39225*a^5*e^(-8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 8520*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 68160*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 238560*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 477120*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 477120*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 238560*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 68160*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 596400*a^5*e^(8*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 8520*a^5*e^(-8*I*c)*log(I*e^(I*d*x + I*c) - 1) - 39225*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 313800*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1098300*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2196600*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2196600*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1098300*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 313800*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2745750*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 39225*a^5*e^(-8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 8520*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 68160*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 238560*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 477120*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 477120*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 238560*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 68160*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 596400*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 8520*a^5*e^(-8*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 15*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 120*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 420*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 840*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 840*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 420*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 120*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 1050*a^5*e^(8*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) + 15*a^5*e^(-8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 15*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 120*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 420*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 840*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 840*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 420*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 120*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 1050*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) - 15*a^5*e^(-8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 8192*I*a^5*e^(19*I*d*x + 11*I*c) + 16384*I*a^5*e^(17*I*d*x + 9*I*c) - 176128*I*a^5*e^(15*I*d*x + 7*I*c) - 1003520*I*a^5*e^(13*I*d*x + 5*I*c) - 2437120*I*a^5*e^(11*I*d*x + 3*I*c) - 3411968*I*a^5*e^(9*I*d*x + I*c) - 2953216*I*a^5*e^(7*I*d*x - I*c) - 1568768*I*a^5*e^(5*I*d*x - 3*I*c) - 471040*I*a^5*e^(3*I*d*x - 5*I*c) - 61440*I*a^5*e^(I*d*x - 7*I*c))/(d*e^(16*I*d*x + 8*I*c) + 8*d*e^(14*I*d*x + 6*I*c) + 28*d*e^(12*I*d*x + 4*I*c) + 56*d*e^(10*I*d*x + 2*I*c) + 56*d*e^(6*I*d*x - 2*I*c) + 28*d*e^(4*I*d*x - 4*I*c) + 8*d*e^(2*I*d*x - 6*I*c) + 70*d*e^(8*I*d*x) + d*e^(-8*I*c))","B",0
73,1,1669,0,6.630089," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{34125 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 273000 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 955500 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1911000 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1911000 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 955500 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 273000 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2388750 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 34125 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 34770 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 278160 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 973560 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1947120 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1947120 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 973560 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 278160 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 2433900 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 34770 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 34125 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 273000 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 955500 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1911000 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1911000 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 955500 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 273000 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2388750 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 34125 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 34770 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 278160 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 973560 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1947120 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1947120 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 973560 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 278160 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 2433900 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 34770 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 645 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 5160 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 18060 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 36120 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 36120 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 18060 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 5160 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 45150 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 645 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 645 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 5160 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 18060 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 36120 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 36120 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 18060 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 5160 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 45150 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 645 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 24576 i \, a^{5} e^{\left(21 i \, d x + 13 i \, c\right)} + 196608 i \, a^{5} e^{\left(19 i \, d x + 11 i \, c\right)} + 688128 i \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} + 1376256 i \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} + 1720320 i \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} + 1376256 i \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} + 688128 i \, a^{5} e^{\left(9 i \, d x + i \, c\right)} + 196608 i \, a^{5} e^{\left(7 i \, d x - i \, c\right)} + 24576 i \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)}}{122880 \, {\left(d e^{\left(16 i \, d x + 8 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 4 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 2 i \, c\right)} + 56 \, d e^{\left(6 i \, d x - 2 i \, c\right)} + 28 \, d e^{\left(4 i \, d x - 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x - 6 i \, c\right)} + 70 \, d e^{\left(8 i \, d x\right)} + d e^{\left(-8 i \, c\right)}\right)}}"," ",0,"-1/122880*(34125*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 273000*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 955500*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1911000*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1911000*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 955500*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 273000*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2388750*a^5*e^(8*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 34125*a^5*e^(-8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 34770*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 278160*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 973560*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1947120*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1947120*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 973560*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 278160*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 2433900*a^5*e^(8*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 34770*a^5*e^(-8*I*c)*log(I*e^(I*d*x + I*c) - 1) - 34125*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 273000*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 955500*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1911000*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1911000*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 955500*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 273000*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2388750*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 34125*a^5*e^(-8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 34770*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 278160*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 973560*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1947120*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1947120*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 973560*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 278160*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 2433900*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 34770*a^5*e^(-8*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 645*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 5160*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 18060*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 36120*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 36120*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 18060*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 5160*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 45150*a^5*e^(8*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) + 645*a^5*e^(-8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 645*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 5160*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 18060*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 36120*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 36120*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 18060*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 5160*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 45150*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) - 645*a^5*e^(-8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 24576*I*a^5*e^(21*I*d*x + 13*I*c) + 196608*I*a^5*e^(19*I*d*x + 11*I*c) + 688128*I*a^5*e^(17*I*d*x + 9*I*c) + 1376256*I*a^5*e^(15*I*d*x + 7*I*c) + 1720320*I*a^5*e^(13*I*d*x + 5*I*c) + 1376256*I*a^5*e^(11*I*d*x + 3*I*c) + 688128*I*a^5*e^(9*I*d*x + I*c) + 196608*I*a^5*e^(7*I*d*x - I*c) + 24576*I*a^5*e^(5*I*d*x - 3*I*c))/(d*e^(16*I*d*x + 8*I*c) + 8*d*e^(14*I*d*x + 6*I*c) + 28*d*e^(12*I*d*x + 4*I*c) + 56*d*e^(10*I*d*x + 2*I*c) + 56*d*e^(6*I*d*x - 2*I*c) + 28*d*e^(4*I*d*x - 4*I*c) + 8*d*e^(2*I*d*x - 6*I*c) + 70*d*e^(8*I*d*x) + d*e^(-8*I*c))","B",0
74,1,1697,0,6.694185," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{7357770 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 58862160 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 206017560 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 412035120 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 412035120 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 206017560 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 58862160 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 515043900 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 7357770 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 7390425 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 59123400 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 206931900 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 413863800 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 413863800 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 206931900 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 59123400 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 517329750 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 7390425 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7357770 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 58862160 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 206017560 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 412035120 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 412035120 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 206017560 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 58862160 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 515043900 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 7357770 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 7390425 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 59123400 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 206931900 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 413863800 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 413863800 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 206931900 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 59123400 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 517329750 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7390425 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 32655 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 261240 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 914340 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1828680 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1828680 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 914340 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 261240 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2285850 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 32655 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 32655 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 261240 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 914340 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1828680 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1828680 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 914340 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 261240 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2285850 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 32655 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 122880 i \, a^{5} e^{\left(23 i \, d x + 15 i \, c\right)} + 1327104 i \, a^{5} e^{\left(21 i \, d x + 13 i \, c\right)} + 6479872 i \, a^{5} e^{\left(19 i \, d x + 11 i \, c\right)} + 18808832 i \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} + 35897344 i \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} + 47022080 i \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} + 42778624 i \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} + 26673152 i \, a^{5} e^{\left(9 i \, d x + i \, c\right)} + 10903552 i \, a^{5} e^{\left(7 i \, d x - i \, c\right)} + 2637824 i \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} + 286720 i \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)}}{3440640 \, {\left(d e^{\left(16 i \, d x + 8 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 4 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 2 i \, c\right)} + 56 \, d e^{\left(6 i \, d x - 2 i \, c\right)} + 28 \, d e^{\left(4 i \, d x - 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x - 6 i \, c\right)} + 70 \, d e^{\left(8 i \, d x\right)} + d e^{\left(-8 i \, c\right)}\right)}}"," ",0,"-1/3440640*(7357770*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 58862160*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 206017560*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 412035120*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 412035120*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 206017560*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 58862160*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 515043900*a^5*e^(8*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 7357770*a^5*e^(-8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 7390425*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 59123400*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 206931900*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 413863800*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 413863800*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 206931900*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 59123400*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 517329750*a^5*e^(8*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 7390425*a^5*e^(-8*I*c)*log(I*e^(I*d*x + I*c) - 1) - 7357770*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 58862160*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 206017560*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 412035120*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 412035120*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 206017560*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 58862160*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 515043900*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 7357770*a^5*e^(-8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 7390425*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 59123400*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 206931900*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 413863800*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 413863800*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 206931900*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 59123400*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 517329750*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 7390425*a^5*e^(-8*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 32655*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 261240*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 914340*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 1828680*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 1828680*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 914340*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 261240*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 2285850*a^5*e^(8*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) + 32655*a^5*e^(-8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 32655*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 261240*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 914340*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 1828680*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 1828680*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 914340*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 261240*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 2285850*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) - 32655*a^5*e^(-8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 122880*I*a^5*e^(23*I*d*x + 15*I*c) + 1327104*I*a^5*e^(21*I*d*x + 13*I*c) + 6479872*I*a^5*e^(19*I*d*x + 11*I*c) + 18808832*I*a^5*e^(17*I*d*x + 9*I*c) + 35897344*I*a^5*e^(15*I*d*x + 7*I*c) + 47022080*I*a^5*e^(13*I*d*x + 5*I*c) + 42778624*I*a^5*e^(11*I*d*x + 3*I*c) + 26673152*I*a^5*e^(9*I*d*x + I*c) + 10903552*I*a^5*e^(7*I*d*x - I*c) + 2637824*I*a^5*e^(5*I*d*x - 3*I*c) + 286720*I*a^5*e^(3*I*d*x - 5*I*c))/(d*e^(16*I*d*x + 8*I*c) + 8*d*e^(14*I*d*x + 6*I*c) + 28*d*e^(12*I*d*x + 4*I*c) + 56*d*e^(10*I*d*x + 2*I*c) + 56*d*e^(6*I*d*x - 2*I*c) + 28*d*e^(4*I*d*x - 4*I*c) + 8*d*e^(2*I*d*x - 6*I*c) + 70*d*e^(8*I*d*x) + d*e^(-8*I*c))","B",0
75,1,1725,0,6.274825," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{69853455 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 558827640 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1955896740 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3911793480 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3911793480 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1955896740 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 558827640 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 4889741850 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 69853455 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 70703325 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 565626600 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1979693100 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3959386200 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3959386200 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1979693100 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 565626600 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 4949232750 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 70703325 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 69853455 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 558827640 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1955896740 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3911793480 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3911793480 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1955896740 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 558827640 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 4889741850 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 69853455 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 70703325 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 565626600 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1979693100 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3959386200 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3959386200 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1979693100 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 565626600 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 4949232750 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 70703325 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 849870 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 6798960 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23796360 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 47592720 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 47592720 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23796360 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 6798960 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 59490900 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 849870 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 849870 \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 6798960 \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23796360 \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 47592720 \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 47592720 \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23796360 \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 6798960 \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 59490900 \, a^{5} e^{\left(8 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 849870 \, a^{5} e^{\left(-8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 286720 i \, a^{5} e^{\left(25 i \, d x + 17 i \, c\right)} + 3768320 i \, a^{5} e^{\left(23 i \, d x + 15 i \, c\right)} + 22921216 i \, a^{5} e^{\left(21 i \, d x + 13 i \, c\right)} + 85557248 i \, a^{5} e^{\left(19 i \, d x + 11 i \, c\right)} + 219455488 i \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} + 409665536 i \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} + 572293120 i \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} + 602341376 i \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} + 472096768 i \, a^{5} e^{\left(9 i \, d x + i \, c\right)} + 267091968 i \, a^{5} e^{\left(7 i \, d x - i \, c\right)} + 102875136 i \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} + 24084480 i \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)} + 2580480 i \, a^{5} e^{\left(i \, d x - 7 i \, c\right)}}{41287680 \, {\left(d e^{\left(16 i \, d x + 8 i \, c\right)} + 8 \, d e^{\left(14 i \, d x + 6 i \, c\right)} + 28 \, d e^{\left(12 i \, d x + 4 i \, c\right)} + 56 \, d e^{\left(10 i \, d x + 2 i \, c\right)} + 56 \, d e^{\left(6 i \, d x - 2 i \, c\right)} + 28 \, d e^{\left(4 i \, d x - 4 i \, c\right)} + 8 \, d e^{\left(2 i \, d x - 6 i \, c\right)} + 70 \, d e^{\left(8 i \, d x\right)} + d e^{\left(-8 i \, c\right)}\right)}}"," ",0,"-1/41287680*(69853455*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 558827640*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1955896740*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3911793480*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3911793480*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1955896740*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 558827640*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 4889741850*a^5*e^(8*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 69853455*a^5*e^(-8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 70703325*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 565626600*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1979693100*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 3959386200*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 3959386200*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1979693100*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 565626600*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 4949232750*a^5*e^(8*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 70703325*a^5*e^(-8*I*c)*log(I*e^(I*d*x + I*c) - 1) - 69853455*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 558827640*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1955896740*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3911793480*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3911793480*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1955896740*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 558827640*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 4889741850*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 69853455*a^5*e^(-8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 70703325*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 565626600*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1979693100*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3959386200*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3959386200*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1979693100*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 565626600*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 4949232750*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 70703325*a^5*e^(-8*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 849870*a^5*e^(16*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 6798960*a^5*e^(14*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 23796360*a^5*e^(12*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 47592720*a^5*e^(10*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 47592720*a^5*e^(6*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 23796360*a^5*e^(4*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 6798960*a^5*e^(2*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 59490900*a^5*e^(8*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) + 849870*a^5*e^(-8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 849870*a^5*e^(16*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 6798960*a^5*e^(14*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 23796360*a^5*e^(12*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 47592720*a^5*e^(10*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 47592720*a^5*e^(6*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 23796360*a^5*e^(4*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 6798960*a^5*e^(2*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 59490900*a^5*e^(8*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) - 849870*a^5*e^(-8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 286720*I*a^5*e^(25*I*d*x + 17*I*c) + 3768320*I*a^5*e^(23*I*d*x + 15*I*c) + 22921216*I*a^5*e^(21*I*d*x + 13*I*c) + 85557248*I*a^5*e^(19*I*d*x + 11*I*c) + 219455488*I*a^5*e^(17*I*d*x + 9*I*c) + 409665536*I*a^5*e^(15*I*d*x + 7*I*c) + 572293120*I*a^5*e^(13*I*d*x + 5*I*c) + 602341376*I*a^5*e^(11*I*d*x + 3*I*c) + 472096768*I*a^5*e^(9*I*d*x + I*c) + 267091968*I*a^5*e^(7*I*d*x - I*c) + 102875136*I*a^5*e^(5*I*d*x - 3*I*c) + 24084480*I*a^5*e^(3*I*d*x - 5*I*c) + 2580480*I*a^5*e^(I*d*x - 7*I*c))/(d*e^(16*I*d*x + 8*I*c) + 8*d*e^(14*I*d*x + 6*I*c) + 28*d*e^(12*I*d*x + 4*I*c) + 56*d*e^(10*I*d*x + 2*I*c) + 56*d*e^(6*I*d*x - 2*I*c) + 28*d*e^(4*I*d*x - 4*I*c) + 8*d*e^(2*I*d*x - 6*I*c) + 70*d*e^(8*I*d*x) + d*e^(-8*I*c))","B",0
76,1,1807,0,6.905155," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","-\frac{168111405 \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1344891240 \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 4707119340 \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9414238680 \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 11767798350 \, a^{5} e^{\left(9 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9414238680 \, a^{5} e^{\left(7 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 4707119340 \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1344891240 \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 168111405 \, a^{5} e^{\left(i \, d x - 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 170251620 \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1362012960 \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 4767045360 \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 9534090720 \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 11917613400 \, a^{5} e^{\left(9 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 9534090720 \, a^{5} e^{\left(7 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 4767045360 \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1362012960 \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 170251620 \, a^{5} e^{\left(i \, d x - 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 168111405 \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1344891240 \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 4707119340 \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9414238680 \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 11767798350 \, a^{5} e^{\left(9 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9414238680 \, a^{5} e^{\left(7 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 4707119340 \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1344891240 \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 168111405 \, a^{5} e^{\left(i \, d x - 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 170251620 \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1362012960 \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 4767045360 \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9534090720 \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 11917613400 \, a^{5} e^{\left(9 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9534090720 \, a^{5} e^{\left(7 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 4767045360 \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1362012960 \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 170251620 \, a^{5} e^{\left(i \, d x - 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 2140215 \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 17121720 \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 59926020 \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 119852040 \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 149815050 \, a^{5} e^{\left(9 i \, d x + i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 119852040 \, a^{5} e^{\left(7 i \, d x - i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 59926020 \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 17121720 \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2140215 \, a^{5} e^{\left(i \, d x - 7 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2140215 \, a^{5} e^{\left(17 i \, d x + 9 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 17121720 \, a^{5} e^{\left(15 i \, d x + 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 59926020 \, a^{5} e^{\left(13 i \, d x + 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 119852040 \, a^{5} e^{\left(11 i \, d x + 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 149815050 \, a^{5} e^{\left(9 i \, d x + i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 119852040 \, a^{5} e^{\left(7 i \, d x - i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 59926020 \, a^{5} e^{\left(5 i \, d x - 3 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 17121720 \, a^{5} e^{\left(3 i \, d x - 5 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2140215 \, a^{5} e^{\left(i \, d x - 7 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 172032 i \, a^{5} e^{\left(28 i \, d x + 20 i \, c\right)} + 2637824 i \, a^{5} e^{\left(26 i \, d x + 18 i \, c\right)} + 18964480 i \, a^{5} e^{\left(24 i \, d x + 16 i \, c\right)} + 84967424 i \, a^{5} e^{\left(22 i \, d x + 14 i \, c\right)} + 266248192 i \, a^{5} e^{\left(20 i \, d x + 12 i \, c\right)} + 624017408 i \, a^{5} e^{\left(18 i \, d x + 10 i \, c\right)} + 1137074176 i \, a^{5} e^{\left(16 i \, d x + 8 i \, c\right)} + 1626275840 i \, a^{5} e^{\left(14 i \, d x + 6 i \, c\right)} + 1792860160 i \, a^{5} e^{\left(12 i \, d x + 4 i \, c\right)} + 1464320000 i \, a^{5} e^{\left(10 i \, d x + 2 i \, c\right)} + 295206912 i \, a^{5} e^{\left(6 i \, d x - 2 i \, c\right)} + 47308800 i \, a^{5} e^{\left(4 i \, d x - 4 i \, c\right)} - 3784704 i \, a^{5} e^{\left(2 i \, d x - 6 i \, c\right)} + 832905216 i \, a^{5} e^{\left(8 i \, d x\right)} - 1892352 i \, a^{5} e^{\left(-8 i \, c\right)}}{121110528 \, {\left(d e^{\left(17 i \, d x + 9 i \, c\right)} + 8 \, d e^{\left(15 i \, d x + 7 i \, c\right)} + 28 \, d e^{\left(13 i \, d x + 5 i \, c\right)} + 56 \, d e^{\left(11 i \, d x + 3 i \, c\right)} + 70 \, d e^{\left(9 i \, d x + i \, c\right)} + 56 \, d e^{\left(7 i \, d x - i \, c\right)} + 28 \, d e^{\left(5 i \, d x - 3 i \, c\right)} + 8 \, d e^{\left(3 i \, d x - 5 i \, c\right)} + d e^{\left(i \, d x - 7 i \, c\right)}\right)}}"," ",0,"-1/121110528*(168111405*a^5*e^(17*I*d*x + 9*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1344891240*a^5*e^(15*I*d*x + 7*I*c)*log(I*e^(I*d*x + I*c) + 1) + 4707119340*a^5*e^(13*I*d*x + 5*I*c)*log(I*e^(I*d*x + I*c) + 1) + 9414238680*a^5*e^(11*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 11767798350*a^5*e^(9*I*d*x + I*c)*log(I*e^(I*d*x + I*c) + 1) + 9414238680*a^5*e^(7*I*d*x - I*c)*log(I*e^(I*d*x + I*c) + 1) + 4707119340*a^5*e^(5*I*d*x - 3*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1344891240*a^5*e^(3*I*d*x - 5*I*c)*log(I*e^(I*d*x + I*c) + 1) + 168111405*a^5*e^(I*d*x - 7*I*c)*log(I*e^(I*d*x + I*c) + 1) + 170251620*a^5*e^(17*I*d*x + 9*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1362012960*a^5*e^(15*I*d*x + 7*I*c)*log(I*e^(I*d*x + I*c) - 1) + 4767045360*a^5*e^(13*I*d*x + 5*I*c)*log(I*e^(I*d*x + I*c) - 1) + 9534090720*a^5*e^(11*I*d*x + 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 11917613400*a^5*e^(9*I*d*x + I*c)*log(I*e^(I*d*x + I*c) - 1) + 9534090720*a^5*e^(7*I*d*x - I*c)*log(I*e^(I*d*x + I*c) - 1) + 4767045360*a^5*e^(5*I*d*x - 3*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1362012960*a^5*e^(3*I*d*x - 5*I*c)*log(I*e^(I*d*x + I*c) - 1) + 170251620*a^5*e^(I*d*x - 7*I*c)*log(I*e^(I*d*x + I*c) - 1) - 168111405*a^5*e^(17*I*d*x + 9*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1344891240*a^5*e^(15*I*d*x + 7*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 4707119340*a^5*e^(13*I*d*x + 5*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 9414238680*a^5*e^(11*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 11767798350*a^5*e^(9*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) + 1) - 9414238680*a^5*e^(7*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) + 1) - 4707119340*a^5*e^(5*I*d*x - 3*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1344891240*a^5*e^(3*I*d*x - 5*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 168111405*a^5*e^(I*d*x - 7*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 170251620*a^5*e^(17*I*d*x + 9*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1362012960*a^5*e^(15*I*d*x + 7*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 4767045360*a^5*e^(13*I*d*x + 5*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 9534090720*a^5*e^(11*I*d*x + 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 11917613400*a^5*e^(9*I*d*x + I*c)*log(-I*e^(I*d*x + I*c) - 1) - 9534090720*a^5*e^(7*I*d*x - I*c)*log(-I*e^(I*d*x + I*c) - 1) - 4767045360*a^5*e^(5*I*d*x - 3*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1362012960*a^5*e^(3*I*d*x - 5*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 170251620*a^5*e^(I*d*x - 7*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 2140215*a^5*e^(17*I*d*x + 9*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 17121720*a^5*e^(15*I*d*x + 7*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 59926020*a^5*e^(13*I*d*x + 5*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 119852040*a^5*e^(11*I*d*x + 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 149815050*a^5*e^(9*I*d*x + I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 119852040*a^5*e^(7*I*d*x - I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 59926020*a^5*e^(5*I*d*x - 3*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 17121720*a^5*e^(3*I*d*x - 5*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 2140215*a^5*e^(I*d*x - 7*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2140215*a^5*e^(17*I*d*x + 9*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 17121720*a^5*e^(15*I*d*x + 7*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 59926020*a^5*e^(13*I*d*x + 5*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 119852040*a^5*e^(11*I*d*x + 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 149815050*a^5*e^(9*I*d*x + I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 119852040*a^5*e^(7*I*d*x - I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 59926020*a^5*e^(5*I*d*x - 3*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 17121720*a^5*e^(3*I*d*x - 5*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 2140215*a^5*e^(I*d*x - 7*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 172032*I*a^5*e^(28*I*d*x + 20*I*c) + 2637824*I*a^5*e^(26*I*d*x + 18*I*c) + 18964480*I*a^5*e^(24*I*d*x + 16*I*c) + 84967424*I*a^5*e^(22*I*d*x + 14*I*c) + 266248192*I*a^5*e^(20*I*d*x + 12*I*c) + 624017408*I*a^5*e^(18*I*d*x + 10*I*c) + 1137074176*I*a^5*e^(16*I*d*x + 8*I*c) + 1626275840*I*a^5*e^(14*I*d*x + 6*I*c) + 1792860160*I*a^5*e^(12*I*d*x + 4*I*c) + 1464320000*I*a^5*e^(10*I*d*x + 2*I*c) + 295206912*I*a^5*e^(6*I*d*x - 2*I*c) + 47308800*I*a^5*e^(4*I*d*x - 4*I*c) - 3784704*I*a^5*e^(2*I*d*x - 6*I*c) + 832905216*I*a^5*e^(8*I*d*x) - 1892352*I*a^5*e^(-8*I*c))/(d*e^(17*I*d*x + 9*I*c) + 8*d*e^(15*I*d*x + 7*I*c) + 28*d*e^(13*I*d*x + 5*I*c) + 56*d*e^(11*I*d*x + 3*I*c) + 70*d*e^(9*I*d*x + I*c) + 56*d*e^(7*I*d*x - I*c) + 28*d*e^(5*I*d*x - 3*I*c) + 8*d*e^(3*I*d*x - 5*I*c) + d*e^(I*d*x - 7*I*c))","B",0
77,1,186,0,5.276274," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{91 \, a^{8} \tan\left(d x + c\right)^{15} - 780 i \, a^{8} \tan\left(d x + c\right)^{14} - 2625 \, a^{8} \tan\left(d x + c\right)^{13} + 3640 i \, a^{8} \tan\left(d x + c\right)^{12} - 1365 \, a^{8} \tan\left(d x + c\right)^{11} + 12012 i \, a^{8} \tan\left(d x + c\right)^{10} + 15015 \, a^{8} \tan\left(d x + c\right)^{9} + 19305 \, a^{8} \tan\left(d x + c\right)^{7} - 20020 i \, a^{8} \tan\left(d x + c\right)^{6} - 3003 \, a^{8} \tan\left(d x + c\right)^{5} - 10920 i \, a^{8} \tan\left(d x + c\right)^{4} - 11375 \, a^{8} \tan\left(d x + c\right)^{3} + 5460 i \, a^{8} \tan\left(d x + c\right)^{2} + 1365 \, a^{8} \tan\left(d x + c\right)}{1365 \, d}"," ",0,"1/1365*(91*a^8*tan(d*x + c)^15 - 780*I*a^8*tan(d*x + c)^14 - 2625*a^8*tan(d*x + c)^13 + 3640*I*a^8*tan(d*x + c)^12 - 1365*a^8*tan(d*x + c)^11 + 12012*I*a^8*tan(d*x + c)^10 + 15015*a^8*tan(d*x + c)^9 + 19305*a^8*tan(d*x + c)^7 - 20020*I*a^8*tan(d*x + c)^6 - 3003*a^8*tan(d*x + c)^5 - 10920*I*a^8*tan(d*x + c)^4 - 11375*a^8*tan(d*x + c)^3 + 5460*I*a^8*tan(d*x + c)^2 + 1365*a^8*tan(d*x + c))/d","B",0
78,1,173,0,4.334469," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{33 \, a^{8} \tan\left(d x + c\right)^{13} - 286 i \, a^{8} \tan\left(d x + c\right)^{12} - 1014 \, a^{8} \tan\left(d x + c\right)^{11} + 1716 i \, a^{8} \tan\left(d x + c\right)^{10} + 715 \, a^{8} \tan\left(d x + c\right)^{9} + 2574 i \, a^{8} \tan\left(d x + c\right)^{8} + 5148 \, a^{8} \tan\left(d x + c\right)^{7} - 3432 i \, a^{8} \tan\left(d x + c\right)^{6} + 1287 \, a^{8} \tan\left(d x + c\right)^{5} - 4290 i \, a^{8} \tan\left(d x + c\right)^{4} - 3718 \, a^{8} \tan\left(d x + c\right)^{3} + 1716 i \, a^{8} \tan\left(d x + c\right)^{2} + 429 \, a^{8} \tan\left(d x + c\right)}{429 \, d}"," ",0,"1/429*(33*a^8*tan(d*x + c)^13 - 286*I*a^8*tan(d*x + c)^12 - 1014*a^8*tan(d*x + c)^11 + 1716*I*a^8*tan(d*x + c)^10 + 715*a^8*tan(d*x + c)^9 + 2574*I*a^8*tan(d*x + c)^8 + 5148*a^8*tan(d*x + c)^7 - 3432*I*a^8*tan(d*x + c)^6 + 1287*a^8*tan(d*x + c)^5 - 4290*I*a^8*tan(d*x + c)^4 - 3718*a^8*tan(d*x + c)^3 + 1716*I*a^8*tan(d*x + c)^2 + 429*a^8*tan(d*x + c))/d","B",0
79,1,134,0,3.563164," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{5 \, a^{8} \tan\left(d x + c\right)^{11} - 44 i \, a^{8} \tan\left(d x + c\right)^{10} - 165 \, a^{8} \tan\left(d x + c\right)^{9} + 330 i \, a^{8} \tan\left(d x + c\right)^{8} + 330 \, a^{8} \tan\left(d x + c\right)^{7} + 462 \, a^{8} \tan\left(d x + c\right)^{5} - 660 i \, a^{8} \tan\left(d x + c\right)^{4} - 495 \, a^{8} \tan\left(d x + c\right)^{3} + 220 i \, a^{8} \tan\left(d x + c\right)^{2} + 55 \, a^{8} \tan\left(d x + c\right)}{55 \, d}"," ",0,"1/55*(5*a^8*tan(d*x + c)^11 - 44*I*a^8*tan(d*x + c)^10 - 165*a^8*tan(d*x + c)^9 + 330*I*a^8*tan(d*x + c)^8 + 330*a^8*tan(d*x + c)^7 + 462*a^8*tan(d*x + c)^5 - 660*I*a^8*tan(d*x + c)^4 - 495*a^8*tan(d*x + c)^3 + 220*I*a^8*tan(d*x + c)^2 + 55*a^8*tan(d*x + c))/d","B",0
80,1,120,0,4.214997," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{a^{8} \tan\left(d x + c\right)^{9} - 9 i \, a^{8} \tan\left(d x + c\right)^{8} - 36 \, a^{8} \tan\left(d x + c\right)^{7} + 84 i \, a^{8} \tan\left(d x + c\right)^{6} + 126 \, a^{8} \tan\left(d x + c\right)^{5} - 126 i \, a^{8} \tan\left(d x + c\right)^{4} - 84 \, a^{8} \tan\left(d x + c\right)^{3} + 36 i \, a^{8} \tan\left(d x + c\right)^{2} + 9 \, a^{8} \tan\left(d x + c\right)}{9 \, d}"," ",0,"1/9*(a^8*tan(d*x + c)^9 - 9*I*a^8*tan(d*x + c)^8 - 36*a^8*tan(d*x + c)^7 + 84*I*a^8*tan(d*x + c)^6 + 126*a^8*tan(d*x + c)^5 - 126*I*a^8*tan(d*x + c)^4 - 84*a^8*tan(d*x + c)^3 + 36*I*a^8*tan(d*x + c)^2 + 9*a^8*tan(d*x + c))/d","B",0
81,1,378,0,1.315754," ","integrate((a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{-13440 i \, a^{8} e^{\left(14 i \, d x + 14 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 94080 i \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 282240 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 470400 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 470400 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 282240 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 94080 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 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)} - 13440 i \, a^{8} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 34848 i \, a^{8}}{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*(-13440*I*a^8*e^(14*I*d*x + 14*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 94080*I*a^8*e^(12*I*d*x + 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 282240*I*a^8*e^(10*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 470400*I*a^8*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 470400*I*a^8*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 282240*I*a^8*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 94080*I*a^8*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 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) - 13440*I*a^8*log(e^(2*I*d*x + 2*I*c) + 1) - 34848*I*a^8)/(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
82,1,302,0,5.528175," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{960 i \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 4800 i \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 9600 i \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 9600 i \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 4800 i \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 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)} + 960 i \, a^{8} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 1392 i \, a^{8}}{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*(960*I*a^8*e^(10*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 4800*I*a^8*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 9600*I*a^8*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 9600*I*a^8*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 4800*I*a^8*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 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) + 960*I*a^8*log(e^(2*I*d*x + 2*I*c) + 1) + 1392*I*a^8)/(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
83,1,785,0,7.986062," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{-107520 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 1505280 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 9784320 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 39137280 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 107627520 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 215255040 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 322882560 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 322882560 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 215255040 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 107627520 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 39137280 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 9784320 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 1505280 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 369008640 i \, a^{8} e^{\left(14 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 107520 i \, a^{8} e^{\left(-14 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 5376 i \, a^{8} e^{\left(32 i \, d x + 18 i \, c\right)} - 32256 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} + 112896 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} + 1849344 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} + 8902656 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} + 24220672 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} + 40941824 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} + 39542272 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} + 5795328 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} - 80602368 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} - 77650944 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} - 49588224 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} - 21590016 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} - 6212864 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} - 1071616 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} - 46007808 i \, a^{8} e^{\left(14 i \, d x\right)} - 84224 i \, a^{8} e^{\left(-14 i \, c\right)}}{1344 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/1344*(-107520*I*a^8*e^(28*I*d*x + 14*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 1505280*I*a^8*e^(26*I*d*x + 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 9784320*I*a^8*e^(24*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 39137280*I*a^8*e^(22*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 107627520*I*a^8*e^(20*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 215255040*I*a^8*e^(18*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 322882560*I*a^8*e^(16*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 322882560*I*a^8*e^(12*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 215255040*I*a^8*e^(10*I*d*x - 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 107627520*I*a^8*e^(8*I*d*x - 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 39137280*I*a^8*e^(6*I*d*x - 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 9784320*I*a^8*e^(4*I*d*x - 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 1505280*I*a^8*e^(2*I*d*x - 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 369008640*I*a^8*e^(14*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) - 107520*I*a^8*e^(-14*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 5376*I*a^8*e^(32*I*d*x + 18*I*c) - 32256*I*a^8*e^(30*I*d*x + 16*I*c) + 112896*I*a^8*e^(28*I*d*x + 14*I*c) + 1849344*I*a^8*e^(26*I*d*x + 12*I*c) + 8902656*I*a^8*e^(24*I*d*x + 10*I*c) + 24220672*I*a^8*e^(22*I*d*x + 8*I*c) + 40941824*I*a^8*e^(20*I*d*x + 6*I*c) + 39542272*I*a^8*e^(18*I*d*x + 4*I*c) + 5795328*I*a^8*e^(16*I*d*x + 2*I*c) - 80602368*I*a^8*e^(12*I*d*x - 2*I*c) - 77650944*I*a^8*e^(10*I*d*x - 4*I*c) - 49588224*I*a^8*e^(8*I*d*x - 6*I*c) - 21590016*I*a^8*e^(6*I*d*x - 8*I*c) - 6212864*I*a^8*e^(4*I*d*x - 10*I*c) - 1071616*I*a^8*e^(2*I*d*x - 12*I*c) - 46007808*I*a^8*e^(14*I*d*x) - 84224*I*a^8*e^(-14*I*c))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
84,1,799,0,7.480932," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{107520 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 1505280 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 9784320 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 39137280 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 107627520 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 215255040 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 322882560 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 322882560 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 215255040 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 107627520 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 39137280 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 9784320 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 1505280 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 369008640 i \, a^{8} e^{\left(14 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 107520 i \, a^{8} e^{\left(-14 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 8960 i \, a^{8} e^{\left(34 i \, d x + 20 i \, c\right)} - 98560 i \, a^{8} e^{\left(32 i \, d x + 18 i \, c\right)} - 519680 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} - 1944320 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} - 6496000 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} - 20034560 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} - 51717120 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} - 103783680 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} - 157597440 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} - 179379200 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} - 91669760 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} - 37157120 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} - 7813120 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} + 716800 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} + 994560 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} + 268800 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} - 151191040 i \, a^{8} e^{\left(14 i \, d x\right)} + 26880 i \, a^{8} e^{\left(-14 i \, c\right)}}{13440 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/13440*(107520*I*a^8*e^(28*I*d*x + 14*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 1505280*I*a^8*e^(26*I*d*x + 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 9784320*I*a^8*e^(24*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 39137280*I*a^8*e^(22*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 107627520*I*a^8*e^(20*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 215255040*I*a^8*e^(18*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 322882560*I*a^8*e^(16*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 322882560*I*a^8*e^(12*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 215255040*I*a^8*e^(10*I*d*x - 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 107627520*I*a^8*e^(8*I*d*x - 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 39137280*I*a^8*e^(6*I*d*x - 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 9784320*I*a^8*e^(4*I*d*x - 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 1505280*I*a^8*e^(2*I*d*x - 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 369008640*I*a^8*e^(14*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) + 107520*I*a^8*e^(-14*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 8960*I*a^8*e^(34*I*d*x + 20*I*c) - 98560*I*a^8*e^(32*I*d*x + 18*I*c) - 519680*I*a^8*e^(30*I*d*x + 16*I*c) - 1944320*I*a^8*e^(28*I*d*x + 14*I*c) - 6496000*I*a^8*e^(26*I*d*x + 12*I*c) - 20034560*I*a^8*e^(24*I*d*x + 10*I*c) - 51717120*I*a^8*e^(22*I*d*x + 8*I*c) - 103783680*I*a^8*e^(20*I*d*x + 6*I*c) - 157597440*I*a^8*e^(18*I*d*x + 4*I*c) - 179379200*I*a^8*e^(16*I*d*x + 2*I*c) - 91669760*I*a^8*e^(12*I*d*x - 2*I*c) - 37157120*I*a^8*e^(10*I*d*x - 4*I*c) - 7813120*I*a^8*e^(8*I*d*x - 6*I*c) + 716800*I*a^8*e^(6*I*d*x - 8*I*c) + 994560*I*a^8*e^(4*I*d*x - 10*I*c) + 268800*I*a^8*e^(2*I*d*x - 12*I*c) - 151191040*I*a^8*e^(14*I*d*x) + 26880*I*a^8*e^(-14*I*c))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
85,1,381,0,11.978785," ","integrate(cos(d*x+c)^8*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{-3840 i \, a^{8} e^{\left(36 i \, d x + 22 i \, c\right)} - 53760 i \, a^{8} e^{\left(34 i \, d x + 20 i \, c\right)} - 349440 i \, a^{8} e^{\left(32 i \, d x + 18 i \, c\right)} - 1397760 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} - 3843840 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} - 7687680 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} - 11531520 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} - 13178880 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} - 11531520 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} - 7687680 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} - 3843840 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} - 349440 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} - 53760 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} - 3840 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} - 1397760 i \, a^{8} e^{\left(14 i \, d x\right)}}{30720 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/30720*(-3840*I*a^8*e^(36*I*d*x + 22*I*c) - 53760*I*a^8*e^(34*I*d*x + 20*I*c) - 349440*I*a^8*e^(32*I*d*x + 18*I*c) - 1397760*I*a^8*e^(30*I*d*x + 16*I*c) - 3843840*I*a^8*e^(28*I*d*x + 14*I*c) - 7687680*I*a^8*e^(26*I*d*x + 12*I*c) - 11531520*I*a^8*e^(24*I*d*x + 10*I*c) - 13178880*I*a^8*e^(22*I*d*x + 8*I*c) - 11531520*I*a^8*e^(20*I*d*x + 6*I*c) - 7687680*I*a^8*e^(18*I*d*x + 4*I*c) - 3843840*I*a^8*e^(16*I*d*x + 2*I*c) - 349440*I*a^8*e^(12*I*d*x - 2*I*c) - 53760*I*a^8*e^(10*I*d*x - 4*I*c) - 3840*I*a^8*e^(8*I*d*x - 6*I*c) - 1397760*I*a^8*e^(14*I*d*x))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
86,1,409,0,13.551065," ","integrate(cos(d*x+c)^10*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{-10752 i \, a^{8} e^{\left(38 i \, d x + 24 i \, c\right)} - 177408 i \, a^{8} e^{\left(36 i \, d x + 22 i \, c\right)} - 1372672 i \, a^{8} e^{\left(34 i \, d x + 20 i \, c\right)} - 6610688 i \, a^{8} e^{\left(32 i \, d x + 18 i \, c\right)} - 22177792 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} - 54955264 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} - 104039936 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} - 153497344 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} - 178354176 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} - 163747584 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} - 118390272 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} - 66696448 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} - 9119488 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} - 2017792 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} - 277760 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} - 17920 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} - 28700672 i \, a^{8} e^{\left(14 i \, d x\right)}}{430080 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/430080*(-10752*I*a^8*e^(38*I*d*x + 24*I*c) - 177408*I*a^8*e^(36*I*d*x + 22*I*c) - 1372672*I*a^8*e^(34*I*d*x + 20*I*c) - 6610688*I*a^8*e^(32*I*d*x + 18*I*c) - 22177792*I*a^8*e^(30*I*d*x + 16*I*c) - 54955264*I*a^8*e^(28*I*d*x + 14*I*c) - 104039936*I*a^8*e^(26*I*d*x + 12*I*c) - 153497344*I*a^8*e^(24*I*d*x + 10*I*c) - 178354176*I*a^8*e^(22*I*d*x + 8*I*c) - 163747584*I*a^8*e^(20*I*d*x + 6*I*c) - 118390272*I*a^8*e^(18*I*d*x + 4*I*c) - 66696448*I*a^8*e^(16*I*d*x + 2*I*c) - 9119488*I*a^8*e^(12*I*d*x - 2*I*c) - 2017792*I*a^8*e^(10*I*d*x - 4*I*c) - 277760*I*a^8*e^(8*I*d*x - 6*I*c) - 17920*I*a^8*e^(6*I*d*x - 8*I*c) - 28700672*I*a^8*e^(14*I*d*x))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
87,1,437,0,15.232293," ","integrate(cos(d*x+c)^12*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{-8960 i \, a^{8} e^{\left(40 i \, d x + 26 i \, c\right)} - 168448 i \, a^{8} e^{\left(38 i \, d x + 24 i \, c\right)} - 1498112 i \, a^{8} e^{\left(36 i \, d x + 22 i \, c\right)} - 8375808 i \, a^{8} e^{\left(34 i \, d x + 20 i \, c\right)} - 32992512 i \, a^{8} e^{\left(32 i \, d x + 18 i \, c\right)} - 97241088 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} - 222267136 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} - 402881024 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} - 587082496 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} - 692916224 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} - 663959296 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} - 515260928 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} - 321414912 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} - 60947712 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} - 17479168 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} - 3530240 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} - 448000 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} - 26880 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} - 158957568 i \, a^{8} e^{\left(14 i \, d x\right)}}{1720320 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/1720320*(-8960*I*a^8*e^(40*I*d*x + 26*I*c) - 168448*I*a^8*e^(38*I*d*x + 24*I*c) - 1498112*I*a^8*e^(36*I*d*x + 22*I*c) - 8375808*I*a^8*e^(34*I*d*x + 20*I*c) - 32992512*I*a^8*e^(32*I*d*x + 18*I*c) - 97241088*I*a^8*e^(30*I*d*x + 16*I*c) - 222267136*I*a^8*e^(28*I*d*x + 14*I*c) - 402881024*I*a^8*e^(26*I*d*x + 12*I*c) - 587082496*I*a^8*e^(24*I*d*x + 10*I*c) - 692916224*I*a^8*e^(22*I*d*x + 8*I*c) - 663959296*I*a^8*e^(20*I*d*x + 6*I*c) - 515260928*I*a^8*e^(18*I*d*x + 4*I*c) - 321414912*I*a^8*e^(16*I*d*x + 2*I*c) - 60947712*I*a^8*e^(12*I*d*x - 2*I*c) - 17479168*I*a^8*e^(10*I*d*x - 4*I*c) - 3530240*I*a^8*e^(8*I*d*x - 6*I*c) - 448000*I*a^8*e^(6*I*d*x - 8*I*c) - 26880*I*a^8*e^(4*I*d*x - 10*I*c) - 158957568*I*a^8*e^(14*I*d*x))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
88,1,465,0,17.002317," ","integrate(cos(d*x+c)^14*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{-3840 i \, a^{8} e^{\left(42 i \, d x + 28 i \, c\right)} - 80640 i \, a^{8} e^{\left(40 i \, d x + 26 i \, c\right)} - 806400 i \, a^{8} e^{\left(38 i \, d x + 24 i \, c\right)} - 5107200 i \, a^{8} e^{\left(36 i \, d x + 22 i \, c\right)} - 22982400 i \, a^{8} e^{\left(34 i \, d x + 20 i \, c\right)} - 78140160 i \, a^{8} e^{\left(32 i \, d x + 18 i \, c\right)} - 208373760 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} - 446511360 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} - 781347840 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} - 1128341760 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} - 1353031680 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} - 1350585600 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} - 1121003520 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} - 769870080 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} - 196842240 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} - 70452480 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} - 19138560 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} - 3709440 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} - 456960 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} - 26880 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} - 433336320 i \, a^{8} e^{\left(14 i \, d x\right)}}{3440640 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/3440640*(-3840*I*a^8*e^(42*I*d*x + 28*I*c) - 80640*I*a^8*e^(40*I*d*x + 26*I*c) - 806400*I*a^8*e^(38*I*d*x + 24*I*c) - 5107200*I*a^8*e^(36*I*d*x + 22*I*c) - 22982400*I*a^8*e^(34*I*d*x + 20*I*c) - 78140160*I*a^8*e^(32*I*d*x + 18*I*c) - 208373760*I*a^8*e^(30*I*d*x + 16*I*c) - 446511360*I*a^8*e^(28*I*d*x + 14*I*c) - 781347840*I*a^8*e^(26*I*d*x + 12*I*c) - 1128341760*I*a^8*e^(24*I*d*x + 10*I*c) - 1353031680*I*a^8*e^(22*I*d*x + 8*I*c) - 1350585600*I*a^8*e^(20*I*d*x + 6*I*c) - 1121003520*I*a^8*e^(18*I*d*x + 4*I*c) - 769870080*I*a^8*e^(16*I*d*x + 2*I*c) - 196842240*I*a^8*e^(12*I*d*x - 2*I*c) - 70452480*I*a^8*e^(10*I*d*x - 4*I*c) - 19138560*I*a^8*e^(8*I*d*x - 6*I*c) - 3709440*I*a^8*e^(6*I*d*x - 8*I*c) - 456960*I*a^8*e^(4*I*d*x - 10*I*c) - 26880*I*a^8*e^(2*I*d*x - 12*I*c) - 433336320*I*a^8*e^(14*I*d*x))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
89,1,1457,0,18.053113," ","integrate(cos(d*x+c)^16*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{215040 \, a^{8} d x e^{\left(28 i \, d x + 14 i \, c\right)} + 3010560 \, a^{8} d x e^{\left(26 i \, d x + 12 i \, c\right)} + 19568640 \, a^{8} d x e^{\left(24 i \, d x + 10 i \, c\right)} + 78274560 \, a^{8} d x e^{\left(22 i \, d x + 8 i \, c\right)} + 215255040 \, a^{8} d x e^{\left(20 i \, d x + 6 i \, c\right)} + 430510080 \, a^{8} d x e^{\left(18 i \, d x + 4 i \, c\right)} + 645765120 \, a^{8} d x e^{\left(16 i \, d x + 2 i \, c\right)} + 645765120 \, a^{8} d x e^{\left(12 i \, d x - 2 i \, c\right)} + 430510080 \, a^{8} d x e^{\left(10 i \, d x - 4 i \, c\right)} + 215255040 \, a^{8} d x e^{\left(8 i \, d x - 6 i \, c\right)} + 78274560 \, a^{8} d x e^{\left(6 i \, d x - 8 i \, c\right)} + 19568640 \, a^{8} d x e^{\left(4 i \, d x - 10 i \, c\right)} + 3010560 \, a^{8} d x e^{\left(2 i \, d x - 12 i \, c\right)} + 738017280 \, a^{8} d x e^{\left(14 i \, d x\right)} + 215040 \, a^{8} d x e^{\left(-14 i \, c\right)} - 103740 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 1452360 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 9440340 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 37761360 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 103843740 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 207687480 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 311531220 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 311531220 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 207687480 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 103843740 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 37761360 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 9440340 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 1452360 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 356035680 i \, a^{8} e^{\left(14 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 103740 i \, a^{8} e^{\left(-14 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 103740 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 1452360 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 9440340 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 37761360 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 103843740 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 207687480 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 311531220 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 311531220 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 207687480 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 103843740 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 37761360 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 9440340 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 1452360 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 356035680 i \, a^{8} e^{\left(14 i \, d x\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 103740 i \, a^{8} e^{\left(-14 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 13440 i \, a^{8} e^{\left(44 i \, d x + 30 i \, c\right)} - 311040 i \, a^{8} e^{\left(42 i \, d x + 28 i \, c\right)} - 3445120 i \, a^{8} e^{\left(40 i \, d x + 26 i \, c\right)} - 24303104 i \, a^{8} e^{\left(38 i \, d x + 24 i \, c\right)} - 122582656 i \, a^{8} e^{\left(36 i \, d x + 22 i \, c\right)} - 470484224 i \, a^{8} e^{\left(34 i \, d x + 20 i \, c\right)} - 1427794816 i \, a^{8} e^{\left(32 i \, d x + 18 i \, c\right)} - 3514563584 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} - 7142793088 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} - 12136447232 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} - 17387563648 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} - 21108086272 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} - 21740071808 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} - 18942724864 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} - 13859732096 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} - 4147974656 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} - 1619129344 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} - 480058880 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} - 101355520 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} - 13547520 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} - 860160 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} - 8407312384 i \, a^{8} e^{\left(14 i \, d x\right)}}{55050240 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/55050240*(215040*a^8*d*x*e^(28*I*d*x + 14*I*c) + 3010560*a^8*d*x*e^(26*I*d*x + 12*I*c) + 19568640*a^8*d*x*e^(24*I*d*x + 10*I*c) + 78274560*a^8*d*x*e^(22*I*d*x + 8*I*c) + 215255040*a^8*d*x*e^(20*I*d*x + 6*I*c) + 430510080*a^8*d*x*e^(18*I*d*x + 4*I*c) + 645765120*a^8*d*x*e^(16*I*d*x + 2*I*c) + 645765120*a^8*d*x*e^(12*I*d*x - 2*I*c) + 430510080*a^8*d*x*e^(10*I*d*x - 4*I*c) + 215255040*a^8*d*x*e^(8*I*d*x - 6*I*c) + 78274560*a^8*d*x*e^(6*I*d*x - 8*I*c) + 19568640*a^8*d*x*e^(4*I*d*x - 10*I*c) + 3010560*a^8*d*x*e^(2*I*d*x - 12*I*c) + 738017280*a^8*d*x*e^(14*I*d*x) + 215040*a^8*d*x*e^(-14*I*c) - 103740*I*a^8*e^(28*I*d*x + 14*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 1452360*I*a^8*e^(26*I*d*x + 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 9440340*I*a^8*e^(24*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 37761360*I*a^8*e^(22*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 103843740*I*a^8*e^(20*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 207687480*I*a^8*e^(18*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 311531220*I*a^8*e^(16*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 311531220*I*a^8*e^(12*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 207687480*I*a^8*e^(10*I*d*x - 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 103843740*I*a^8*e^(8*I*d*x - 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 37761360*I*a^8*e^(6*I*d*x - 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 9440340*I*a^8*e^(4*I*d*x - 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 1452360*I*a^8*e^(2*I*d*x - 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 356035680*I*a^8*e^(14*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) - 103740*I*a^8*e^(-14*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 103740*I*a^8*e^(28*I*d*x + 14*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 1452360*I*a^8*e^(26*I*d*x + 12*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 9440340*I*a^8*e^(24*I*d*x + 10*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 37761360*I*a^8*e^(22*I*d*x + 8*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 103843740*I*a^8*e^(20*I*d*x + 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 207687480*I*a^8*e^(18*I*d*x + 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 311531220*I*a^8*e^(16*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 311531220*I*a^8*e^(12*I*d*x - 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 207687480*I*a^8*e^(10*I*d*x - 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 103843740*I*a^8*e^(8*I*d*x - 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 37761360*I*a^8*e^(6*I*d*x - 8*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 9440340*I*a^8*e^(4*I*d*x - 10*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 1452360*I*a^8*e^(2*I*d*x - 12*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 356035680*I*a^8*e^(14*I*d*x)*log(e^(2*I*d*x) + e^(-2*I*c)) + 103740*I*a^8*e^(-14*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) - 13440*I*a^8*e^(44*I*d*x + 30*I*c) - 311040*I*a^8*e^(42*I*d*x + 28*I*c) - 3445120*I*a^8*e^(40*I*d*x + 26*I*c) - 24303104*I*a^8*e^(38*I*d*x + 24*I*c) - 122582656*I*a^8*e^(36*I*d*x + 22*I*c) - 470484224*I*a^8*e^(34*I*d*x + 20*I*c) - 1427794816*I*a^8*e^(32*I*d*x + 18*I*c) - 3514563584*I*a^8*e^(30*I*d*x + 16*I*c) - 7142793088*I*a^8*e^(28*I*d*x + 14*I*c) - 12136447232*I*a^8*e^(26*I*d*x + 12*I*c) - 17387563648*I*a^8*e^(24*I*d*x + 10*I*c) - 21108086272*I*a^8*e^(22*I*d*x + 8*I*c) - 21740071808*I*a^8*e^(20*I*d*x + 6*I*c) - 18942724864*I*a^8*e^(18*I*d*x + 4*I*c) - 13859732096*I*a^8*e^(16*I*d*x + 2*I*c) - 4147974656*I*a^8*e^(12*I*d*x - 2*I*c) - 1619129344*I*a^8*e^(10*I*d*x - 4*I*c) - 480058880*I*a^8*e^(8*I*d*x - 6*I*c) - 101355520*I*a^8*e^(6*I*d*x - 8*I*c) - 13547520*I*a^8*e^(4*I*d*x - 10*I*c) - 860160*I*a^8*e^(2*I*d*x - 12*I*c) - 8407312384*I*a^8*e^(14*I*d*x))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
90,1,1514,0,23.628694," ","integrate(cos(d*x+c)^18*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{3225600 \, a^{8} d x e^{\left(30 i \, d x + 16 i \, c\right)} + 45158400 \, a^{8} d x e^{\left(28 i \, d x + 14 i \, c\right)} + 293529600 \, a^{8} d x e^{\left(26 i \, d x + 12 i \, c\right)} + 1174118400 \, a^{8} d x e^{\left(24 i \, d x + 10 i \, c\right)} + 3228825600 \, a^{8} d x e^{\left(22 i \, d x + 8 i \, c\right)} + 6457651200 \, a^{8} d x e^{\left(20 i \, d x + 6 i \, c\right)} + 9686476800 \, a^{8} d x e^{\left(18 i \, d x + 4 i \, c\right)} + 11070259200 \, a^{8} d x e^{\left(16 i \, d x + 2 i \, c\right)} + 6457651200 \, a^{8} d x e^{\left(12 i \, d x - 2 i \, c\right)} + 3228825600 \, a^{8} d x e^{\left(10 i \, d x - 4 i \, c\right)} + 1174118400 \, a^{8} d x e^{\left(8 i \, d x - 6 i \, c\right)} + 293529600 \, a^{8} d x e^{\left(6 i \, d x - 8 i \, c\right)} + 45158400 \, a^{8} d x e^{\left(4 i \, d x - 10 i \, c\right)} + 3225600 \, a^{8} d x e^{\left(2 i \, d x - 12 i \, c\right)} + 9686476800 \, a^{8} d x e^{\left(14 i \, d x\right)} - 1515780 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 21220920 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 137935980 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 551743920 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 1517295780 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 3034591560 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 4551887340 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 5202156960 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 3034591560 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 1517295780 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 551743920 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 137935980 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 21220920 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 1515780 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 4551887340 i \, a^{8} e^{\left(14 i \, d x\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 1515780 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 21220920 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 137935980 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 551743920 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 1517295780 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 3034591560 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 4551887340 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 5202156960 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 3034591560 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 1517295780 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 551743920 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 137935980 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 21220920 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 1515780 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) + 4551887340 i \, a^{8} e^{\left(14 i \, d x\right)} \log\left(e^{\left(2 i \, d x\right)} + e^{\left(-2 i \, c\right)}\right) - 17920 i \, a^{8} e^{\left(48 i \, d x + 34 i \, c\right)} - 452480 i \, a^{8} e^{\left(46 i \, d x + 32 i \, c\right)} - 5489920 i \, a^{8} e^{\left(44 i \, d x + 30 i \, c\right)} - 42609280 i \, a^{8} e^{\left(42 i \, d x + 28 i \, c\right)} - 237601280 i \, a^{8} e^{\left(40 i \, d x + 26 i \, c\right)} - 1013595520 i \, a^{8} e^{\left(38 i \, d x + 24 i \, c\right)} - 3439322880 i \, a^{8} e^{\left(36 i \, d x + 22 i \, c\right)} - 9529403520 i \, a^{8} e^{\left(34 i \, d x + 20 i \, c\right)} - 21965959680 i \, a^{8} e^{\left(32 i \, d x + 18 i \, c\right)} - 42709532800 i \, a^{8} e^{\left(30 i \, d x + 16 i \, c\right)} - 70772038400 i \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} - 100658185600 i \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} - 123309222400 i \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} - 129974633600 i \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} - 117140020480 i \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} - 89191105920 i \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} - 56345172480 i \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} - 11479265280 i \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} - 3367687680 i \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} - 645765120 i \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} - 52577280 i \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} + 7418880 i \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} + 2257920 i \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} - 28794769920 i \, a^{8} e^{\left(14 i \, d x\right)} + 161280 i \, a^{8} e^{\left(-14 i \, c\right)}}{330301440 \, {\left(d e^{\left(30 i \, d x + 16 i \, c\right)} + 14 \, d e^{\left(28 i \, d x + 14 i \, c\right)} + 91 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 364 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 1001 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 2002 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 3003 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3432 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 2002 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 1001 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 364 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 91 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 14 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + d e^{\left(2 i \, d x - 12 i \, c\right)} + 3003 \, d e^{\left(14 i \, d x\right)}\right)}}"," ",0,"1/330301440*(3225600*a^8*d*x*e^(30*I*d*x + 16*I*c) + 45158400*a^8*d*x*e^(28*I*d*x + 14*I*c) + 293529600*a^8*d*x*e^(26*I*d*x + 12*I*c) + 1174118400*a^8*d*x*e^(24*I*d*x + 10*I*c) + 3228825600*a^8*d*x*e^(22*I*d*x + 8*I*c) + 6457651200*a^8*d*x*e^(20*I*d*x + 6*I*c) + 9686476800*a^8*d*x*e^(18*I*d*x + 4*I*c) + 11070259200*a^8*d*x*e^(16*I*d*x + 2*I*c) + 6457651200*a^8*d*x*e^(12*I*d*x - 2*I*c) + 3228825600*a^8*d*x*e^(10*I*d*x - 4*I*c) + 1174118400*a^8*d*x*e^(8*I*d*x - 6*I*c) + 293529600*a^8*d*x*e^(6*I*d*x - 8*I*c) + 45158400*a^8*d*x*e^(4*I*d*x - 10*I*c) + 3225600*a^8*d*x*e^(2*I*d*x - 12*I*c) + 9686476800*a^8*d*x*e^(14*I*d*x) - 1515780*I*a^8*e^(30*I*d*x + 16*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 21220920*I*a^8*e^(28*I*d*x + 14*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 137935980*I*a^8*e^(26*I*d*x + 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 551743920*I*a^8*e^(24*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 1517295780*I*a^8*e^(22*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 3034591560*I*a^8*e^(20*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 4551887340*I*a^8*e^(18*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 5202156960*I*a^8*e^(16*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 3034591560*I*a^8*e^(12*I*d*x - 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 1517295780*I*a^8*e^(10*I*d*x - 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 551743920*I*a^8*e^(8*I*d*x - 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 137935980*I*a^8*e^(6*I*d*x - 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 21220920*I*a^8*e^(4*I*d*x - 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 1515780*I*a^8*e^(2*I*d*x - 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 4551887340*I*a^8*e^(14*I*d*x)*log(e^(2*I*d*x + 2*I*c) + 1) + 1515780*I*a^8*e^(30*I*d*x + 16*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 21220920*I*a^8*e^(28*I*d*x + 14*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 137935980*I*a^8*e^(26*I*d*x + 12*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 551743920*I*a^8*e^(24*I*d*x + 10*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 1517295780*I*a^8*e^(22*I*d*x + 8*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 3034591560*I*a^8*e^(20*I*d*x + 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 4551887340*I*a^8*e^(18*I*d*x + 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 5202156960*I*a^8*e^(16*I*d*x + 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 3034591560*I*a^8*e^(12*I*d*x - 2*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 1517295780*I*a^8*e^(10*I*d*x - 4*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 551743920*I*a^8*e^(8*I*d*x - 6*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 137935980*I*a^8*e^(6*I*d*x - 8*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 21220920*I*a^8*e^(4*I*d*x - 10*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 1515780*I*a^8*e^(2*I*d*x - 12*I*c)*log(e^(2*I*d*x) + e^(-2*I*c)) + 4551887340*I*a^8*e^(14*I*d*x)*log(e^(2*I*d*x) + e^(-2*I*c)) - 17920*I*a^8*e^(48*I*d*x + 34*I*c) - 452480*I*a^8*e^(46*I*d*x + 32*I*c) - 5489920*I*a^8*e^(44*I*d*x + 30*I*c) - 42609280*I*a^8*e^(42*I*d*x + 28*I*c) - 237601280*I*a^8*e^(40*I*d*x + 26*I*c) - 1013595520*I*a^8*e^(38*I*d*x + 24*I*c) - 3439322880*I*a^8*e^(36*I*d*x + 22*I*c) - 9529403520*I*a^8*e^(34*I*d*x + 20*I*c) - 21965959680*I*a^8*e^(32*I*d*x + 18*I*c) - 42709532800*I*a^8*e^(30*I*d*x + 16*I*c) - 70772038400*I*a^8*e^(28*I*d*x + 14*I*c) - 100658185600*I*a^8*e^(26*I*d*x + 12*I*c) - 123309222400*I*a^8*e^(24*I*d*x + 10*I*c) - 129974633600*I*a^8*e^(22*I*d*x + 8*I*c) - 117140020480*I*a^8*e^(20*I*d*x + 6*I*c) - 89191105920*I*a^8*e^(18*I*d*x + 4*I*c) - 56345172480*I*a^8*e^(16*I*d*x + 2*I*c) - 11479265280*I*a^8*e^(12*I*d*x - 2*I*c) - 3367687680*I*a^8*e^(10*I*d*x - 4*I*c) - 645765120*I*a^8*e^(8*I*d*x - 6*I*c) - 52577280*I*a^8*e^(6*I*d*x - 8*I*c) + 7418880*I*a^8*e^(4*I*d*x - 10*I*c) + 2257920*I*a^8*e^(2*I*d*x - 12*I*c) - 28794769920*I*a^8*e^(14*I*d*x) + 161280*I*a^8*e^(-14*I*c))/(d*e^(30*I*d*x + 16*I*c) + 14*d*e^(28*I*d*x + 14*I*c) + 91*d*e^(26*I*d*x + 12*I*c) + 364*d*e^(24*I*d*x + 10*I*c) + 1001*d*e^(22*I*d*x + 8*I*c) + 2002*d*e^(20*I*d*x + 6*I*c) + 3003*d*e^(18*I*d*x + 4*I*c) + 3432*d*e^(16*I*d*x + 2*I*c) + 2002*d*e^(12*I*d*x - 2*I*c) + 1001*d*e^(10*I*d*x - 4*I*c) + 364*d*e^(8*I*d*x - 6*I*c) + 91*d*e^(6*I*d*x - 8*I*c) + 14*d*e^(4*I*d*x - 10*I*c) + d*e^(2*I*d*x - 12*I*c) + 3003*d*e^(14*I*d*x))","B",0
91,1,924,0,5.356073," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{11512215 \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 69073290 \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 172683225 \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 230244300 \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 172683225 \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 69073290 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 19305 \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 115830 \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 289575 \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 386100 \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 289575 \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 115830 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 11512215 \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 69073290 \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 172683225 \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 230244300 \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 172683225 \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 69073290 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 19305 \, a^{8} e^{\left(12 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 115830 \, a^{8} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 289575 \, a^{8} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 386100 \, a^{8} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 289575 \, a^{8} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 115830 \, a^{8} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7864320 i \, a^{8} e^{\left(13 i \, d x + 13 i \, c\right)} - 79173120 i \, a^{8} e^{\left(11 i \, d x + 11 i \, c\right)} - 244175360 i \, a^{8} e^{\left(9 i \, d x + 9 i \, c\right)} - 370326528 i \, a^{8} e^{\left(7 i \, d x + 7 i \, c\right)} - 304432128 i \, a^{8} e^{\left(5 i \, d x + 5 i \, c\right)} - 130690560 i \, a^{8} e^{\left(3 i \, d x + 3 i \, c\right)} - 23063040 i \, a^{8} e^{\left(i \, d x + i \, c\right)} + 11512215 \, a^{8} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 19305 \, a^{8} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 11512215 \, a^{8} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 19305 \, a^{8} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right)}{61440 \, {\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,"1/61440*(11512215*a^8*e^(12*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 69073290*a^8*e^(10*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 172683225*a^8*e^(8*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 230244300*a^8*e^(6*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 172683225*a^8*e^(4*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 69073290*a^8*e^(2*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) - 19305*a^8*e^(12*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) - 1) - 115830*a^8*e^(10*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) - 1) - 289575*a^8*e^(8*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) - 386100*a^8*e^(6*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) - 289575*a^8*e^(4*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) - 115830*a^8*e^(2*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) - 11512215*a^8*e^(12*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 69073290*a^8*e^(10*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 172683225*a^8*e^(8*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 230244300*a^8*e^(6*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 172683225*a^8*e^(4*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 69073290*a^8*e^(2*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) + 19305*a^8*e^(12*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 115830*a^8*e^(10*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 289575*a^8*e^(8*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 386100*a^8*e^(6*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 289575*a^8*e^(4*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) + 115830*a^8*e^(2*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 7864320*I*a^8*e^(13*I*d*x + 13*I*c) - 79173120*I*a^8*e^(11*I*d*x + 11*I*c) - 244175360*I*a^8*e^(9*I*d*x + 9*I*c) - 370326528*I*a^8*e^(7*I*d*x + 7*I*c) - 304432128*I*a^8*e^(5*I*d*x + 5*I*c) - 130690560*I*a^8*e^(3*I*d*x + 3*I*c) - 23063040*I*a^8*e^(I*d*x + I*c) + 11512215*a^8*log(I*e^(I*d*x + I*c) + 1) - 19305*a^8*log(I*e^(I*d*x + I*c) - 1) - 11512215*a^8*log(-I*e^(I*d*x + I*c) + 1) + 19305*a^8*log(-I*e^(I*d*x + 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
92,1,2835,0,7.397722," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{26725545 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 374157630 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2432024595 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9728098380 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 26752270545 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 53504541090 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 80256811635 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 80256811635 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 53504541090 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 26752270545 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9728098380 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2432024595 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 374157630 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 91722070440 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 26725545 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 523464480 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 7328502720 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 47635267680 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 190541070720 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 523987944480 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1047975888960 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1571963833440 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1571963833440 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1047975888960 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 523987944480 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 190541070720 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 47635267680 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 7328502720 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1796530095360 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 523464480 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 26725545 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 374157630 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2432024595 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9728098380 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 26752270545 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 53504541090 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 80256811635 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 80256811635 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 53504541090 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 26752270545 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9728098380 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2432024595 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 374157630 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 91722070440 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 26725545 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 523464480 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7328502720 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 47635267680 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 190541070720 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 523987944480 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1047975888960 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1571963833440 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1571963833440 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1047975888960 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 523987944480 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 190541070720 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 47635267680 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7328502720 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1796530095360 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 523464480 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3465 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 48510 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 315315 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1261260 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3468465 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 6936930 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 10405395 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 10405395 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 6936930 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3468465 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1261260 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 315315 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 48510 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 11891880 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 3465 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3465 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 48510 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 315315 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1261260 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3468465 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 6936930 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 10405395 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 10405395 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 6936930 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3468465 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1261260 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 315315 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 48510 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 11891880 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 3465 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 36700160 i \, a^{8} e^{\left(31 i \, d x + 17 i \, c\right)} + 36700160 i \, a^{8} e^{\left(29 i \, d x + 15 i \, c\right)} + 5025341440 i \, a^{8} e^{\left(27 i \, d x + 13 i \, c\right)} + 44995829760 i \, a^{8} e^{\left(25 i \, d x + 11 i \, c\right)} + 211521945600 i \, a^{8} e^{\left(23 i \, d x + 9 i \, c\right)} + 647303086080 i \, a^{8} e^{\left(21 i \, d x + 7 i \, c\right)} + 1402445291520 i \, a^{8} e^{\left(19 i \, d x + 5 i \, c\right)} + 2242792366080 i \, a^{8} e^{\left(17 i \, d x + 3 i \, c\right)} + 2703768453120 i \, a^{8} e^{\left(15 i \, d x + i \, c\right)} + 2476532531200 i \, a^{8} e^{\left(13 i \, d x - i \, c\right)} + 1718329303040 i \, a^{8} e^{\left(11 i \, d x - 3 i \, c\right)} + 890140303360 i \, a^{8} e^{\left(9 i \, d x - 5 i \, c\right)} + 334132592640 i \, a^{8} e^{\left(7 i \, d x - 7 i \, c\right)} + 85969551360 i \, a^{8} e^{\left(5 i \, d x - 9 i \, c\right)} + 13577625600 i \, a^{8} e^{\left(3 i \, d x - 11 i \, c\right)} + 993484800 i \, a^{8} e^{\left(i \, d x - 13 i \, c\right)}}{3440640 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/3440640*(26725545*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 374157630*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2432024595*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 9728098380*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 26752270545*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 53504541090*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 80256811635*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 80256811635*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 53504541090*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 26752270545*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 9728098380*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2432024595*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 374157630*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 91722070440*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 26725545*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 523464480*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) - 1) + 7328502720*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 47635267680*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 190541070720*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 523987944480*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1047975888960*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1571963833440*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1571963833440*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1047975888960*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 523987944480*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 190541070720*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 47635267680*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 7328502720*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1796530095360*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 523464480*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) - 1) - 26725545*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 374157630*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2432024595*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 9728098380*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 26752270545*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 53504541090*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 80256811635*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 80256811635*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 53504541090*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 26752270545*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 9728098380*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2432024595*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 374157630*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 91722070440*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 26725545*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 523464480*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 7328502720*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 47635267680*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 190541070720*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 523987944480*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1047975888960*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1571963833440*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1571963833440*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1047975888960*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 523987944480*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 190541070720*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 47635267680*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 7328502720*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1796530095360*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 523464480*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3465*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 48510*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 315315*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 1261260*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 3468465*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 6936930*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 10405395*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 10405395*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 6936930*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 3468465*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 1261260*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 315315*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 48510*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 11891880*a^8*e^(14*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 3465*a^8*e^(-14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 3465*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 48510*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 315315*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 1261260*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 3468465*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 6936930*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 10405395*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 10405395*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 6936930*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 3468465*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 1261260*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 315315*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 48510*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 11891880*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 3465*a^8*e^(-14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 36700160*I*a^8*e^(31*I*d*x + 17*I*c) + 36700160*I*a^8*e^(29*I*d*x + 15*I*c) + 5025341440*I*a^8*e^(27*I*d*x + 13*I*c) + 44995829760*I*a^8*e^(25*I*d*x + 11*I*c) + 211521945600*I*a^8*e^(23*I*d*x + 9*I*c) + 647303086080*I*a^8*e^(21*I*d*x + 7*I*c) + 1402445291520*I*a^8*e^(19*I*d*x + 5*I*c) + 2242792366080*I*a^8*e^(17*I*d*x + 3*I*c) + 2703768453120*I*a^8*e^(15*I*d*x + I*c) + 2476532531200*I*a^8*e^(13*I*d*x - I*c) + 1718329303040*I*a^8*e^(11*I*d*x - 3*I*c) + 890140303360*I*a^8*e^(9*I*d*x - 5*I*c) + 334132592640*I*a^8*e^(7*I*d*x - 7*I*c) + 85969551360*I*a^8*e^(5*I*d*x - 9*I*c) + 13577625600*I*a^8*e^(3*I*d*x - 11*I*c) + 993484800*I*a^8*e^(I*d*x - 13*I*c))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
93,1,2849,0,9.398362," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{882454545 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 12354363630 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 80303363595 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 321213454380 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 883336999545 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1766673999090 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2650010998635 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2650010998635 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1766673999090 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 883336999545 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 321213454380 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 80303363595 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 12354363630 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3028583998440 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 882454545 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 448908075 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 6284713050 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 40850634825 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 163402539300 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 449356983075 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 898713966150 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1348070949225 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1348070949225 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 898713966150 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 449356983075 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 163402539300 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 40850634825 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 6284713050 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1540652513400 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 448908075 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 882454545 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 12354363630 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 80303363595 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 321213454380 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 883336999545 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1766673999090 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2650010998635 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2650010998635 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1766673999090 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 883336999545 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 321213454380 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 80303363595 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 12354363630 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3028583998440 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 882454545 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 448908075 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 6284713050 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 40850634825 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 163402539300 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 449356983075 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 898713966150 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1348070949225 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1348070949225 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 898713966150 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 449356983075 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 163402539300 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 40850634825 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 6284713050 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1540652513400 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 448908075 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 25830 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 361620 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2350530 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 9402120 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 25855830 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 51711660 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 77567490 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 77567490 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 51711660 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 25855830 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 9402120 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2350530 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 361620 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 88648560 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 25830 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 25830 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 361620 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2350530 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 9402120 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 25855830 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 51711660 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 77567490 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 77567490 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 51711660 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 25855830 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 9402120 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2350530 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 361620 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 88648560 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 25830 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 22020096 i \, a^{8} e^{\left(33 i \, d x + 19 i \, c\right)} - 198180864 i \, a^{8} e^{\left(31 i \, d x + 17 i \, c\right)} - 1123024896 i \, a^{8} e^{\left(29 i \, d x + 15 i \, c\right)} - 7478575104 i \, a^{8} e^{\left(27 i \, d x + 13 i \, c\right)} - 45094404096 i \, a^{8} e^{\left(25 i \, d x + 11 i \, c\right)} - 192251953152 i \, a^{8} e^{\left(23 i \, d x + 9 i \, c\right)} - 572065579008 i \, a^{8} e^{\left(21 i \, d x + 7 i \, c\right)} - 1228696584192 i \, a^{8} e^{\left(19 i \, d x + 5 i \, c\right)} - 1959538065408 i \, a^{8} e^{\left(17 i \, d x + 3 i \, c\right)} - 2360323080192 i \, a^{8} e^{\left(15 i \, d x + i \, c\right)} - 2161459593216 i \, a^{8} e^{\left(13 i \, d x - i \, c\right)} - 1499642855424 i \, a^{8} e^{\left(11 i \, d x - 3 i \, c\right)} - 776849719296 i \, a^{8} e^{\left(9 i \, d x - 5 i \, c\right)} - 291606626304 i \, a^{8} e^{\left(7 i \, d x - 7 i \, c\right)} - 75027972096 i \, a^{8} e^{\left(5 i \, d x - 9 i \, c\right)} - 11849564160 i \, a^{8} e^{\left(3 i \, d x - 11 i \, c\right)} - 867041280 i \, a^{8} e^{\left(i \, d x - 13 i \, c\right)}}{13762560 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/13762560*(882454545*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 12354363630*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 80303363595*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 321213454380*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 883336999545*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1766673999090*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2650010998635*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2650010998635*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1766673999090*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 883336999545*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 321213454380*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 80303363595*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 12354363630*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3028583998440*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 882454545*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 448908075*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) - 1) + 6284713050*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 40850634825*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 163402539300*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 449356983075*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 898713966150*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1348070949225*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1348070949225*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 898713966150*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 449356983075*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 163402539300*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 40850634825*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 6284713050*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1540652513400*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 448908075*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) - 1) - 882454545*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 12354363630*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 80303363595*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 321213454380*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 883336999545*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1766673999090*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2650010998635*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2650010998635*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1766673999090*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 883336999545*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 321213454380*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 80303363595*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 12354363630*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3028583998440*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 882454545*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 448908075*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 6284713050*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 40850634825*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 163402539300*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 449356983075*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 898713966150*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1348070949225*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1348070949225*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 898713966150*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 449356983075*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 163402539300*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 40850634825*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 6284713050*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1540652513400*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 448908075*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 25830*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 361620*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2350530*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 9402120*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 25855830*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 51711660*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 77567490*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 77567490*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 51711660*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 25855830*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 9402120*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2350530*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 361620*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 88648560*a^8*e^(14*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 25830*a^8*e^(-14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 25830*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 361620*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 2350530*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 9402120*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 25855830*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 51711660*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 77567490*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 77567490*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 51711660*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 25855830*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 9402120*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 2350530*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 361620*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 88648560*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 25830*a^8*e^(-14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 22020096*I*a^8*e^(33*I*d*x + 19*I*c) - 198180864*I*a^8*e^(31*I*d*x + 17*I*c) - 1123024896*I*a^8*e^(29*I*d*x + 15*I*c) - 7478575104*I*a^8*e^(27*I*d*x + 13*I*c) - 45094404096*I*a^8*e^(25*I*d*x + 11*I*c) - 192251953152*I*a^8*e^(23*I*d*x + 9*I*c) - 572065579008*I*a^8*e^(21*I*d*x + 7*I*c) - 1228696584192*I*a^8*e^(19*I*d*x + 5*I*c) - 1959538065408*I*a^8*e^(17*I*d*x + 3*I*c) - 2360323080192*I*a^8*e^(15*I*d*x + I*c) - 2161459593216*I*a^8*e^(13*I*d*x - I*c) - 1499642855424*I*a^8*e^(11*I*d*x - 3*I*c) - 776849719296*I*a^8*e^(9*I*d*x - 5*I*c) - 291606626304*I*a^8*e^(7*I*d*x - 7*I*c) - 75027972096*I*a^8*e^(5*I*d*x - 9*I*c) - 11849564160*I*a^8*e^(3*I*d*x - 11*I*c) - 867041280*I*a^8*e^(I*d*x - 13*I*c))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
94,1,2863,0,12.318266," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{1635552135 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 22897729890 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 148835244285 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 595340977140 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1637187687135 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3274375374270 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 4911563061405 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 4911563061405 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3274375374270 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1637187687135 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 595340977140 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 148835244285 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 22897729890 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5613214927320 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1635552135 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1690450650 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 23666309100 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 153831009150 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 615324036600 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1692141100650 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3384282201300 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 5076423301950 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 5076423301950 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3384282201300 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1692141100650 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 615324036600 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 153831009150 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 23666309100 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 5801626630800 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1690450650 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1635552135 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 22897729890 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 148835244285 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 595340977140 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1637187687135 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3274375374270 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 4911563061405 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 4911563061405 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3274375374270 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1637187687135 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 595340977140 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 148835244285 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 22897729890 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5613214927320 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1635552135 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1690450650 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 23666309100 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 153831009150 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 615324036600 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1692141100650 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3384282201300 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5076423301950 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5076423301950 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3384282201300 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1692141100650 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 615324036600 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 153831009150 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 23666309100 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5801626630800 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1690450650 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 151725 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2124150 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 13806975 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 55227900 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 151876725 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 303753450 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 455630175 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 455630175 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 303753450 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 151876725 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 55227900 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 13806975 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2124150 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 520720200 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 151725 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 151725 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2124150 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 13806975 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 55227900 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 151876725 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 303753450 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 455630175 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 455630175 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 303753450 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 151876725 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 55227900 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 13806975 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2124150 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 520720200 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 151725 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 15728640 i \, a^{8} e^{\left(35 i \, d x + 21 i \, c\right)} - 198180864 i \, a^{8} e^{\left(33 i \, d x + 19 i \, c\right)} - 1159725056 i \, a^{8} e^{\left(31 i \, d x + 17 i \, c\right)} - 4125097984 i \, a^{8} e^{\left(29 i \, d x + 15 i \, c\right)} - 9527361536 i \, a^{8} e^{\left(27 i \, d x + 13 i \, c\right)} - 12786335744 i \, a^{8} e^{\left(25 i \, d x + 11 i \, c\right)} + 190840832 i \, a^{8} e^{\left(23 i \, d x + 9 i \, c\right)} + 48882515968 i \, a^{8} e^{\left(21 i \, d x + 7 i \, c\right)} + 138550444032 i \, a^{8} e^{\left(19 i \, d x + 5 i \, c\right)} + 239314403328 i \, a^{8} e^{\left(17 i \, d x + 3 i \, c\right)} + 295994130432 i \, a^{8} e^{\left(15 i \, d x + i \, c\right)} + 273474912256 i \, a^{8} e^{\left(13 i \, d x - i \, c\right)} + 190268309504 i \, a^{8} e^{\left(11 i \, d x - 3 i \, c\right)} + 98635350016 i \, a^{8} e^{\left(9 i \, d x - 5 i \, c\right)} + 37029412864 i \, a^{8} e^{\left(7 i \, d x - 7 i \, c\right)} + 9527361536 i \, a^{8} e^{\left(5 i \, d x - 9 i \, c\right)} + 1504706560 i \, a^{8} e^{\left(3 i \, d x - 11 i \, c\right)} + 110100480 i \, a^{8} e^{\left(i \, d x - 13 i \, c\right)}}{55050240 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/55050240*(1635552135*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 22897729890*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 148835244285*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 595340977140*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1637187687135*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3274375374270*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 4911563061405*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 4911563061405*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3274375374270*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1637187687135*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 595340977140*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 148835244285*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 22897729890*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 5613214927320*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 1635552135*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1690450650*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) - 1) + 23666309100*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 153831009150*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 615324036600*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1692141100650*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 3384282201300*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 5076423301950*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 5076423301950*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 3384282201300*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1692141100650*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 615324036600*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 153831009150*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 23666309100*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 5801626630800*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 1690450650*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) - 1) - 1635552135*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 22897729890*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 148835244285*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 595340977140*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1637187687135*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3274375374270*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 4911563061405*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 4911563061405*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3274375374270*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1637187687135*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 595340977140*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 148835244285*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 22897729890*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 5613214927320*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 1635552135*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1690450650*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 23666309100*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 153831009150*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 615324036600*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1692141100650*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3384282201300*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 5076423301950*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 5076423301950*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3384282201300*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1692141100650*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 615324036600*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 153831009150*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 23666309100*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 5801626630800*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 1690450650*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 151725*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2124150*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 13806975*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 55227900*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 151876725*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 303753450*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 455630175*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 455630175*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 303753450*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 151876725*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 55227900*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 13806975*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2124150*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 520720200*a^8*e^(14*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 151725*a^8*e^(-14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 151725*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 2124150*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 13806975*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 55227900*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 151876725*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 303753450*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 455630175*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 455630175*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 303753450*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 151876725*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 55227900*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 13806975*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 2124150*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 520720200*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 151725*a^8*e^(-14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 15728640*I*a^8*e^(35*I*d*x + 21*I*c) - 198180864*I*a^8*e^(33*I*d*x + 19*I*c) - 1159725056*I*a^8*e^(31*I*d*x + 17*I*c) - 4125097984*I*a^8*e^(29*I*d*x + 15*I*c) - 9527361536*I*a^8*e^(27*I*d*x + 13*I*c) - 12786335744*I*a^8*e^(25*I*d*x + 11*I*c) + 190840832*I*a^8*e^(23*I*d*x + 9*I*c) + 48882515968*I*a^8*e^(21*I*d*x + 7*I*c) + 138550444032*I*a^8*e^(19*I*d*x + 5*I*c) + 239314403328*I*a^8*e^(17*I*d*x + 3*I*c) + 295994130432*I*a^8*e^(15*I*d*x + I*c) + 273474912256*I*a^8*e^(13*I*d*x - I*c) + 190268309504*I*a^8*e^(11*I*d*x - 3*I*c) + 98635350016*I*a^8*e^(9*I*d*x - 5*I*c) + 37029412864*I*a^8*e^(7*I*d*x - 7*I*c) + 9527361536*I*a^8*e^(5*I*d*x - 9*I*c) + 1504706560*I*a^8*e^(3*I*d*x - 11*I*c) + 110100480*I*a^8*e^(I*d*x - 13*I*c))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
95,1,2451,0,15.789382," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{7096716585 \, a^{8} e^{\left(24 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 85160599020 \, a^{8} e^{\left(22 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 468383294610 \, a^{8} e^{\left(20 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1561277648700 \, a^{8} e^{\left(18 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3512874709575 \, a^{8} e^{\left(16 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5620599535320 \, a^{8} e^{\left(14 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5620599535320 \, a^{8} e^{\left(10 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3512874709575 \, a^{8} e^{\left(8 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1561277648700 \, a^{8} e^{\left(6 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 468383294610 \, a^{8} e^{\left(4 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 85160599020 \, a^{8} e^{\left(2 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 6557366124540 \, a^{8} e^{\left(12 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 7096716585 \, a^{8} e^{\left(-12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 7095485250 \, a^{8} e^{\left(24 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 85145823000 \, a^{8} e^{\left(22 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 468302026500 \, a^{8} e^{\left(20 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1561006755000 \, a^{8} e^{\left(18 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3512265198750 \, a^{8} e^{\left(16 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 5619624318000 \, a^{8} e^{\left(14 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 5619624318000 \, a^{8} e^{\left(10 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3512265198750 \, a^{8} e^{\left(8 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1561006755000 \, a^{8} e^{\left(6 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 468302026500 \, a^{8} e^{\left(4 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 85145823000 \, a^{8} e^{\left(2 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 6556228371000 \, a^{8} e^{\left(12 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 7095485250 \, a^{8} e^{\left(-12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7096716585 \, a^{8} e^{\left(24 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 85160599020 \, a^{8} e^{\left(22 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 468383294610 \, a^{8} e^{\left(20 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1561277648700 \, a^{8} e^{\left(18 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3512874709575 \, a^{8} e^{\left(16 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5620599535320 \, a^{8} e^{\left(14 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5620599535320 \, a^{8} e^{\left(10 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3512874709575 \, a^{8} e^{\left(8 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1561277648700 \, a^{8} e^{\left(6 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 468383294610 \, a^{8} e^{\left(4 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 85160599020 \, a^{8} e^{\left(2 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 6557366124540 \, a^{8} e^{\left(12 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 7096716585 \, a^{8} e^{\left(-12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 7095485250 \, a^{8} e^{\left(24 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 85145823000 \, a^{8} e^{\left(22 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 468302026500 \, a^{8} e^{\left(20 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1561006755000 \, a^{8} e^{\left(18 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3512265198750 \, a^{8} e^{\left(16 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5619624318000 \, a^{8} e^{\left(14 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5619624318000 \, a^{8} e^{\left(10 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3512265198750 \, a^{8} e^{\left(8 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1561006755000 \, a^{8} e^{\left(6 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 468302026500 \, a^{8} e^{\left(4 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 85145823000 \, a^{8} e^{\left(2 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 6556228371000 \, a^{8} e^{\left(12 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7095485250 \, a^{8} e^{\left(-12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1231335 \, a^{8} e^{\left(24 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 14776020 \, a^{8} e^{\left(22 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 81268110 \, a^{8} e^{\left(20 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 270893700 \, a^{8} e^{\left(18 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 609510825 \, a^{8} e^{\left(16 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 975217320 \, a^{8} e^{\left(14 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 975217320 \, a^{8} e^{\left(10 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 609510825 \, a^{8} e^{\left(8 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 270893700 \, a^{8} e^{\left(6 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 81268110 \, a^{8} e^{\left(4 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 14776020 \, a^{8} e^{\left(2 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1137753540 \, a^{8} e^{\left(12 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1231335 \, a^{8} e^{\left(-12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1231335 \, a^{8} e^{\left(24 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 14776020 \, a^{8} e^{\left(22 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 81268110 \, a^{8} e^{\left(20 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 270893700 \, a^{8} e^{\left(18 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 609510825 \, a^{8} e^{\left(16 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 975217320 \, a^{8} e^{\left(14 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 975217320 \, a^{8} e^{\left(10 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 609510825 \, a^{8} e^{\left(8 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 270893700 \, a^{8} e^{\left(6 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 81268110 \, a^{8} e^{\left(4 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 14776020 \, a^{8} e^{\left(2 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1137753540 \, a^{8} e^{\left(12 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1231335 \, a^{8} e^{\left(-12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 18350080 i \, a^{8} e^{\left(33 i \, d x + 21 i \, c\right)} - 243793920 i \, a^{8} e^{\left(31 i \, d x + 19 i \, c\right)} - 1494220800 i \, a^{8} e^{\left(29 i \, d x + 17 i \, c\right)} - 5594152960 i \, a^{8} e^{\left(27 i \, d x + 15 i \, c\right)} - 14273740800 i \, a^{8} e^{\left(25 i \, d x + 13 i \, c\right)} - 26211778560 i \, a^{8} e^{\left(23 i \, d x + 11 i \, c\right)} - 35641098240 i \, a^{8} e^{\left(21 i \, d x + 9 i \, c\right)} - 36333158400 i \, a^{8} e^{\left(19 i \, d x + 7 i \, c\right)} - 27768913920 i \, a^{8} e^{\left(17 i \, d x + 5 i \, c\right)} - 15715532800 i \, a^{8} e^{\left(15 i \, d x + 3 i \, c\right)} - 6401556480 i \, a^{8} e^{\left(13 i \, d x + i \, c\right)} - 1777336320 i \, a^{8} e^{\left(11 i \, d x - i \, c\right)} - 301465600 i \, a^{8} e^{\left(9 i \, d x - 3 i \, c\right)} - 23592960 i \, a^{8} e^{\left(7 i \, d x - 5 i \, c\right)}}{330301440 \, {\left(d e^{\left(24 i \, d x + 12 i \, c\right)} + 12 \, d e^{\left(22 i \, d x + 10 i \, c\right)} + 66 \, d e^{\left(20 i \, d x + 8 i \, c\right)} + 220 \, d e^{\left(18 i \, d x + 6 i \, c\right)} + 495 \, d e^{\left(16 i \, d x + 4 i \, c\right)} + 792 \, d e^{\left(14 i \, d x + 2 i \, c\right)} + 792 \, d e^{\left(10 i \, d x - 2 i \, c\right)} + 495 \, d e^{\left(8 i \, d x - 4 i \, c\right)} + 220 \, d e^{\left(6 i \, d x - 6 i \, c\right)} + 66 \, d e^{\left(4 i \, d x - 8 i \, c\right)} + 12 \, d e^{\left(2 i \, d x - 10 i \, c\right)} + 924 \, d e^{\left(12 i \, d x\right)} + d e^{\left(-12 i \, c\right)}\right)}}"," ",0,"1/330301440*(7096716585*a^8*e^(24*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 85160599020*a^8*e^(22*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 468383294610*a^8*e^(20*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1561277648700*a^8*e^(18*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3512874709575*a^8*e^(16*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 5620599535320*a^8*e^(14*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 5620599535320*a^8*e^(10*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3512874709575*a^8*e^(8*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1561277648700*a^8*e^(6*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 468383294610*a^8*e^(4*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 85160599020*a^8*e^(2*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 6557366124540*a^8*e^(12*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 7096716585*a^8*e^(-12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 7095485250*a^8*e^(24*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 85145823000*a^8*e^(22*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 468302026500*a^8*e^(20*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1561006755000*a^8*e^(18*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 3512265198750*a^8*e^(16*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 5619624318000*a^8*e^(14*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 5619624318000*a^8*e^(10*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 3512265198750*a^8*e^(8*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1561006755000*a^8*e^(6*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 468302026500*a^8*e^(4*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 85145823000*a^8*e^(2*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 6556228371000*a^8*e^(12*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 7095485250*a^8*e^(-12*I*c)*log(I*e^(I*d*x + I*c) - 1) - 7096716585*a^8*e^(24*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 85160599020*a^8*e^(22*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 468383294610*a^8*e^(20*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1561277648700*a^8*e^(18*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3512874709575*a^8*e^(16*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 5620599535320*a^8*e^(14*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 5620599535320*a^8*e^(10*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3512874709575*a^8*e^(8*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1561277648700*a^8*e^(6*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 468383294610*a^8*e^(4*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 85160599020*a^8*e^(2*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 6557366124540*a^8*e^(12*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 7096716585*a^8*e^(-12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 7095485250*a^8*e^(24*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 85145823000*a^8*e^(22*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 468302026500*a^8*e^(20*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1561006755000*a^8*e^(18*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3512265198750*a^8*e^(16*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 5619624318000*a^8*e^(14*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 5619624318000*a^8*e^(10*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3512265198750*a^8*e^(8*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1561006755000*a^8*e^(6*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 468302026500*a^8*e^(4*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 85145823000*a^8*e^(2*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 6556228371000*a^8*e^(12*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 7095485250*a^8*e^(-12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1231335*a^8*e^(24*I*d*x + 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 14776020*a^8*e^(22*I*d*x + 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 81268110*a^8*e^(20*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 270893700*a^8*e^(18*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 609510825*a^8*e^(16*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 975217320*a^8*e^(14*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 975217320*a^8*e^(10*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 609510825*a^8*e^(8*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 270893700*a^8*e^(6*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 81268110*a^8*e^(4*I*d*x - 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 14776020*a^8*e^(2*I*d*x - 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 1137753540*a^8*e^(12*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 1231335*a^8*e^(-12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 1231335*a^8*e^(24*I*d*x + 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 14776020*a^8*e^(22*I*d*x + 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 81268110*a^8*e^(20*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 270893700*a^8*e^(18*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 609510825*a^8*e^(16*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 975217320*a^8*e^(14*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 975217320*a^8*e^(10*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 609510825*a^8*e^(8*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 270893700*a^8*e^(6*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 81268110*a^8*e^(4*I*d*x - 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 14776020*a^8*e^(2*I*d*x - 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 1137753540*a^8*e^(12*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 1231335*a^8*e^(-12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 18350080*I*a^8*e^(33*I*d*x + 21*I*c) - 243793920*I*a^8*e^(31*I*d*x + 19*I*c) - 1494220800*I*a^8*e^(29*I*d*x + 17*I*c) - 5594152960*I*a^8*e^(27*I*d*x + 15*I*c) - 14273740800*I*a^8*e^(25*I*d*x + 13*I*c) - 26211778560*I*a^8*e^(23*I*d*x + 11*I*c) - 35641098240*I*a^8*e^(21*I*d*x + 9*I*c) - 36333158400*I*a^8*e^(19*I*d*x + 7*I*c) - 27768913920*I*a^8*e^(17*I*d*x + 5*I*c) - 15715532800*I*a^8*e^(15*I*d*x + 3*I*c) - 6401556480*I*a^8*e^(13*I*d*x + I*c) - 1777336320*I*a^8*e^(11*I*d*x - I*c) - 301465600*I*a^8*e^(9*I*d*x - 3*I*c) - 23592960*I*a^8*e^(7*I*d*x - 5*I*c))/(d*e^(24*I*d*x + 12*I*c) + 12*d*e^(22*I*d*x + 10*I*c) + 66*d*e^(20*I*d*x + 8*I*c) + 220*d*e^(18*I*d*x + 6*I*c) + 495*d*e^(16*I*d*x + 4*I*c) + 792*d*e^(14*I*d*x + 2*I*c) + 792*d*e^(10*I*d*x - 2*I*c) + 495*d*e^(8*I*d*x - 4*I*c) + 220*d*e^(6*I*d*x - 6*I*c) + 66*d*e^(4*I*d*x - 8*I*c) + 12*d*e^(2*I*d*x - 10*I*c) + 924*d*e^(12*I*d*x) + d*e^(-12*I*c))","B",0
96,1,2863,0,16.290674," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{82027951005 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1148391314070 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 7464543541455 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 29858174165820 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 82109978956005 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 164219957912010 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 246329936868015 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 246329936868015 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 164219957912010 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 82109978956005 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 29858174165820 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 7464543541455 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 1148391314070 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 281519927849160 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 82027951005 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 82004266575 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1148059732050 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 7462388258325 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 29849553033300 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 82086270841575 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 164172541683150 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 246258812524725 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 246258812524725 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 164172541683150 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 82086270841575 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 29849553033300 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 7462388258325 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 1148059732050 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 281438642885400 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 82004266575 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 82027951005 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1148391314070 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 7464543541455 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 29858174165820 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 82109978956005 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 164219957912010 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 246329936868015 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 246329936868015 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 164219957912010 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 82109978956005 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 29858174165820 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 7464543541455 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 1148391314070 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 281519927849160 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 82027951005 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 82004266575 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1148059732050 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7462388258325 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 29849553033300 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 82086270841575 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 164172541683150 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 246258812524725 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 246258812524725 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 164172541683150 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 82086270841575 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 29849553033300 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7462388258325 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 1148059732050 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 281438642885400 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 82004266575 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 23684430 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 331582020 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2155283130 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 8621132520 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23708114430 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 47416228860 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 71124343290 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 71124343290 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 47416228860 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23708114430 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 8621132520 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2155283130 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 331582020 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 81284963760 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23684430 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23684430 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 331582020 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2155283130 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 8621132520 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23708114430 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 47416228860 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 71124343290 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 71124343290 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 47416228860 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23708114430 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 8621132520 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2155283130 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 331582020 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 81284963760 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23684430 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 55050240 i \, a^{8} e^{\left(39 i \, d x + 25 i \, c\right)} - 972554240 i \, a^{8} e^{\left(37 i \, d x + 23 i \, c\right)} - 8095006720 i \, a^{8} e^{\left(35 i \, d x + 21 i \, c\right)} - 42161143808 i \, a^{8} e^{\left(33 i \, d x + 19 i \, c\right)} - 153891110912 i \, a^{8} e^{\left(31 i \, d x + 17 i \, c\right)} - 417750581248 i \, a^{8} e^{\left(29 i \, d x + 15 i \, c\right)} - 873287647232 i \, a^{8} e^{\left(27 i \, d x + 13 i \, c\right)} - 1435886419968 i \, a^{8} e^{\left(25 i \, d x + 11 i \, c\right)} - 1879877615616 i \, a^{8} e^{\left(23 i \, d x + 9 i \, c\right)} - 1970745114624 i \, a^{8} e^{\left(21 i \, d x + 7 i \, c\right)} - 1654208331776 i \, a^{8} e^{\left(19 i \, d x + 5 i \, c\right)} - 1105350098944 i \, a^{8} e^{\left(17 i \, d x + 3 i \, c\right)} - 580728651776 i \, a^{8} e^{\left(15 i \, d x + i \, c\right)} - 234836983808 i \, a^{8} e^{\left(13 i \, d x - i \, c\right)} - 70581747712 i \, a^{8} e^{\left(11 i \, d x - 3 i \, c\right)} - 14856224768 i \, a^{8} e^{\left(9 i \, d x - 5 i \, c\right)} - 1955069952 i \, a^{8} e^{\left(7 i \, d x - 7 i \, c\right)} - 121110528 i \, a^{8} e^{\left(5 i \, d x - 9 i \, c\right)}}{4844421120 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/4844421120*(82027951005*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1148391314070*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 7464543541455*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 29858174165820*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 82109978956005*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 164219957912010*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 246329936868015*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 246329936868015*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 164219957912010*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 82109978956005*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 29858174165820*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 7464543541455*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 1148391314070*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 281519927849160*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 82027951005*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 82004266575*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1148059732050*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 7462388258325*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 29849553033300*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 82086270841575*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 164172541683150*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 246258812524725*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 246258812524725*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 164172541683150*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 82086270841575*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 29849553033300*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 7462388258325*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 1148059732050*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 281438642885400*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 82004266575*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) - 1) - 82027951005*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1148391314070*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 7464543541455*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 29858174165820*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 82109978956005*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 164219957912010*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 246329936868015*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 246329936868015*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 164219957912010*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 82109978956005*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 29858174165820*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 7464543541455*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 1148391314070*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 281519927849160*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 82027951005*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 82004266575*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1148059732050*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 7462388258325*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 29849553033300*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 82086270841575*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 164172541683150*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 246258812524725*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 246258812524725*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 164172541683150*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 82086270841575*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 29849553033300*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 7462388258325*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 1148059732050*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 281438642885400*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 82004266575*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 23684430*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 331582020*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2155283130*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 8621132520*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 23708114430*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 47416228860*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 71124343290*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 71124343290*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 47416228860*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 23708114430*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 8621132520*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2155283130*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 331582020*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 81284963760*a^8*e^(14*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 23684430*a^8*e^(-14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 23684430*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 331582020*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 2155283130*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 8621132520*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 23708114430*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 47416228860*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 71124343290*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 71124343290*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 47416228860*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 23708114430*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 8621132520*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 2155283130*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 331582020*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 81284963760*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 23684430*a^8*e^(-14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 55050240*I*a^8*e^(39*I*d*x + 25*I*c) - 972554240*I*a^8*e^(37*I*d*x + 23*I*c) - 8095006720*I*a^8*e^(35*I*d*x + 21*I*c) - 42161143808*I*a^8*e^(33*I*d*x + 19*I*c) - 153891110912*I*a^8*e^(31*I*d*x + 17*I*c) - 417750581248*I*a^8*e^(29*I*d*x + 15*I*c) - 873287647232*I*a^8*e^(27*I*d*x + 13*I*c) - 1435886419968*I*a^8*e^(25*I*d*x + 11*I*c) - 1879877615616*I*a^8*e^(23*I*d*x + 9*I*c) - 1970745114624*I*a^8*e^(21*I*d*x + 7*I*c) - 1654208331776*I*a^8*e^(19*I*d*x + 5*I*c) - 1105350098944*I*a^8*e^(17*I*d*x + 3*I*c) - 580728651776*I*a^8*e^(15*I*d*x + I*c) - 234836983808*I*a^8*e^(13*I*d*x - I*c) - 70581747712*I*a^8*e^(11*I*d*x - 3*I*c) - 14856224768*I*a^8*e^(9*I*d*x - 5*I*c) - 1955069952*I*a^8*e^(7*I*d*x - 7*I*c) - 121110528*I*a^8*e^(5*I*d*x - 9*I*c))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
97,1,2891,0,18.196342," ","integrate(cos(d*x+c)^13*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{9725263833285 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 136153693665990 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 884999008828935 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3539996035315740 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9734989097118285 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 19469978194236570 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 29204967291354855 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 29204967291354855 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 19469978194236570 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9734989097118285 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 3539996035315740 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 884999008828935 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 136153693665990 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 33377105475834120 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9725263833285 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 9720402036345 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 136085628508830 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 884556585307395 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3538226341229580 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 9730122438381345 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 19460244876762690 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 29190367315144035 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 29190367315144035 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 19460244876762690 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 9730122438381345 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 3538226341229580 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 884556585307395 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 136085628508830 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 33360419788736040 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 9720402036345 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9725263833285 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 136153693665990 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 884999008828935 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3539996035315740 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9734989097118285 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 19469978194236570 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 29204967291354855 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 29204967291354855 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 19469978194236570 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9734989097118285 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 3539996035315740 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 884999008828935 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 136153693665990 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 33377105475834120 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9725263833285 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 9720402036345 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 136085628508830 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 884556585307395 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3538226341229580 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9730122438381345 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 19460244876762690 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 29190367315144035 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 29190367315144035 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 19460244876762690 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9730122438381345 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 3538226341229580 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 884556585307395 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 136085628508830 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 33360419788736040 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 9720402036345 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 4861796940 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 68065157160 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 442423521540 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1769694086160 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 4866658736940 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 9733317473880 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 14599976210820 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 14599976210820 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 9733317473880 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 4866658736940 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1769694086160 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 442423521540 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 68065157160 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 16685687098080 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 4861796940 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 4861796940 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 68065157160 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 442423521540 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1769694086160 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 4866658736940 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 9733317473880 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 14599976210820 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 14599976210820 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 9733317473880 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 4866658736940 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 1769694086160 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 442423521540 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 68065157160 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 16685687098080 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 4861796940 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 1816657920 i \, a^{8} e^{\left(41 i \, d x + 27 i \, c\right)} - 36168007680 i \, a^{8} e^{\left(39 i \, d x + 25 i \, c\right)} - 341843640320 i \, a^{8} e^{\left(37 i \, d x + 23 i \, c\right)} - 2039236526080 i \, a^{8} e^{\left(35 i \, d x + 21 i \, c\right)} - 8609784135680 i \, a^{8} e^{\left(33 i \, d x + 19 i \, c\right)} - 27342720204800 i \, a^{8} e^{\left(31 i \, d x + 17 i \, c\right)} - 67753266380800 i \, a^{8} e^{\left(29 i \, d x + 15 i \, c\right)} - 134089539584000 i \, a^{8} e^{\left(27 i \, d x + 13 i \, c\right)} - 215146797465600 i \, a^{8} e^{\left(25 i \, d x + 11 i \, c\right)} - 282406740295680 i \, a^{8} e^{\left(23 i \, d x + 9 i \, c\right)} - 304579309731840 i \, a^{8} e^{\left(21 i \, d x + 7 i \, c\right)} - 269947696578560 i \, a^{8} e^{\left(19 i \, d x + 5 i \, c\right)} - 195820823511040 i \, a^{8} e^{\left(17 i \, d x + 3 i \, c\right)} - 115246062632960 i \, a^{8} e^{\left(15 i \, d x + i \, c\right)} - 54220889784320 i \, a^{8} e^{\left(13 i \, d x - i \, c\right)} - 19924737064960 i \, a^{8} e^{\left(11 i \, d x - 3 i \, c\right)} - 5513153085440 i \, a^{8} e^{\left(9 i \, d x - 5 i \, c\right)} - 1080738447360 i \, a^{8} e^{\left(7 i \, d x - 7 i \, c\right)} - 133827133440 i \, a^{8} e^{\left(5 i \, d x - 9 i \, c\right)} - 7872184320 i \, a^{8} e^{\left(3 i \, d x - 11 i \, c\right)}}{755729694720 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/755729694720*(9725263833285*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 136153693665990*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 884999008828935*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3539996035315740*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 9734989097118285*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 19469978194236570*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 29204967291354855*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 29204967291354855*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 19469978194236570*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 9734989097118285*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 3539996035315740*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 884999008828935*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 136153693665990*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 33377105475834120*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 9725263833285*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 9720402036345*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) - 1) + 136085628508830*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 884556585307395*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 3538226341229580*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 9730122438381345*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 19460244876762690*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 29190367315144035*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 29190367315144035*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 19460244876762690*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 9730122438381345*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 3538226341229580*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 884556585307395*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 136085628508830*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 33360419788736040*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 9720402036345*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) - 1) - 9725263833285*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 136153693665990*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 884999008828935*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3539996035315740*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 9734989097118285*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 19469978194236570*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 29204967291354855*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 29204967291354855*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 19469978194236570*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 9734989097118285*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 3539996035315740*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 884999008828935*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 136153693665990*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 33377105475834120*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 9725263833285*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 9720402036345*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 136085628508830*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 884556585307395*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3538226341229580*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 9730122438381345*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 19460244876762690*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 29190367315144035*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 29190367315144035*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 19460244876762690*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 9730122438381345*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 3538226341229580*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 884556585307395*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 136085628508830*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 33360419788736040*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 9720402036345*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 4861796940*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 68065157160*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 442423521540*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 1769694086160*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 4866658736940*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 9733317473880*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 14599976210820*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 14599976210820*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 9733317473880*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 4866658736940*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 1769694086160*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 442423521540*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 68065157160*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 16685687098080*a^8*e^(14*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 4861796940*a^8*e^(-14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 4861796940*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 68065157160*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 442423521540*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 1769694086160*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 4866658736940*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 9733317473880*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 14599976210820*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 14599976210820*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 9733317473880*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 4866658736940*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 1769694086160*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 442423521540*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 68065157160*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 16685687098080*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 4861796940*a^8*e^(-14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 1816657920*I*a^8*e^(41*I*d*x + 27*I*c) - 36168007680*I*a^8*e^(39*I*d*x + 25*I*c) - 341843640320*I*a^8*e^(37*I*d*x + 23*I*c) - 2039236526080*I*a^8*e^(35*I*d*x + 21*I*c) - 8609784135680*I*a^8*e^(33*I*d*x + 19*I*c) - 27342720204800*I*a^8*e^(31*I*d*x + 17*I*c) - 67753266380800*I*a^8*e^(29*I*d*x + 15*I*c) - 134089539584000*I*a^8*e^(27*I*d*x + 13*I*c) - 215146797465600*I*a^8*e^(25*I*d*x + 11*I*c) - 282406740295680*I*a^8*e^(23*I*d*x + 9*I*c) - 304579309731840*I*a^8*e^(21*I*d*x + 7*I*c) - 269947696578560*I*a^8*e^(19*I*d*x + 5*I*c) - 195820823511040*I*a^8*e^(17*I*d*x + 3*I*c) - 115246062632960*I*a^8*e^(15*I*d*x + I*c) - 54220889784320*I*a^8*e^(13*I*d*x - I*c) - 19924737064960*I*a^8*e^(11*I*d*x - 3*I*c) - 5513153085440*I*a^8*e^(9*I*d*x - 5*I*c) - 1080738447360*I*a^8*e^(7*I*d*x - 7*I*c) - 133827133440*I*a^8*e^(5*I*d*x - 9*I*c) - 7872184320*I*a^8*e^(3*I*d*x - 11*I*c))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
98,1,2919,0,18.209196," ","integrate(cos(d*x+c)^15*(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{5682101344920 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 79549418828880 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 517071222387720 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2068284889550880 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5687783446264920 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 11375566892529840 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 17063350338794760 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 17063350338794760 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 11375566892529840 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5687783446264920 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 2068284889550880 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 517071222387720 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 79549418828880 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 19500971815765440 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5682101344920 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} + 1\right) + 5674116082635 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 79437625156890 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 516344563519785 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 2065378254079140 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 5679790198717635 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 11359580397435270 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 17039370596152905 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 17039370596152905 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 11359580397435270 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 5679790198717635 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 2065378254079140 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 516344563519785 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 79437625156890 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 19473566395603320 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) + 5674116082635 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5682101344920 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 79549418828880 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 517071222387720 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2068284889550880 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5687783446264920 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 11375566892529840 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 17063350338794760 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 17063350338794760 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 11375566892529840 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5687783446264920 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 2068284889550880 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 517071222387720 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 79549418828880 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 19500971815765440 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5682101344920 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} + 1\right) - 5674116082635 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 79437625156890 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 516344563519785 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 2065378254079140 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5679790198717635 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 11359580397435270 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 17039370596152905 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 17039370596152905 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 11359580397435270 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5679790198717635 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 2065378254079140 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 516344563519785 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 79437625156890 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 19473566395603320 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 5674116082635 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x + i \, c\right)} - 1\right) - 7985262285 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 111793671990 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 726658867935 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2906635471740 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 7993247547285 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 15986495094570 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23979742641855 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 23979742641855 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 15986495094570 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 7993247547285 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 2906635471740 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 726658867935 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 111793671990 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 27405420162120 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 7985262285 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 7985262285 \, a^{8} e^{\left(28 i \, d x + 14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 111793671990 \, a^{8} e^{\left(26 i \, d x + 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 726658867935 \, a^{8} e^{\left(24 i \, d x + 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2906635471740 \, a^{8} e^{\left(22 i \, d x + 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 7993247547285 \, a^{8} e^{\left(20 i \, d x + 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 15986495094570 \, a^{8} e^{\left(18 i \, d x + 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23979742641855 \, a^{8} e^{\left(16 i \, d x + 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 23979742641855 \, a^{8} e^{\left(12 i \, d x - 2 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 15986495094570 \, a^{8} e^{\left(10 i \, d x - 4 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 7993247547285 \, a^{8} e^{\left(8 i \, d x - 6 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 2906635471740 \, a^{8} e^{\left(6 i \, d x - 8 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 726658867935 \, a^{8} e^{\left(4 i \, d x - 10 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 111793671990 \, a^{8} e^{\left(2 i \, d x - 12 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 27405420162120 \, a^{8} e^{\left(14 i \, d x\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) + 7985262285 \, a^{8} e^{\left(-14 i \, c\right)} \log\left(-i \, e^{\left(i \, d x\right)} + e^{\left(-i \, c\right)}\right) - 449839104 i \, a^{8} e^{\left(43 i \, d x + 29 i \, c\right)} - 9931063296 i \, a^{8} e^{\left(41 i \, d x + 27 i \, c\right)} - 104683536384 i \, a^{8} e^{\left(39 i \, d x + 25 i \, c\right)} - 700958375936 i \, a^{8} e^{\left(37 i \, d x + 23 i \, c\right)} - 3346162253824 i \, a^{8} e^{\left(35 i \, d x + 21 i \, c\right)} - 12115053117440 i \, a^{8} e^{\left(33 i \, d x + 19 i \, c\right)} - 34553641041920 i \, a^{8} e^{\left(31 i \, d x + 17 i \, c\right)} - 79597529989120 i \, a^{8} e^{\left(29 i \, d x + 15 i \, c\right)} - 150652615393280 i \, a^{8} e^{\left(27 i \, d x + 13 i \, c\right)} - 237078702981120 i \, a^{8} e^{\left(25 i \, d x + 11 i \, c\right)} - 312733543170048 i \, a^{8} e^{\left(23 i \, d x + 9 i \, c\right)} - 347558287245312 i \, a^{8} e^{\left(21 i \, d x + 7 i \, c\right)} - 326158241497088 i \, a^{8} e^{\left(19 i \, d x + 5 i \, c\right)} - 258238371069952 i \, a^{8} e^{\left(17 i \, d x + 3 i \, c\right)} - 171721273376768 i \, a^{8} e^{\left(15 i \, d x + i \, c\right)} - 95003913224192 i \, a^{8} e^{\left(13 i \, d x - i \, c\right)} - 43034893877248 i \, a^{8} e^{\left(11 i \, d x - 3 i \, c\right)} - 15562783588352 i \, a^{8} e^{\left(9 i \, d x - 5 i \, c\right)} - 4319355076608 i \, a^{8} e^{\left(7 i \, d x - 7 i \, c\right)} - 862791401472 i \, a^{8} e^{\left(5 i \, d x - 9 i \, c\right)} - 110210580480 i \, a^{8} e^{\left(3 i \, d x - 11 i \, c\right)} - 6747586560 i \, a^{8} e^{\left(i \, d x - 13 i \, c\right)}}{863691079680 \, {\left(d e^{\left(28 i \, d x + 14 i \, c\right)} + 14 \, d e^{\left(26 i \, d x + 12 i \, c\right)} + 91 \, d e^{\left(24 i \, d x + 10 i \, c\right)} + 364 \, d e^{\left(22 i \, d x + 8 i \, c\right)} + 1001 \, d e^{\left(20 i \, d x + 6 i \, c\right)} + 2002 \, d e^{\left(18 i \, d x + 4 i \, c\right)} + 3003 \, d e^{\left(16 i \, d x + 2 i \, c\right)} + 3003 \, d e^{\left(12 i \, d x - 2 i \, c\right)} + 2002 \, d e^{\left(10 i \, d x - 4 i \, c\right)} + 1001 \, d e^{\left(8 i \, d x - 6 i \, c\right)} + 364 \, d e^{\left(6 i \, d x - 8 i \, c\right)} + 91 \, d e^{\left(4 i \, d x - 10 i \, c\right)} + 14 \, d e^{\left(2 i \, d x - 12 i \, c\right)} + 3432 \, d e^{\left(14 i \, d x\right)} + d e^{\left(-14 i \, c\right)}\right)}}"," ",0,"1/863691079680*(5682101344920*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 79549418828880*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 517071222387720*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2068284889550880*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 5687783446264920*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 11375566892529840*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 17063350338794760*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 17063350338794760*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) + 1) + 11375566892529840*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) + 1) + 5687783446264920*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) + 1) + 2068284889550880*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) + 1) + 517071222387720*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) + 1) + 79549418828880*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) + 1) + 19500971815765440*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) + 1) + 5682101344920*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) + 1) + 5674116082635*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x + I*c) - 1) + 79437625156890*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 516344563519785*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 2065378254079140*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 5679790198717635*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 11359580397435270*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 17039370596152905*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 17039370596152905*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x + I*c) - 1) + 11359580397435270*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x + I*c) - 1) + 5679790198717635*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x + I*c) - 1) + 2065378254079140*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x + I*c) - 1) + 516344563519785*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x + I*c) - 1) + 79437625156890*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x + I*c) - 1) + 19473566395603320*a^8*e^(14*I*d*x)*log(I*e^(I*d*x + I*c) - 1) + 5674116082635*a^8*e^(-14*I*c)*log(I*e^(I*d*x + I*c) - 1) - 5682101344920*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 79549418828880*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 517071222387720*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2068284889550880*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 5687783446264920*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 11375566892529840*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 17063350338794760*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 17063350338794760*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 11375566892529840*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 5687783446264920*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 2068284889550880*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 517071222387720*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 79549418828880*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 19500971815765440*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) + 1) - 5682101344920*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) + 1) - 5674116082635*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 79437625156890*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 516344563519785*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 2065378254079140*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 5679790198717635*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 11359580397435270*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 17039370596152905*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 17039370596152905*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 11359580397435270*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 5679790198717635*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 2065378254079140*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 516344563519785*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 79437625156890*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 19473566395603320*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x + I*c) - 1) - 5674116082635*a^8*e^(-14*I*c)*log(-I*e^(I*d*x + I*c) - 1) - 7985262285*a^8*e^(28*I*d*x + 14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 111793671990*a^8*e^(26*I*d*x + 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 726658867935*a^8*e^(24*I*d*x + 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2906635471740*a^8*e^(22*I*d*x + 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 7993247547285*a^8*e^(20*I*d*x + 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 15986495094570*a^8*e^(18*I*d*x + 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 23979742641855*a^8*e^(16*I*d*x + 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 23979742641855*a^8*e^(12*I*d*x - 2*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 15986495094570*a^8*e^(10*I*d*x - 4*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 7993247547285*a^8*e^(8*I*d*x - 6*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 2906635471740*a^8*e^(6*I*d*x - 8*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 726658867935*a^8*e^(4*I*d*x - 10*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 111793671990*a^8*e^(2*I*d*x - 12*I*c)*log(I*e^(I*d*x) + e^(-I*c)) - 27405420162120*a^8*e^(14*I*d*x)*log(I*e^(I*d*x) + e^(-I*c)) - 7985262285*a^8*e^(-14*I*c)*log(I*e^(I*d*x) + e^(-I*c)) + 7985262285*a^8*e^(28*I*d*x + 14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 111793671990*a^8*e^(26*I*d*x + 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 726658867935*a^8*e^(24*I*d*x + 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 2906635471740*a^8*e^(22*I*d*x + 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 7993247547285*a^8*e^(20*I*d*x + 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 15986495094570*a^8*e^(18*I*d*x + 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 23979742641855*a^8*e^(16*I*d*x + 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 23979742641855*a^8*e^(12*I*d*x - 2*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 15986495094570*a^8*e^(10*I*d*x - 4*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 7993247547285*a^8*e^(8*I*d*x - 6*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 2906635471740*a^8*e^(6*I*d*x - 8*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 726658867935*a^8*e^(4*I*d*x - 10*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 111793671990*a^8*e^(2*I*d*x - 12*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) + 27405420162120*a^8*e^(14*I*d*x)*log(-I*e^(I*d*x) + e^(-I*c)) + 7985262285*a^8*e^(-14*I*c)*log(-I*e^(I*d*x) + e^(-I*c)) - 449839104*I*a^8*e^(43*I*d*x + 29*I*c) - 9931063296*I*a^8*e^(41*I*d*x + 27*I*c) - 104683536384*I*a^8*e^(39*I*d*x + 25*I*c) - 700958375936*I*a^8*e^(37*I*d*x + 23*I*c) - 3346162253824*I*a^8*e^(35*I*d*x + 21*I*c) - 12115053117440*I*a^8*e^(33*I*d*x + 19*I*c) - 34553641041920*I*a^8*e^(31*I*d*x + 17*I*c) - 79597529989120*I*a^8*e^(29*I*d*x + 15*I*c) - 150652615393280*I*a^8*e^(27*I*d*x + 13*I*c) - 237078702981120*I*a^8*e^(25*I*d*x + 11*I*c) - 312733543170048*I*a^8*e^(23*I*d*x + 9*I*c) - 347558287245312*I*a^8*e^(21*I*d*x + 7*I*c) - 326158241497088*I*a^8*e^(19*I*d*x + 5*I*c) - 258238371069952*I*a^8*e^(17*I*d*x + 3*I*c) - 171721273376768*I*a^8*e^(15*I*d*x + I*c) - 95003913224192*I*a^8*e^(13*I*d*x - I*c) - 43034893877248*I*a^8*e^(11*I*d*x - 3*I*c) - 15562783588352*I*a^8*e^(9*I*d*x - 5*I*c) - 4319355076608*I*a^8*e^(7*I*d*x - 7*I*c) - 862791401472*I*a^8*e^(5*I*d*x - 9*I*c) - 110210580480*I*a^8*e^(3*I*d*x - 11*I*c) - 6747586560*I*a^8*e^(I*d*x - 13*I*c))/(d*e^(28*I*d*x + 14*I*c) + 14*d*e^(26*I*d*x + 12*I*c) + 91*d*e^(24*I*d*x + 10*I*c) + 364*d*e^(22*I*d*x + 8*I*c) + 1001*d*e^(20*I*d*x + 6*I*c) + 2002*d*e^(18*I*d*x + 4*I*c) + 3003*d*e^(16*I*d*x + 2*I*c) + 3003*d*e^(12*I*d*x - 2*I*c) + 2002*d*e^(10*I*d*x - 4*I*c) + 1001*d*e^(8*I*d*x - 6*I*c) + 364*d*e^(6*I*d*x - 8*I*c) + 91*d*e^(4*I*d*x - 10*I*c) + 14*d*e^(2*I*d*x - 12*I*c) + 3432*d*e^(14*I*d*x) + d*e^(-14*I*c))","B",0
99,1,87,0,0.692254," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{35 i \, \tan\left(d x + c\right)^{8} - 40 \, \tan\left(d x + c\right)^{7} + 140 i \, \tan\left(d x + c\right)^{6} - 168 \, \tan\left(d x + c\right)^{5} + 210 i \, \tan\left(d x + c\right)^{4} - 280 \, \tan\left(d x + c\right)^{3} + 140 i \, \tan\left(d x + c\right)^{2} - 280 \, \tan\left(d x + c\right)}{280 \, a d}"," ",0,"-1/280*(35*I*tan(d*x + c)^8 - 40*tan(d*x + c)^7 + 140*I*tan(d*x + c)^6 - 168*tan(d*x + c)^5 + 210*I*tan(d*x + c)^4 - 280*tan(d*x + c)^3 + 140*I*tan(d*x + c)^2 - 280*tan(d*x + c))/(a*d)","A",0
100,1,67,0,0.684067," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{5 i \, \tan\left(d x + c\right)^{6} - 6 \, \tan\left(d x + c\right)^{5} + 15 i \, \tan\left(d x + c\right)^{4} - 20 \, \tan\left(d x + c\right)^{3} + 15 i \, \tan\left(d x + c\right)^{2} - 30 \, \tan\left(d x + c\right)}{30 \, a d}"," ",0,"-1/30*(5*I*tan(d*x + c)^6 - 6*tan(d*x + c)^5 + 15*I*tan(d*x + c)^4 - 20*tan(d*x + c)^3 + 15*I*tan(d*x + c)^2 - 30*tan(d*x + c))/(a*d)","A",0
101,1,47,0,0.561082," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{3 i \, \tan\left(d x + c\right)^{4} - 4 \, \tan\left(d x + c\right)^{3} + 6 i \, \tan\left(d x + c\right)^{2} - 12 \, \tan\left(d x + c\right)}{12 \, a d}"," ",0,"-1/12*(3*I*tan(d*x + c)^4 - 4*tan(d*x + c)^3 + 6*I*tan(d*x + c)^2 - 12*tan(d*x + c))/(a*d)","A",0
102,1,27,0,1.417246," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{i \, \tan\left(d x + c\right)^{2} - 2 \, \tan\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(I*tan(d*x + c)^2 - 2*tan(d*x + c))/(a*d)","A",0
103,1,57,0,2.265538," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-\frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a} + \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a} - \frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a}}{d}"," ",0,"-(-I*log(tan(1/2*d*x + 1/2*c) + 1)/a + 2*I*log(tan(1/2*d*x + 1/2*c) - I)/a - I*log(tan(1/2*d*x + 1/2*c) - 1)/a)/d","B",0
104,1,60,0,0.401025," ","integrate(1/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{i \, \log\left(\tan\left(d x + c\right) - i\right)}{a} - \frac{i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a} + \frac{-i \, \tan\left(d x + c\right) - 3}{a {\left(\tan\left(d x + c\right) - i\right)}}}{4 \, d}"," ",0,"-1/4*(I*log(tan(d*x + c) - I)/a - I*log(-I*tan(d*x + c) + 1)/a + (-I*tan(d*x + c) - 3)/(a*(tan(d*x + c) - I)))/d","B",0
105,1,99,0,0.892789," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a} - \frac{6 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a} + \frac{2 \, {\left(3 \, \tan\left(d x + c\right) + 5 i\right)}}{a {\left(-i \, \tan\left(d x + c\right) + 1\right)}} + \frac{-9 i \, \tan\left(d x + c\right)^{2} - 26 \, \tan\left(d x + c\right) + 21 i}{a {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{32 \, d}"," ",0,"-1/32*(6*I*log(I*tan(d*x + c) + 1)/a - 6*I*log(I*tan(d*x + c) - 1)/a + 2*(3*tan(d*x + c) + 5*I)/(a*(-I*tan(d*x + c) + 1)) + (-9*I*tan(d*x + c)^2 - 26*tan(d*x + c) + 21*I)/(a*(tan(d*x + c) - I)^2))/d","A",0
106,1,116,0,2.221688," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-\frac{30 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a} + \frac{30 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a} + \frac{3 \, {\left(-15 i \, \tan\left(d x + c\right)^{2} + 38 \, \tan\left(d x + c\right) + 25 i\right)}}{a {\left(-i \, \tan\left(d x + c\right) + 1\right)}^{2}} - \frac{55 i \, \tan\left(d x + c\right)^{3} + 201 \, \tan\left(d x + c\right)^{2} - 255 i \, \tan\left(d x + c\right) - 117}{a {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{192 \, d}"," ",0,"-1/192*(-30*I*log(tan(d*x + c) + I)/a + 30*I*log(tan(d*x + c) - I)/a + 3*(-15*I*tan(d*x + c)^2 + 38*tan(d*x + c) + 25*I)/(a*(-I*tan(d*x + c) + 1)^2) - (55*I*tan(d*x + c)^3 + 201*tan(d*x + c)^2 - 255*I*tan(d*x + c) - 117)/(a*(tan(d*x + c) - I)^3))/d","A",0
107,1,138,0,0.720103," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a} - \frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a} + \frac{2 \, {\left(25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 40 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 80 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} a}}{40 \, d}"," ",0,"1/40*(15*log(tan(1/2*d*x + 1/2*c) + 1)/a - 15*log(tan(1/2*d*x + 1/2*c) - 1)/a + 2*(25*tan(1/2*d*x + 1/2*c)^9 + 40*I*tan(1/2*d*x + 1/2*c)^8 - 10*tan(1/2*d*x + 1/2*c)^7 + 80*I*tan(1/2*d*x + 1/2*c)^4 + 10*tan(1/2*d*x + 1/2*c)^3 - 25*tan(1/2*d*x + 1/2*c) + 8*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*a))/d","A",0
108,1,99,0,0.733840," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a} - \frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a} + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a}}{6 \, d}"," ",0,"1/6*(3*log(tan(1/2*d*x + 1/2*c) + 1)/a - 3*log(tan(1/2*d*x + 1/2*c) - 1)/a + 2*(3*tan(1/2*d*x + 1/2*c)^5 + 6*I*tan(1/2*d*x + 1/2*c)^4 - 3*tan(1/2*d*x + 1/2*c) + 2*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a))/d","A",0
109,1,58,0,0.700507," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a} - \frac{\log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a} + \frac{2 i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a}}{d}"," ",0,"(log(tan(1/2*d*x + 1/2*c) + 1)/a - log(tan(1/2*d*x + 1/2*c) - 1)/a + 2*I/((tan(1/2*d*x + 1/2*c)^2 - 1)*a))/d","A",0
110,1,21,0,0.701889," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{2}{a d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}}"," ",0,"2/(a*d*(tan(1/2*d*x + 1/2*c) - I))","A",0
111,1,67,0,0.654090," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}} + \frac{9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3/(a*(tan(1/2*d*x + 1/2*c) + I)) + (9*tan(1/2*d*x + 1/2*c)^2 - 12*I*tan(1/2*d*x + 1/2*c) - 7)/(a*(tan(1/2*d*x + 1/2*c) - I)^3))/d","A",0
112,1,119,0,0.645265," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{5 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 13\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{3}} + \frac{165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 650 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 400 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 113}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{5}}}{120 \, d}"," ",0,"1/120*(5*(15*tan(1/2*d*x + 1/2*c)^2 + 24*I*tan(1/2*d*x + 1/2*c) - 13)/(a*(tan(1/2*d*x + 1/2*c) + I)^3) + (165*tan(1/2*d*x + 1/2*c)^4 - 480*I*tan(1/2*d*x + 1/2*c)^3 - 650*tan(1/2*d*x + 1/2*c)^2 + 400*I*tan(1/2*d*x + 1/2*c) + 113)/(a*(tan(1/2*d*x + 1/2*c) - I)^5))/d","B",0
113,1,171,0,0.708004," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{7 \, {\left(55 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 180 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 250 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 160 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 43\right)}}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{5}} + \frac{735 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 3360 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 7315 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8820 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6321 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2492 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 461}{a {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{7}}}{560 \, d}"," ",0,"1/560*(7*(55*tan(1/2*d*x + 1/2*c)^4 + 180*I*tan(1/2*d*x + 1/2*c)^3 - 250*tan(1/2*d*x + 1/2*c)^2 - 160*I*tan(1/2*d*x + 1/2*c) + 43)/(a*(tan(1/2*d*x + 1/2*c) + I)^5) + (735*tan(1/2*d*x + 1/2*c)^6 - 3360*I*tan(1/2*d*x + 1/2*c)^5 - 7315*tan(1/2*d*x + 1/2*c)^4 + 8820*I*tan(1/2*d*x + 1/2*c)^3 + 6321*tan(1/2*d*x + 1/2*c)^2 - 2492*I*tan(1/2*d*x + 1/2*c) - 461)/(a*(tan(1/2*d*x + 1/2*c) - I)^7))/d","B",0
114,1,77,0,1.031493," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{15 \, \tan\left(d x + c\right)^{7} + 35 i \, \tan\left(d x + c\right)^{6} + 21 \, \tan\left(d x + c\right)^{5} + 105 i \, \tan\left(d x + c\right)^{4} - 35 \, \tan\left(d x + c\right)^{3} + 105 i \, \tan\left(d x + c\right)^{2} - 105 \, \tan\left(d x + c\right)}{105 \, a^{2} d}"," ",0,"-1/105*(15*tan(d*x + c)^7 + 35*I*tan(d*x + c)^6 + 21*tan(d*x + c)^5 + 105*I*tan(d*x + c)^4 - 35*tan(d*x + c)^3 + 105*I*tan(d*x + c)^2 - 105*tan(d*x + c))/(a^2*d)","A",0
115,1,47,0,0.853634," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, \tan\left(d x + c\right)^{5} + 5 i \, \tan\left(d x + c\right)^{4} + 10 i \, \tan\left(d x + c\right)^{2} - 10 \, \tan\left(d x + c\right)}{10 \, a^{2} d}"," ",0,"-1/10*(2*tan(d*x + c)^5 + 5*I*tan(d*x + c)^4 + 10*I*tan(d*x + c)^2 - 10*tan(d*x + c))/(a^2*d)","A",0
116,1,35,0,0.994322," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\tan\left(d x + c\right)^{3} + 3 i \, \tan\left(d x + c\right)^{2} - 3 \, \tan\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"-1/3*(tan(d*x + c)^3 + 3*I*tan(d*x + c)^2 - 3*tan(d*x + c))/(a^2*d)","A",0
117,1,100,0,0.981160," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{2}} + \frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} + \frac{-i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{2}}\right)}}{d}"," ",0,"2*(I*log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - 2*I*log(tan(1/2*d*x + 1/2*c) - I)/a^2 + I*log(tan(1/2*d*x + 1/2*c) - 1)/a^2 + (-I*tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + I)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^2))/d","B",0
118,1,30,0,0.846320," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{2}}"," ",0,"-2*tan(1/2*d*x + 1/2*c)/(a^2*d*(tan(1/2*d*x + 1/2*c) - I)^2)","A",0
119,1,72,0,0.537833," ","integrate(1/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{2}} - \frac{2 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{2}} + \frac{-3 i \, \tan\left(d x + c\right)^{2} - 10 \, \tan\left(d x + c\right) + 11 i}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(2*I*log(I*tan(d*x + c) + 1)/a^2 - 2*I*log(I*tan(d*x + c) - 1)/a^2 + (-3*I*tan(d*x + c)^2 - 10*tan(d*x + c) + 11*I)/(a^2*(tan(d*x + c) - I)^2))/d","A",0
120,1,103,0,0.935668," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{-\frac{6 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{2}} + \frac{6 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} + \frac{3 \, {\left(2 i \, \tan\left(d x + c\right) - 3\right)}}{a^{2} {\left(\tan\left(d x + c\right) + i\right)}} + \frac{-11 i \, \tan\left(d x + c\right)^{3} - 42 \, \tan\left(d x + c\right)^{2} + 57 i \, \tan\left(d x + c\right) + 30}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{48 \, d}"," ",0,"-1/48*(-6*I*log(tan(d*x + c) + I)/a^2 + 6*I*log(tan(d*x + c) - I)/a^2 + 3*(2*I*tan(d*x + c) - 3)/(a^2*(tan(d*x + c) + I)) + (-11*I*tan(d*x + c)^3 - 42*tan(d*x + c)^2 + 57*I*tan(d*x + c) + 30)/(a^2*(tan(d*x + c) - I)^3))/d","A",0
121,1,127,0,0.932095," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{60 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{2}} - \frac{60 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{2}} + \frac{2 \, {\left(45 i \, \tan\left(d x + c\right)^{2} - 110 \, \tan\left(d x + c\right) - 69 i\right)}}{a^{2} {\left(\tan\left(d x + c\right) + i\right)}^{2}} + \frac{-125 i \, \tan\left(d x + c\right)^{4} - 580 \, \tan\left(d x + c\right)^{3} + 1038 i \, \tan\left(d x + c\right)^{2} + 868 \, \tan\left(d x + c\right) - 301 i}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{512 \, d}"," ",0,"-1/512*(60*I*log(I*tan(d*x + c) + 1)/a^2 - 60*I*log(I*tan(d*x + c) - 1)/a^2 + 2*(45*I*tan(d*x + c)^2 - 110*tan(d*x + c) - 69*I)/(a^2*(tan(d*x + c) + I)^2) + (-125*I*tan(d*x + c)^4 - 580*tan(d*x + c)^3 + 1038*I*tan(d*x + c)^2 + 868*tan(d*x + c) - 301*I)/(a^2*(tan(d*x + c) - I)^4))/d","A",0
122,1,203,0,1.116071," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} + \frac{2 \, {\left(135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 445 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 330 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 960 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 330 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 960 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 445 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 135 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6} a^{2}}}{240 \, d}"," ",0,"1/240*(105*log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - 105*log(tan(1/2*d*x + 1/2*c) - 1)/a^2 + 2*(135*tan(1/2*d*x + 1/2*c)^11 + 480*I*tan(1/2*d*x + 1/2*c)^10 - 445*tan(1/2*d*x + 1/2*c)^9 - 480*I*tan(1/2*d*x + 1/2*c)^8 - 330*tan(1/2*d*x + 1/2*c)^7 + 960*I*tan(1/2*d*x + 1/2*c)^6 - 330*tan(1/2*d*x + 1/2*c)^5 - 960*I*tan(1/2*d*x + 1/2*c)^4 - 445*tan(1/2*d*x + 1/2*c)^3 + 96*I*tan(1/2*d*x + 1/2*c)^2 + 135*tan(1/2*d*x + 1/2*c) - 96*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^6*a^2))/d","A",0
123,1,151,0,0.948061," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 48 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 48 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 33 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 16 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 16 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4} a^{2}}}{24 \, d}"," ",0,"1/24*(15*log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - 15*log(tan(1/2*d*x + 1/2*c) - 1)/a^2 + 2*(9*tan(1/2*d*x + 1/2*c)^7 + 48*I*tan(1/2*d*x + 1/2*c)^6 - 33*tan(1/2*d*x + 1/2*c)^5 - 48*I*tan(1/2*d*x + 1/2*c)^4 - 33*tan(1/2*d*x + 1/2*c)^3 + 16*I*tan(1/2*d*x + 1/2*c)^2 + 9*tan(1/2*d*x + 1/2*c) - 16*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*a^2))/d","A",0
124,1,95,0,0.901504," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} - \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{2}}}{2 \, d}"," ",0,"1/2*(3*log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - 3*log(tan(1/2*d*x + 1/2*c) - 1)/a^2 - 2*(tan(1/2*d*x + 1/2*c)^3 - 4*I*tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 4*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^2))/d","A",0
125,1,57,0,1.028857," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{\log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{2}} - \frac{\log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{2}} - \frac{4}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}}}{d}"," ",0,"-(log(tan(1/2*d*x + 1/2*c) + 1)/a^2 - log(tan(1/2*d*x + 1/2*c) - 1)/a^2 - 4/(a^2*(tan(1/2*d*x + 1/2*c) - I)))/d","A",0
126,1,47,0,0.833800," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2\right)}}{3 \, a^{2} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}}"," ",0,"2/3*(3*tan(1/2*d*x + 1/2*c)^2 - 3*I*tan(1/2*d*x + 1/2*c) - 2)/(a^2*d*(tan(1/2*d*x + 1/2*c) - I)^3)","A",0
127,1,93,0,1.619972," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{5}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}} + \frac{35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 90 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 70 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{5}}}{20 \, d}"," ",0,"1/20*(5/(a^2*(tan(1/2*d*x + 1/2*c) + I)) + (35*tan(1/2*d*x + 1/2*c)^4 - 90*I*tan(1/2*d*x + 1/2*c)^3 - 120*tan(1/2*d*x + 1/2*c)^2 + 70*I*tan(1/2*d*x + 1/2*c) + 21)/(a^2*(tan(1/2*d*x + 1/2*c) - I)^5))/d","A",0
128,1,145,0,0.926757," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{7 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{3}} + \frac{273 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1155 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2450 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2870 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2037 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 791 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 152}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{7}}}{168 \, d}"," ",0,"1/168*(7*(9*tan(1/2*d*x + 1/2*c)^2 + 15*I*tan(1/2*d*x + 1/2*c) - 8)/(a^2*(tan(1/2*d*x + 1/2*c) + I)^3) + (273*tan(1/2*d*x + 1/2*c)^6 - 1155*I*tan(1/2*d*x + 1/2*c)^5 - 2450*tan(1/2*d*x + 1/2*c)^4 + 2870*I*tan(1/2*d*x + 1/2*c)^3 + 2037*tan(1/2*d*x + 1/2*c)^2 - 791*I*tan(1/2*d*x + 1/2*c) - 152)/(a^2*(tan(1/2*d*x + 1/2*c) - I)^7))/d","A",0
129,1,197,0,1.025383," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(435 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1470 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2060 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1330 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 353\right)}}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{5}} + \frac{4455 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 26460 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 78120 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 137340 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 157374 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 118356 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 57744 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16596 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2339}{a^{2} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{9}}}{2880 \, d}"," ",0,"1/2880*(3*(435*tan(1/2*d*x + 1/2*c)^4 + 1470*I*tan(1/2*d*x + 1/2*c)^3 - 2060*tan(1/2*d*x + 1/2*c)^2 - 1330*I*tan(1/2*d*x + 1/2*c) + 353)/(a^2*(tan(1/2*d*x + 1/2*c) + I)^5) + (4455*tan(1/2*d*x + 1/2*c)^8 - 26460*I*tan(1/2*d*x + 1/2*c)^7 - 78120*tan(1/2*d*x + 1/2*c)^6 + 137340*I*tan(1/2*d*x + 1/2*c)^5 + 157374*tan(1/2*d*x + 1/2*c)^4 - 118356*I*tan(1/2*d*x + 1/2*c)^3 - 57744*tan(1/2*d*x + 1/2*c)^2 + 16596*I*tan(1/2*d*x + 1/2*c) + 2339)/(a^2*(tan(1/2*d*x + 1/2*c) - I)^9))/d","B",0
130,1,87,0,2.356489," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-21 i \, \tan\left(d x + c\right)^{10} + 70 \, \tan\left(d x + c\right)^{9} + 240 \, \tan\left(d x + c\right)^{7} + 210 i \, \tan\left(d x + c\right)^{6} + 252 \, \tan\left(d x + c\right)^{5} + 420 i \, \tan\left(d x + c\right)^{4} + 315 i \, \tan\left(d x + c\right)^{2} - 210 \, \tan\left(d x + c\right)}{210 \, a^{3} d}"," ",0,"-1/210*(-21*I*tan(d*x + c)^10 + 70*tan(d*x + c)^9 + 240*tan(d*x + c)^7 + 210*I*tan(d*x + c)^6 + 252*tan(d*x + c)^5 + 420*I*tan(d*x + c)^4 + 315*I*tan(d*x + c)^2 - 210*tan(d*x + c))/(a^3*d)","A",0
131,1,87,0,1.723920," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-21 i \, \tan\left(d x + c\right)^{8} + 72 \, \tan\left(d x + c\right)^{7} + 28 i \, \tan\left(d x + c\right)^{6} + 168 \, \tan\left(d x + c\right)^{5} + 210 i \, \tan\left(d x + c\right)^{4} + 56 \, \tan\left(d x + c\right)^{3} + 252 i \, \tan\left(d x + c\right)^{2} - 168 \, \tan\left(d x + c\right)}{168 \, a^{3} d}"," ",0,"-1/168*(-21*I*tan(d*x + c)^8 + 72*tan(d*x + c)^7 + 28*I*tan(d*x + c)^6 + 168*tan(d*x + c)^5 + 210*I*tan(d*x + c)^4 + 56*tan(d*x + c)^3 + 252*I*tan(d*x + c)^2 - 168*tan(d*x + c))/(a^3*d)","A",0
132,1,67,0,1.721789," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-5 i \, \tan\left(d x + c\right)^{6} + 18 \, \tan\left(d x + c\right)^{5} + 15 i \, \tan\left(d x + c\right)^{4} + 20 \, \tan\left(d x + c\right)^{3} + 45 i \, \tan\left(d x + c\right)^{2} - 30 \, \tan\left(d x + c\right)}{30 \, a^{3} d}"," ",0,"-1/30*(-5*I*tan(d*x + c)^6 + 18*tan(d*x + c)^5 + 15*I*tan(d*x + c)^4 + 20*tan(d*x + c)^3 + 45*I*tan(d*x + c)^2 - 30*tan(d*x + c))/(a^3*d)","A",0
133,1,47,0,1.431755," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-i \, \tan\left(d x + c\right)^{4} + 4 \, \tan\left(d x + c\right)^{3} + 6 i \, \tan\left(d x + c\right)^{2} - 4 \, \tan\left(d x + c\right)}{4 \, a^{3} d}"," ",0,"-1/4*(-I*tan(d*x + c)^4 + 4*tan(d*x + c)^3 + 6*I*tan(d*x + c)^2 - 4*tan(d*x + c))/(a^3*d)","B",0
134,1,128,0,1.028221," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{4 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{3}} + \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} + \frac{-3 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 7 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{3}}\right)}}{d}"," ",0,"2*(2*I*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 4*I*log(tan(1/2*d*x + 1/2*c) - I)/a^3 + 2*I*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 + (-3*I*tan(1/2*d*x + 1/2*c)^4 + 3*tan(1/2*d*x + 1/2*c)^3 + 7*I*tan(1/2*d*x + 1/2*c)^2 - 3*tan(1/2*d*x + 1/2*c) - 3*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^3))/d","B",0
135,1,100,0,1.447912," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{3}} + \frac{i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} + \frac{3 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 i}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{2}}}{d}"," ",0,"-(I*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 2*I*log(tan(1/2*d*x + 1/2*c) - I)/a^3 + I*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 + (3*I*tan(1/2*d*x + 1/2*c)^2 + 10*tan(1/2*d*x + 1/2*c) - 3*I)/(a^3*(tan(1/2*d*x + 1/2*c) - I)^2))/d","B",0
136,1,57,0,1.547254," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{3} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{4}}"," ",0,"-2*(tan(1/2*d*x + 1/2*c)^3 - I*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c))/(a^3*d*(tan(1/2*d*x + 1/2*c) - I)^4)","B",0
137,1,80,0,0.659330," ","integrate(1/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{3}} - \frac{6 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{3}} + \frac{-11 i \, \tan\left(d x + c\right)^{3} - 45 \, \tan\left(d x + c\right)^{2} + 69 i \, \tan\left(d x + c\right) + 51}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(6*I*log(tan(d*x + c) - I)/a^3 - 6*I*log(I*tan(d*x + c) - 1)/a^3 + (-11*I*tan(d*x + c)^3 - 45*tan(d*x + c)^2 + 69*I*tan(d*x + c) + 51)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
138,1,119,0,1.738443," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-\frac{60 i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a^{3}} + \frac{60 i \, \log\left(-i \, \tan\left(d x + c\right) - 1\right)}{a^{3}} - \frac{12 \, {\left(5 \, \tan\left(d x + c\right) + 7 i\right)}}{a^{3} {\left(i \, \tan\left(d x + c\right) - 1\right)}} + \frac{-125 i \, \tan\left(d x + c\right)^{4} - 596 \, \tan\left(d x + c\right)^{3} + 1110 i \, \tan\left(d x + c\right)^{2} + 996 \, \tan\left(d x + c\right) - 405 i}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{768 \, d}"," ",0,"-1/768*(-60*I*log(-I*tan(d*x + c) + 1)/a^3 + 60*I*log(-I*tan(d*x + c) - 1)/a^3 - 12*(5*tan(d*x + c) + 7*I)/(a^3*(I*tan(d*x + c) - 1)) + (-125*I*tan(d*x + c)^4 - 596*tan(d*x + c)^3 + 1110*I*tan(d*x + c)^2 + 996*tan(d*x + c) - 405*I)/(a^3*(tan(d*x + c) - I)^4))/d","A",0
139,1,136,0,2.347988," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-\frac{420 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{3}} + \frac{420 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{3}} + \frac{10 \, {\left(-63 i \, \tan\left(d x + c\right)^{2} + 150 \, \tan\left(d x + c\right) + 91 i\right)}}{a^{3} {\left(i \, \tan\left(d x + c\right) - 1\right)}^{2}} - \frac{959 i \, \tan\left(d x + c\right)^{5} + 5395 \, \tan\left(d x + c\right)^{4} - 12390 i \, \tan\left(d x + c\right)^{3} - 14710 \, \tan\left(d x + c\right)^{2} + 9275 i \, \tan\left(d x + c\right) + 2647}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{5}}}{5120 \, d}"," ",0,"-1/5120*(-420*I*log(tan(d*x + c) + I)/a^3 + 420*I*log(tan(d*x + c) - I)/a^3 + 10*(-63*I*tan(d*x + c)^2 + 150*tan(d*x + c) + 91*I)/(a^3*(I*tan(d*x + c) - 1)^2) - (959*I*tan(d*x + c)^5 + 5395*tan(d*x + c)^4 - 12390*I*tan(d*x + c)^3 - 14710*tan(d*x + c)^2 + 9275*I*tan(d*x + c) + 2647)/(a^3*(tan(d*x + c) - I)^5))/d","A",0
140,1,164,0,1.940795," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} + \frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 360 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 390 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 400 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 390 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 136 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} a^{3}}}{120 \, d}"," ",0,"1/120*(105*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 105*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 + 2*(15*tan(1/2*d*x + 1/2*c)^9 + 360*I*tan(1/2*d*x + 1/2*c)^8 - 390*tan(1/2*d*x + 1/2*c)^7 - 960*I*tan(1/2*d*x + 1/2*c)^6 + 400*I*tan(1/2*d*x + 1/2*c)^4 + 390*tan(1/2*d*x + 1/2*c)^3 - 320*I*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c) + 136*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*a^3))/d","A",0
141,1,112,0,1.538989," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} - \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 48 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 22 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{3}}}{6 \, d}"," ",0,"1/6*(15*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 15*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 - 2*(9*tan(1/2*d*x + 1/2*c)^5 - 18*I*tan(1/2*d*x + 1/2*c)^4 + 48*I*tan(1/2*d*x + 1/2*c)^2 - 9*tan(1/2*d*x + 1/2*c) - 22*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^3))/d","A",0
142,1,110,0,1.549771," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{3}} - \frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{3}} - \frac{2 \, {\left(4 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)} a^{3}}}{d}"," ",0,"-(3*log(tan(1/2*d*x + 1/2*c) + 1)/a^3 - 3*log(tan(1/2*d*x + 1/2*c) - 1)/a^3 - 2*(4*tan(1/2*d*x + 1/2*c)^2 - I*tan(1/2*d*x + 1/2*c) - 5)/((tan(1/2*d*x + 1/2*c)^3 - I*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) + I)*a^3))/d","A",0
143,1,36,0,1.696043," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{3 \, a^{3} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}}"," ",0,"2/3*(3*tan(1/2*d*x + 1/2*c)^2 - 1)/(a^3*d*(tan(1/2*d*x + 1/2*c) - I)^3)","A",0
144,1,73,0,1.120296," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 30 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 40 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7\right)}}{15 \, a^{3} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{5}}"," ",0,"2/15*(15*tan(1/2*d*x + 1/2*c)^4 - 30*I*tan(1/2*d*x + 1/2*c)^3 - 40*tan(1/2*d*x + 1/2*c)^2 + 20*I*tan(1/2*d*x + 1/2*c) + 7)/(a^3*d*(tan(1/2*d*x + 1/2*c) - I)^5)","A",0
145,1,119,0,1.534219," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{35}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}} + \frac{525 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1960 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4025 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3143 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1176 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 243}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{7}}}{280 \, d}"," ",0,"1/280*(35/(a^3*(tan(1/2*d*x + 1/2*c) + I)) + (525*tan(1/2*d*x + 1/2*c)^6 - 1960*I*tan(1/2*d*x + 1/2*c)^5 - 4025*tan(1/2*d*x + 1/2*c)^4 + 4480*I*tan(1/2*d*x + 1/2*c)^3 + 3143*tan(1/2*d*x + 1/2*c)^2 - 1176*I*tan(1/2*d*x + 1/2*c) - 243)/(a^3*(tan(1/2*d*x + 1/2*c) - I)^7))/d","A",0
146,1,171,0,1.662352," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{21 \, {\left(21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 19\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{3}} + \frac{3591 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 19656 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 56196 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 95760 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 107730 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 79464 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 38484 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10944 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1615}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{9}}}{2016 \, d}"," ",0,"1/2016*(21*(21*tan(1/2*d*x + 1/2*c)^2 + 36*I*tan(1/2*d*x + 1/2*c) - 19)/(a^3*(tan(1/2*d*x + 1/2*c) + I)^3) + (3591*tan(1/2*d*x + 1/2*c)^8 - 19656*I*tan(1/2*d*x + 1/2*c)^7 - 56196*tan(1/2*d*x + 1/2*c)^6 + 95760*I*tan(1/2*d*x + 1/2*c)^5 + 107730*tan(1/2*d*x + 1/2*c)^4 - 79464*I*tan(1/2*d*x + 1/2*c)^3 - 38484*tan(1/2*d*x + 1/2*c)^2 + 10944*I*tan(1/2*d*x + 1/2*c) + 1615)/(a^3*(tan(1/2*d*x + 1/2*c) - I)^9))/d","A",0
147,1,223,0,1.739972," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{33 \, {\left(555 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1920 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2710 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1760 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 463\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{5}} + \frac{108405 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 784080 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 2901195 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6652800 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 10407474 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 11435424 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 8949270 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4899840 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 1816265 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 411664 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 47279}{a^{3} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{11}}}{63360 \, d}"," ",0,"1/63360*(33*(555*tan(1/2*d*x + 1/2*c)^4 + 1920*I*tan(1/2*d*x + 1/2*c)^3 - 2710*tan(1/2*d*x + 1/2*c)^2 - 1760*I*tan(1/2*d*x + 1/2*c) + 463)/(a^3*(tan(1/2*d*x + 1/2*c) + I)^5) + (108405*tan(1/2*d*x + 1/2*c)^10 - 784080*I*tan(1/2*d*x + 1/2*c)^9 - 2901195*tan(1/2*d*x + 1/2*c)^8 + 6652800*I*tan(1/2*d*x + 1/2*c)^7 + 10407474*tan(1/2*d*x + 1/2*c)^6 - 11435424*I*tan(1/2*d*x + 1/2*c)^5 - 8949270*tan(1/2*d*x + 1/2*c)^4 + 4899840*I*tan(1/2*d*x + 1/2*c)^3 + 1816265*tan(1/2*d*x + 1/2*c)^2 - 411664*I*tan(1/2*d*x + 1/2*c) - 47279)/(a^3*(tan(1/2*d*x + 1/2*c) - I)^11))/d","A",0
148,1,97,0,3.644594," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{14 \, \tan\left(d x + c\right)^{9} + 63 i \, \tan\left(d x + c\right)^{8} - 72 \, \tan\left(d x + c\right)^{7} + 84 i \, \tan\left(d x + c\right)^{6} - 252 \, \tan\left(d x + c\right)^{5} - 126 i \, \tan\left(d x + c\right)^{4} - 168 \, \tan\left(d x + c\right)^{3} - 252 i \, \tan\left(d x + c\right)^{2} + 126 \, \tan\left(d x + c\right)}{126 \, a^{4} d}"," ",0,"1/126*(14*tan(d*x + c)^9 + 63*I*tan(d*x + c)^8 - 72*tan(d*x + c)^7 + 84*I*tan(d*x + c)^6 - 252*tan(d*x + c)^5 - 126*I*tan(d*x + c)^4 - 168*tan(d*x + c)^3 - 252*I*tan(d*x + c)^2 + 126*tan(d*x + c))/(a^4*d)","A",0
149,1,67,0,1.973645," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, \tan\left(d x + c\right)^{7} + 14 i \, \tan\left(d x + c\right)^{6} - 21 \, \tan\left(d x + c\right)^{5} - 35 \, \tan\left(d x + c\right)^{3} - 42 i \, \tan\left(d x + c\right)^{2} + 21 \, \tan\left(d x + c\right)}{21 \, a^{4} d}"," ",0,"1/21*(3*tan(d*x + c)^7 + 14*I*tan(d*x + c)^6 - 21*tan(d*x + c)^5 - 35*tan(d*x + c)^3 - 42*I*tan(d*x + c)^2 + 21*tan(d*x + c))/(a^4*d)","A",0
150,1,55,0,2.157748," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\tan\left(d x + c\right)^{5} + 5 i \, \tan\left(d x + c\right)^{4} - 10 \, \tan\left(d x + c\right)^{3} - 10 i \, \tan\left(d x + c\right)^{2} + 5 \, \tan\left(d x + c\right)}{5 \, a^{4} d}"," ",0,"1/5*(tan(d*x + c)^5 + 5*I*tan(d*x + c)^4 - 10*tan(d*x + c)^3 - 10*I*tan(d*x + c)^2 + 5*tan(d*x + c))/(a^4*d)","B",0
151,1,154,0,1.993695," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(-\frac{12 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{4}} + \frac{24 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{4}} - \frac{12 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{4}} + \frac{22 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 78 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 46 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 78 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 21 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 22 i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{4}}\right)}}{3 \, d}"," ",0,"-2/3*(-12*I*log(tan(1/2*d*x + 1/2*c) + 1)/a^4 + 24*I*log(tan(1/2*d*x + 1/2*c) - I)/a^4 - 12*I*log(tan(1/2*d*x + 1/2*c) - 1)/a^4 + (22*I*tan(1/2*d*x + 1/2*c)^6 - 21*tan(1/2*d*x + 1/2*c)^5 - 78*I*tan(1/2*d*x + 1/2*c)^4 + 46*tan(1/2*d*x + 1/2*c)^3 + 78*I*tan(1/2*d*x + 1/2*c)^2 - 21*tan(1/2*d*x + 1/2*c) - 22*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^4))/d","A",0
152,1,145,0,1.778861," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{2 \, {\left(-\frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{4}} + \frac{4 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{4}} - \frac{2 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{4}} + \frac{2 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{4}} + \frac{-6 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 i}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{2}}\right)}}{d}"," ",0,"2*(-2*I*log(tan(1/2*d*x + 1/2*c) + 1)/a^4 + 4*I*log(tan(1/2*d*x + 1/2*c) - I)/a^4 - 2*I*log(tan(1/2*d*x + 1/2*c) - 1)/a^4 + (2*I*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) - 2*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^4) + (-6*I*tan(1/2*d*x + 1/2*c)^2 - 16*tan(1/2*d*x + 1/2*c) + 6*I)/(a^4*(tan(1/2*d*x + 1/2*c) - I)^2))/d","B",0
153,1,44,0,1.693654," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{4} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{4}}"," ",0,"-2*(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c))/(a^4*d*(tan(1/2*d*x + 1/2*c) - I)^4)","A",0
154,1,85,0,1.659109," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{3 \, a^{4} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{6}}"," ",0,"-2/3*(3*tan(1/2*d*x + 1/2*c)^5 - 6*I*tan(1/2*d*x + 1/2*c)^4 - 10*tan(1/2*d*x + 1/2*c)^3 + 6*I*tan(1/2*d*x + 1/2*c)^2 + 3*tan(1/2*d*x + 1/2*c))/(a^4*d*(tan(1/2*d*x + 1/2*c) - I)^6)","B",0
155,1,92,0,0.889857," ","integrate(1/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{-\frac{12 i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a^{4}} + \frac{12 i \, \log\left(-i \, \tan\left(d x + c\right) - 1\right)}{a^{4}} + \frac{-25 i \, \tan\left(d x + c\right)^{4} - 124 \, \tan\left(d x + c\right)^{3} + 246 i \, \tan\left(d x + c\right)^{2} + 252 \, \tan\left(d x + c\right) - 153 i}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(-12*I*log(-I*tan(d*x + c) + 1)/a^4 + 12*I*log(-I*tan(d*x + c) - 1)/a^4 + (-25*I*tan(d*x + c)^4 - 124*tan(d*x + c)^3 + 246*I*tan(d*x + c)^2 + 252*tan(d*x + c) - 153*I)/(a^4*(tan(d*x + c) - I)^4))/d","A",0
156,1,123,0,2.119582," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{-\frac{60 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{4}} + \frac{60 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{4}} + \frac{20 \, {\left(3 i \, \tan\left(d x + c\right) - 4\right)}}{a^{4} {\left(\tan\left(d x + c\right) + i\right)}} + \frac{-137 i \, \tan\left(d x + c\right)^{5} - 785 \, \tan\left(d x + c\right)^{4} + 1850 i \, \tan\left(d x + c\right)^{3} + 2290 \, \tan\left(d x + c\right)^{2} - 1565 i \, \tan\left(d x + c\right) - 541}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{5}}}{1280 \, d}"," ",0,"-1/1280*(-60*I*log(tan(d*x + c) + I)/a^4 + 60*I*log(tan(d*x + c) - I)/a^4 + 20*(3*I*tan(d*x + c) - 4)/(a^4*(tan(d*x + c) + I)) + (-137*I*tan(d*x + c)^5 - 785*tan(d*x + c)^4 + 1850*I*tan(d*x + c)^3 + 2290*tan(d*x + c)^2 - 1565*I*tan(d*x + c) - 541)/(a^4*(tan(d*x + c) - I)^5))/d","A",0
157,1,147,0,2.158825," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{-\frac{420 i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a^{4}} + \frac{420 i \, \log\left(-i \, \tan\left(d x + c\right) - 1\right)}{a^{4}} + \frac{30 \, {\left(21 i \, \tan\left(d x + c\right)^{2} - 49 \, \tan\left(d x + c\right) - 29 i\right)}}{a^{4} {\left(\tan\left(d x + c\right) + i\right)}^{2}} + \frac{-1029 i \, \tan\left(d x + c\right)^{6} - 6804 \, \tan\left(d x + c\right)^{5} + 19035 i \, \tan\left(d x + c\right)^{4} + 29080 \, \tan\left(d x + c\right)^{3} - 25995 i \, \tan\left(d x + c\right)^{2} - 13332 \, \tan\left(d x + c\right) + 3317 i}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{6}}}{7680 \, d}"," ",0,"-1/7680*(-420*I*log(-I*tan(d*x + c) + 1)/a^4 + 420*I*log(-I*tan(d*x + c) - 1)/a^4 + 30*(21*I*tan(d*x + c)^2 - 49*tan(d*x + c) - 29*I)/(a^4*(tan(d*x + c) + I)^2) + (-1029*I*tan(d*x + c)^6 - 6804*tan(d*x + c)^5 + 19035*I*tan(d*x + c)^4 + 29080*tan(d*x + c)^3 - 25995*I*tan(d*x + c)^2 - 13332*tan(d*x + c) + 3317*I)/(a^4*(tan(d*x + c) - I)^6))/d","A",0
158,1,151,0,2.114991," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{4}} - \frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{4}} - \frac{2 \, {\left(81 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 96 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 105 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 544 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 81 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 160 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4} a^{4}}}{24 \, d}"," ",0,"1/24*(105*log(tan(1/2*d*x + 1/2*c) + 1)/a^4 - 105*log(tan(1/2*d*x + 1/2*c) - 1)/a^4 - 2*(81*tan(1/2*d*x + 1/2*c)^7 - 96*I*tan(1/2*d*x + 1/2*c)^6 - 105*tan(1/2*d*x + 1/2*c)^5 + 480*I*tan(1/2*d*x + 1/2*c)^4 - 105*tan(1/2*d*x + 1/2*c)^3 - 544*I*tan(1/2*d*x + 1/2*c)^2 + 81*tan(1/2*d*x + 1/2*c) + 160*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*a^4))/d","A",0
159,1,113,0,2.022226," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{4}} - \frac{15 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{4}} - \frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{4}} - \frac{32}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}}}{2 \, d}"," ",0,"-1/2*(15*log(tan(1/2*d*x + 1/2*c) + 1)/a^4 - 15*log(tan(1/2*d*x + 1/2*c) - 1)/a^4 - 2*(tan(1/2*d*x + 1/2*c)^3 - 8*I*tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 8*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^4) - 32/(a^4*(tan(1/2*d*x + 1/2*c) - I)))/d","A",0
160,1,71,0,1.708236," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{4}} - \frac{3 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{4}} + \frac{8 \, {\left(3 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*log(tan(1/2*d*x + 1/2*c) + 1)/a^4 - 3*log(tan(1/2*d*x + 1/2*c) - 1)/a^4 + 8*(3*I*tan(1/2*d*x + 1/2*c) + 1)/(a^4*(tan(1/2*d*x + 1/2*c) - I)^3))/d","A",0
161,1,73,0,1.601794," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 15 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4\right)}}{15 \, a^{4} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{5}}"," ",0,"2/15*(15*tan(1/2*d*x + 1/2*c)^4 - 15*I*tan(1/2*d*x + 1/2*c)^3 - 25*tan(1/2*d*x + 1/2*c)^2 + 5*I*tan(1/2*d*x + 1/2*c) + 4)/(a^4*d*(tan(1/2*d*x + 1/2*c) - I)^5)","A",0
162,1,99,0,1.951958," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{2 \, {\left(35 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 105 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 210 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 147 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 49 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12\right)}}{35 \, a^{4} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{7}}"," ",0,"2/35*(35*tan(1/2*d*x + 1/2*c)^6 - 105*I*tan(1/2*d*x + 1/2*c)^5 - 210*tan(1/2*d*x + 1/2*c)^4 + 210*I*tan(1/2*d*x + 1/2*c)^3 + 147*tan(1/2*d*x + 1/2*c)^2 - 49*I*tan(1/2*d*x + 1/2*c) - 12)/(a^4*d*(tan(1/2*d*x + 1/2*c) - I)^7)","A",0
163,1,145,0,2.292709," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{63}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}} + \frac{1953 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 9450 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 25998 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 42210 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 46368 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 33054 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15858 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4374 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 703}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{9}}}{1008 \, d}"," ",0,"1/1008*(63/(a^4*(tan(1/2*d*x + 1/2*c) + I)) + (1953*tan(1/2*d*x + 1/2*c)^8 - 9450*I*tan(1/2*d*x + 1/2*c)^7 - 25998*tan(1/2*d*x + 1/2*c)^6 + 42210*I*tan(1/2*d*x + 1/2*c)^5 + 46368*tan(1/2*d*x + 1/2*c)^4 - 33054*I*tan(1/2*d*x + 1/2*c)^3 - 15858*tan(1/2*d*x + 1/2*c)^2 + 4374*I*tan(1/2*d*x + 1/2*c) + 703)/(a^4*(tan(1/2*d*x + 1/2*c) - I)^9))/d","A",0
164,1,197,0,2.517645," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{33 \, {\left(12 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 21 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 11\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{3}} + \frac{5940 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 39501 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 141075 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 313236 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 479556 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 516054 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 397914 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 214500 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 79024 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 17765 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2155}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{11}}}{3168 \, d}"," ",0,"1/3168*(33*(12*tan(1/2*d*x + 1/2*c)^2 + 21*I*tan(1/2*d*x + 1/2*c) - 11)/(a^4*(tan(1/2*d*x + 1/2*c) + I)^3) + (5940*tan(1/2*d*x + 1/2*c)^10 - 39501*I*tan(1/2*d*x + 1/2*c)^9 - 141075*tan(1/2*d*x + 1/2*c)^8 + 313236*I*tan(1/2*d*x + 1/2*c)^7 + 479556*tan(1/2*d*x + 1/2*c)^6 - 516054*I*tan(1/2*d*x + 1/2*c)^5 - 397914*tan(1/2*d*x + 1/2*c)^4 + 214500*I*tan(1/2*d*x + 1/2*c)^3 + 79024*tan(1/2*d*x + 1/2*c)^2 - 17765*I*tan(1/2*d*x + 1/2*c) - 2155)/(a^4*(tan(1/2*d*x + 1/2*c) - I)^11))/d","A",0
165,1,249,0,2.447731," ","integrate(cos(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{143 \, {\left(115 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 405 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 575 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 375 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 98\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{5}} + \frac{166595 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 1409265 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 6232655 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 17535375 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 34610004 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 49771722 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 53349582 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 42730974 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 25431835 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 10954229 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3278067 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 614627 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 60094}{a^{4} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{13}}}{91520 \, d}"," ",0,"1/91520*(143*(115*tan(1/2*d*x + 1/2*c)^4 + 405*I*tan(1/2*d*x + 1/2*c)^3 - 575*tan(1/2*d*x + 1/2*c)^2 - 375*I*tan(1/2*d*x + 1/2*c) + 98)/(a^4*(tan(1/2*d*x + 1/2*c) + I)^5) + (166595*tan(1/2*d*x + 1/2*c)^12 - 1409265*I*tan(1/2*d*x + 1/2*c)^11 - 6232655*tan(1/2*d*x + 1/2*c)^10 + 17535375*I*tan(1/2*d*x + 1/2*c)^9 + 34610004*tan(1/2*d*x + 1/2*c)^8 - 49771722*I*tan(1/2*d*x + 1/2*c)^7 - 53349582*tan(1/2*d*x + 1/2*c)^6 + 42730974*I*tan(1/2*d*x + 1/2*c)^5 + 25431835*tan(1/2*d*x + 1/2*c)^4 - 10954229*I*tan(1/2*d*x + 1/2*c)^3 - 3278067*tan(1/2*d*x + 1/2*c)^2 + 614627*I*tan(1/2*d*x + 1/2*c) + 60094)/(a^4*(tan(1/2*d*x + 1/2*c) - I)^13))/d","A",0
166,1,250,0,7.375746," ","integrate(sec(d*x+c)^14/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{480 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{8}} - \frac{960 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{8}} + \frac{480 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{8}} - \frac{5 \, {\left(-288 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 640 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 288 i\right)}}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{2}} + \frac{-1096 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 645 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 5840 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 2780 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 12120 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4286 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12120 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2780 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5840 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 645 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1096 i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5} a^{8}}\right)}}{5 \, d}"," ",0,"-2/5*(480*I*log(tan(1/2*d*x + 1/2*c) + 1)/a^8 - 960*I*log(tan(1/2*d*x + 1/2*c) - I)/a^8 + 480*I*log(tan(1/2*d*x + 1/2*c) - 1)/a^8 - 5*(-288*I*tan(1/2*d*x + 1/2*c)^2 - 640*tan(1/2*d*x + 1/2*c) + 288*I)/(a^8*(tan(1/2*d*x + 1/2*c) - I)^2) + (-1096*I*tan(1/2*d*x + 1/2*c)^10 + 645*tan(1/2*d*x + 1/2*c)^9 + 5840*I*tan(1/2*d*x + 1/2*c)^8 - 2780*tan(1/2*d*x + 1/2*c)^7 - 12120*I*tan(1/2*d*x + 1/2*c)^6 + 4286*tan(1/2*d*x + 1/2*c)^5 + 12120*I*tan(1/2*d*x + 1/2*c)^4 - 2780*tan(1/2*d*x + 1/2*c)^3 - 5840*I*tan(1/2*d*x + 1/2*c)^2 + 645*tan(1/2*d*x + 1/2*c) + 1096*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^5*a^8))/d","B",0
167,1,223,0,4.971559," ","integrate(sec(d*x+c)^12/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(-\frac{120 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{8}} + \frac{240 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{8}} - \frac{120 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{8}} + \frac{220 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 93 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 684 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 190 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 684 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 93 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 220 i}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} a^{8}} + \frac{-500 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2144 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3384 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2144 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 500 i}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{4}}\right)}}{3 \, d}"," ",0,"-2/3*(-120*I*log(tan(1/2*d*x + 1/2*c) + 1)/a^8 + 240*I*log(tan(1/2*d*x + 1/2*c) - I)/a^8 - 120*I*log(tan(1/2*d*x + 1/2*c) - 1)/a^8 + (220*I*tan(1/2*d*x + 1/2*c)^6 - 93*tan(1/2*d*x + 1/2*c)^5 - 684*I*tan(1/2*d*x + 1/2*c)^4 + 190*tan(1/2*d*x + 1/2*c)^3 + 684*I*tan(1/2*d*x + 1/2*c)^2 - 93*tan(1/2*d*x + 1/2*c) - 220*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*a^8) + (-500*I*tan(1/2*d*x + 1/2*c)^4 - 2144*tan(1/2*d*x + 1/2*c)^3 + 3384*I*tan(1/2*d*x + 1/2*c)^2 + 2144*tan(1/2*d*x + 1/2*c) - 500*I)/(a^8*(tan(1/2*d*x + 1/2*c) - I)^4))/d","A",0
168,1,198,0,3.984907," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{60 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{8}} - \frac{120 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}{a^{8}} + \frac{60 i \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{8}} - \frac{15 \, {\left(4 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} a^{8}} + \frac{294 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1884 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4890 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 6920 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4890 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1884 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 294 i}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{6}}\right)}}{15 \, d}"," ",0,"-2/15*(60*I*log(tan(1/2*d*x + 1/2*c) + 1)/a^8 - 120*I*log(tan(1/2*d*x + 1/2*c) - I)/a^8 + 60*I*log(tan(1/2*d*x + 1/2*c) - 1)/a^8 - 15*(4*I*tan(1/2*d*x + 1/2*c)^2 - tan(1/2*d*x + 1/2*c) - 4*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)*a^8) + (294*I*tan(1/2*d*x + 1/2*c)^6 + 1884*tan(1/2*d*x + 1/2*c)^5 - 4890*I*tan(1/2*d*x + 1/2*c)^4 - 6920*tan(1/2*d*x + 1/2*c)^3 + 4890*I*tan(1/2*d*x + 1/2*c)^2 + 1884*tan(1/2*d*x + 1/2*c) - 294*I)/(a^8*(tan(1/2*d*x + 1/2*c) - I)^6))/d","A",0
169,1,70,0,4.799891," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{8}}"," ",0,"-2*(tan(1/2*d*x + 1/2*c)^7 - 7*tan(1/2*d*x + 1/2*c)^5 + 7*tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c))/(a^8*d*(tan(1/2*d*x + 1/2*c) - I)^8)","A",0
170,1,137,0,5.212607," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 30 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 170 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 282 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 170 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 140 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 30 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{15 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{10}}"," ",0,"-2/15*(15*tan(1/2*d*x + 1/2*c)^9 - 30*I*tan(1/2*d*x + 1/2*c)^8 - 140*tan(1/2*d*x + 1/2*c)^7 + 170*I*tan(1/2*d*x + 1/2*c)^6 + 282*tan(1/2*d*x + 1/2*c)^5 - 170*I*tan(1/2*d*x + 1/2*c)^4 - 140*tan(1/2*d*x + 1/2*c)^3 + 30*I*tan(1/2*d*x + 1/2*c)^2 + 15*tan(1/2*d*x + 1/2*c))/(a^8*d*(tan(1/2*d*x + 1/2*c) - I)^10)","B",0
171,1,163,0,3.388489," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 60 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 235 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 822 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 904 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 822 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 480 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 235 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{15 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{12}}"," ",0,"-2/15*(15*tan(1/2*d*x + 1/2*c)^11 - 60*I*tan(1/2*d*x + 1/2*c)^10 - 235*tan(1/2*d*x + 1/2*c)^9 + 480*I*tan(1/2*d*x + 1/2*c)^8 + 822*tan(1/2*d*x + 1/2*c)^7 - 904*I*tan(1/2*d*x + 1/2*c)^6 - 822*tan(1/2*d*x + 1/2*c)^5 + 480*I*tan(1/2*d*x + 1/2*c)^4 + 235*tan(1/2*d*x + 1/2*c)^3 - 60*I*tan(1/2*d*x + 1/2*c)^2 - 15*tan(1/2*d*x + 1/2*c))/(a^8*d*(tan(1/2*d*x + 1/2*c) - I)^12)","B",0
172,1,189,0,3.575885," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{2 \, {\left(7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 42 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 182 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 490 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 1001 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 1484 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1716 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 1484 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 1001 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 490 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 182 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 42 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{7 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{14}}"," ",0,"-2/7*(7*tan(1/2*d*x + 1/2*c)^13 - 42*I*tan(1/2*d*x + 1/2*c)^12 - 182*tan(1/2*d*x + 1/2*c)^11 + 490*I*tan(1/2*d*x + 1/2*c)^10 + 1001*tan(1/2*d*x + 1/2*c)^9 - 1484*I*tan(1/2*d*x + 1/2*c)^8 - 1716*tan(1/2*d*x + 1/2*c)^7 + 1484*I*tan(1/2*d*x + 1/2*c)^6 + 1001*tan(1/2*d*x + 1/2*c)^5 - 490*I*tan(1/2*d*x + 1/2*c)^4 - 182*tan(1/2*d*x + 1/2*c)^3 + 42*I*tan(1/2*d*x + 1/2*c)^2 + 7*tan(1/2*d*x + 1/2*c))/(a^8*d*(tan(1/2*d*x + 1/2*c) - I)^14)","B",0
173,1,132,0,1.598824," ","integrate(1/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{-\frac{840 i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a^{8}} + \frac{840 i \, \log\left(-i \, \tan\left(d x + c\right) - 1\right)}{a^{8}} + \frac{-2283 i \, \tan\left(d x + c\right)^{8} - 19944 \, \tan\left(d x + c\right)^{7} + 77364 i \, \tan\left(d x + c\right)^{6} + 175448 \, \tan\left(d x + c\right)^{5} - 258370 i \, \tan\left(d x + c\right)^{4} - 261464 \, \tan\left(d x + c\right)^{3} + 192052 i \, \tan\left(d x + c\right)^{2} + 114152 \, \tan\left(d x + c\right) - 67819 i}{a^{8} {\left(\tan\left(d x + c\right) - i\right)}^{8}}}{430080 \, d}"," ",0,"-1/430080*(-840*I*log(-I*tan(d*x + c) + 1)/a^8 + 840*I*log(-I*tan(d*x + c) - 1)/a^8 + (-2283*I*tan(d*x + c)^8 - 19944*tan(d*x + c)^7 + 77364*I*tan(d*x + c)^6 + 175448*tan(d*x + c)^5 - 258370*I*tan(d*x + c)^4 - 261464*tan(d*x + c)^3 + 192052*I*tan(d*x + c)^2 + 114152*tan(d*x + c) - 67819*I)/(a^8*(tan(d*x + c) - I)^8))/d","A",0
174,1,163,0,5.751067," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{-\frac{2520 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{8}} + \frac{2520 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{8}} + \frac{504 \, {\left(5 i \, \tan\left(d x + c\right) - 6\right)}}{a^{8} {\left(\tan\left(d x + c\right) + i\right)}} + \frac{-7129 i \, \tan\left(d x + c\right)^{9} - 68697 \, \tan\left(d x + c\right)^{8} + 296964 i \, \tan\left(d x + c\right)^{7} + 758772 \, \tan\left(d x + c\right)^{6} - 1271214 i \, \tan\left(d x + c\right)^{5} - 1465758 \, \tan\left(d x + c\right)^{4} + 1191540 i \, \tan\left(d x + c\right)^{3} + 693828 \, \tan\left(d x + c\right)^{2} - 295425 i \, \tan\left(d x + c\right) - 89553}{a^{8} {\left(\tan\left(d x + c\right) - i\right)}^{9}}}{516096 \, d}"," ",0,"-1/516096*(-2520*I*log(tan(d*x + c) + I)/a^8 + 2520*I*log(tan(d*x + c) - I)/a^8 + 504*(5*I*tan(d*x + c) - 6)/(a^8*(tan(d*x + c) + I)) + (-7129*I*tan(d*x + c)^9 - 68697*tan(d*x + c)^8 + 296964*I*tan(d*x + c)^7 + 758772*tan(d*x + c)^6 - 1271214*I*tan(d*x + c)^5 - 1465758*tan(d*x + c)^4 + 1191540*I*tan(d*x + c)^3 + 693828*tan(d*x + c)^2 - 295425*I*tan(d*x + c) - 89553)/(a^8*(tan(d*x + c) - I)^9))/d","A",0
175,1,188,0,5.546038," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{-\frac{27720 i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a^{8}} + \frac{27720 i \, \log\left(-i \, \tan\left(d x + c\right) - 1\right)}{a^{8}} + \frac{420 \, {\left(99 i \, \tan\left(d x + c\right)^{2} - 220 \, \tan\left(d x + c\right) - 123 i\right)}}{a^{8} {\left(\tan\left(d x + c\right) + i\right)}^{2}} - \frac{81191 i \, \tan\left(d x + c\right)^{10} + 858110 \, \tan\left(d x + c\right)^{9} - 4107195 i \, \tan\left(d x + c\right)^{8} - 11748840 \, \tan\left(d x + c\right)^{7} + 22318590 i \, \tan\left(d x + c\right)^{6} + 29583540 \, \tan\left(d x + c\right)^{5} - 27983550 i \, \tan\left(d x + c\right)^{4} - 19002600 \, \tan\left(d x + c\right)^{3} + 9206235 i \, \tan\left(d x + c\right)^{2} + 3108990 \, \tan\left(d x + c\right) - 648327 i}{a^{8} {\left(\tan\left(d x + c\right) - i\right)}^{10}}}{3440640 \, d}"," ",0,"-1/3440640*(-27720*I*log(-I*tan(d*x + c) + 1)/a^8 + 27720*I*log(-I*tan(d*x + c) - 1)/a^8 + 420*(99*I*tan(d*x + c)^2 - 220*tan(d*x + c) - 123*I)/(a^8*(tan(d*x + c) + I)^2) - (81191*I*tan(d*x + c)^10 + 858110*tan(d*x + c)^9 - 4107195*I*tan(d*x + c)^8 - 11748840*tan(d*x + c)^7 + 22318590*I*tan(d*x + c)^6 + 29583540*tan(d*x + c)^5 - 27983550*I*tan(d*x + c)^4 - 19002600*tan(d*x + c)^3 + 9206235*I*tan(d*x + c)^2 + 3108990*tan(d*x + c) - 648327*I)/(a^8*(tan(d*x + c) - I)^10))/d","A",0
176,1,195,0,6.773640," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{3465 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{8}} - \frac{3465 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{8}} - \frac{1024 \, {\left(6 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 7\right)}}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}} - \frac{2 \, {\left(369 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1728 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 393 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 5568 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 393 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5696 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 369 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1856 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4} a^{8}}}{24 \, d}"," ",0,"1/24*(3465*log(tan(1/2*d*x + 1/2*c) + 1)/a^8 - 3465*log(tan(1/2*d*x + 1/2*c) - 1)/a^8 - 1024*(6*tan(1/2*d*x + 1/2*c)^2 - 15*I*tan(1/2*d*x + 1/2*c) - 7)/(a^8*(tan(1/2*d*x + 1/2*c) - I)^3) - 2*(369*tan(1/2*d*x + 1/2*c)^7 - 1728*I*tan(1/2*d*x + 1/2*c)^6 - 393*tan(1/2*d*x + 1/2*c)^5 + 5568*I*tan(1/2*d*x + 1/2*c)^4 - 393*tan(1/2*d*x + 1/2*c)^3 - 5696*I*tan(1/2*d*x + 1/2*c)^2 + 369*tan(1/2*d*x + 1/2*c) + 1856*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*a^8))/d","A",0
177,1,165,0,5.565977," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","-\frac{\frac{315 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{8}} - \frac{315 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{8}} - \frac{10 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 i\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} a^{8}} - \frac{4 \, {\left(160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 720 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1360 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 880 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 208\right)}}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{5}}}{10 \, d}"," ",0,"-1/10*(315*log(tan(1/2*d*x + 1/2*c) + 1)/a^8 - 315*log(tan(1/2*d*x + 1/2*c) - 1)/a^8 - 10*(tan(1/2*d*x + 1/2*c)^3 - 16*I*tan(1/2*d*x + 1/2*c)^2 + tan(1/2*d*x + 1/2*c) + 16*I)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*a^8) - 4*(160*tan(1/2*d*x + 1/2*c)^4 - 720*I*tan(1/2*d*x + 1/2*c)^3 - 1360*tan(1/2*d*x + 1/2*c)^2 + 880*I*tan(1/2*d*x + 1/2*c) + 208)/(a^8*(tan(1/2*d*x + 1/2*c) - I)^5))/d","A",0
178,1,123,0,4.737528," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{a^{8}} - \frac{105 \, \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right)}{a^{8}} - \frac{2 \, {\left(-840 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1400 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3920 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2352 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1064 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 152\right)}}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{7}}}{105 \, d}"," ",0,"1/105*(105*log(tan(1/2*d*x + 1/2*c) + 1)/a^8 - 105*log(tan(1/2*d*x + 1/2*c) - 1)/a^8 - 2*(-840*I*tan(1/2*d*x + 1/2*c)^5 - 1400*tan(1/2*d*x + 1/2*c)^4 + 3920*I*tan(1/2*d*x + 1/2*c)^3 + 2352*tan(1/2*d*x + 1/2*c)^2 - 1064*I*tan(1/2*d*x + 1/2*c) - 152)/(a^8*(tan(1/2*d*x + 1/2*c) - I)^7))/d","A",0
179,1,125,0,6.554410," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{2 \, {\left(63 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 63 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 483 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 315 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 693 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 189 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 225 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8\right)}}{63 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{9}}"," ",0,"2/63*(63*tan(1/2*d*x + 1/2*c)^8 - 63*I*tan(1/2*d*x + 1/2*c)^7 - 483*tan(1/2*d*x + 1/2*c)^6 + 315*I*tan(1/2*d*x + 1/2*c)^5 + 693*tan(1/2*d*x + 1/2*c)^4 - 189*I*tan(1/2*d*x + 1/2*c)^3 - 225*tan(1/2*d*x + 1/2*c)^2 + 9*I*tan(1/2*d*x + 1/2*c) + 8)/(a^8*d*(tan(1/2*d*x + 1/2*c) - I)^9)","B",0
180,1,151,0,4.866218," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{2 \, {\left(1155 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 3465 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 13860 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 23100 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 37422 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 32802 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27060 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 11220 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4895 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 517 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 152\right)}}{1155 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{11}}"," ",0,"2/1155*(1155*tan(1/2*d*x + 1/2*c)^10 - 3465*I*tan(1/2*d*x + 1/2*c)^9 - 13860*tan(1/2*d*x + 1/2*c)^8 + 23100*I*tan(1/2*d*x + 1/2*c)^7 + 37422*tan(1/2*d*x + 1/2*c)^6 - 32802*I*tan(1/2*d*x + 1/2*c)^5 - 27060*tan(1/2*d*x + 1/2*c)^4 + 11220*I*tan(1/2*d*x + 1/2*c)^3 + 4895*tan(1/2*d*x + 1/2*c)^2 - 517*I*tan(1/2*d*x + 1/2*c) - 152)/(a^8*d*(tan(1/2*d*x + 1/2*c) - I)^11)","A",0
181,1,177,0,3.947217," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{2 \, {\left(9009 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 45045 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 183183 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 435435 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 810810 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1051050 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 1076790 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 785070 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 451165 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 171457 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 51675 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 7111 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1240\right)}}{9009 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{13}}"," ",0,"2/9009*(9009*tan(1/2*d*x + 1/2*c)^12 - 45045*I*tan(1/2*d*x + 1/2*c)^11 - 183183*tan(1/2*d*x + 1/2*c)^10 + 435435*I*tan(1/2*d*x + 1/2*c)^9 + 810810*tan(1/2*d*x + 1/2*c)^8 - 1051050*I*tan(1/2*d*x + 1/2*c)^7 - 1076790*tan(1/2*d*x + 1/2*c)^6 + 785070*I*tan(1/2*d*x + 1/2*c)^5 + 451165*tan(1/2*d*x + 1/2*c)^4 - 171457*I*tan(1/2*d*x + 1/2*c)^3 - 51675*tan(1/2*d*x + 1/2*c)^2 + 7111*I*tan(1/2*d*x + 1/2*c) + 1240)/(a^8*d*(tan(1/2*d*x + 1/2*c) - I)^13)","A",0
182,1,203,0,3.576797," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{2 \, {\left(6435 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 45045 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 210210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 630630 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1414413 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 2357355 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 3063060 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 3063060 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 2407405 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 1444443 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 668850 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 222950 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 54915 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7845 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 952\right)}}{6435 \, a^{8} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{15}}"," ",0,"2/6435*(6435*tan(1/2*d*x + 1/2*c)^14 - 45045*I*tan(1/2*d*x + 1/2*c)^13 - 210210*tan(1/2*d*x + 1/2*c)^12 + 630630*I*tan(1/2*d*x + 1/2*c)^11 + 1414413*tan(1/2*d*x + 1/2*c)^10 - 2357355*I*tan(1/2*d*x + 1/2*c)^9 - 3063060*tan(1/2*d*x + 1/2*c)^8 + 3063060*I*tan(1/2*d*x + 1/2*c)^7 + 2407405*tan(1/2*d*x + 1/2*c)^6 - 1444443*I*tan(1/2*d*x + 1/2*c)^5 - 668850*tan(1/2*d*x + 1/2*c)^4 + 222950*I*tan(1/2*d*x + 1/2*c)^3 + 54915*tan(1/2*d*x + 1/2*c)^2 - 7845*I*tan(1/2*d*x + 1/2*c) - 952)/(a^8*d*(tan(1/2*d*x + 1/2*c) - I)^15)","A",0
183,1,249,0,5.561283," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{12155}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}} + \frac{6211205 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} - 55791450 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 303072770 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} + 1091397450 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2909561798 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 5901218466 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 9405145178 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 11877161010 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 12017308160 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 9710430158 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 6263238566 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3172666718 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 1247921210 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 365303990 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 77883902 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 10498214 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 982907}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{17}}}{3111680 \, d}"," ",0,"1/3111680*(12155/(a^8*(tan(1/2*d*x + 1/2*c) + I)) + (6211205*tan(1/2*d*x + 1/2*c)^16 - 55791450*I*tan(1/2*d*x + 1/2*c)^15 - 303072770*tan(1/2*d*x + 1/2*c)^14 + 1091397450*I*tan(1/2*d*x + 1/2*c)^13 + 2909561798*tan(1/2*d*x + 1/2*c)^12 - 5901218466*I*tan(1/2*d*x + 1/2*c)^11 - 9405145178*tan(1/2*d*x + 1/2*c)^10 + 11877161010*I*tan(1/2*d*x + 1/2*c)^9 + 12017308160*tan(1/2*d*x + 1/2*c)^8 - 9710430158*I*tan(1/2*d*x + 1/2*c)^7 - 6263238566*tan(1/2*d*x + 1/2*c)^6 + 3172666718*I*tan(1/2*d*x + 1/2*c)^5 + 1247921210*tan(1/2*d*x + 1/2*c)^4 - 365303990*I*tan(1/2*d*x + 1/2*c)^3 - 77883902*tan(1/2*d*x + 1/2*c)^2 + 10498214*I*tan(1/2*d*x + 1/2*c) + 982907)/(a^8*(tan(1/2*d*x + 1/2*c) - I)^17))/d","A",0
184,1,301,0,5.931441," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^8,x, algorithm=""giac"")","\frac{\frac{4199 \, {\left(18 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 33 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 17\right)}}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{3}} + \frac{12823746 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{18} - 140368371 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{17} - 879644311 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{16} + 3693272440 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 11467502592 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 27403194676 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 51919375300 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 79183835016 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 98304418212 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 99750226290 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 82860874122 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 56110430792 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 30766700912 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 13462452660 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4616712644 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 1197851960 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 226248618 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 27911475 i \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2143959}{a^{8} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{19}}}{6449664 \, d}"," ",0,"1/6449664*(4199*(18*tan(1/2*d*x + 1/2*c)^2 + 33*I*tan(1/2*d*x + 1/2*c) - 17)/(a^8*(tan(1/2*d*x + 1/2*c) + I)^3) + (12823746*tan(1/2*d*x + 1/2*c)^18 - 140368371*I*tan(1/2*d*x + 1/2*c)^17 - 879644311*tan(1/2*d*x + 1/2*c)^16 + 3693272440*I*tan(1/2*d*x + 1/2*c)^15 + 11467502592*tan(1/2*d*x + 1/2*c)^14 - 27403194676*I*tan(1/2*d*x + 1/2*c)^13 - 51919375300*tan(1/2*d*x + 1/2*c)^12 + 79183835016*I*tan(1/2*d*x + 1/2*c)^11 + 98304418212*tan(1/2*d*x + 1/2*c)^10 - 99750226290*I*tan(1/2*d*x + 1/2*c)^9 - 82860874122*tan(1/2*d*x + 1/2*c)^8 + 56110430792*I*tan(1/2*d*x + 1/2*c)^7 + 30766700912*tan(1/2*d*x + 1/2*c)^6 - 13462452660*I*tan(1/2*d*x + 1/2*c)^5 - 4616712644*tan(1/2*d*x + 1/2*c)^4 + 1197851960*I*tan(1/2*d*x + 1/2*c)^3 + 226248618*tan(1/2*d*x + 1/2*c)^2 - 27911475*I*tan(1/2*d*x + 1/2*c) - 2143959)/(a^8*(tan(1/2*d*x + 1/2*c) - I)^19))/d","A",0
185,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(7/2)*(I*a*tan(d*x + c) + a), x)","F",0
186,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/2)*(I*a*tan(d*x + c) + a), x)","F",0
187,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a), x)","F",0
188,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a), x)","F",0
189,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\sqrt{e \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/sqrt(e*sec(d*x + c)), x)","F",0
190,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*sec(d*x + c))^(3/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*sec(d*x + c))^(5/2), x)","F",0
192,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*sec(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*sec(d*x + c))^(7/2), x)","F",0
193,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a)^2, x)","F",0
194,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a)^2, x)","F",0
195,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\sqrt{e \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/sqrt(e*sec(d*x + c)), x)","F",0
196,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(3/2), x)","F",0
197,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(5/2), x)","F",0
198,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(7/2), x)","F",0
199,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(9/2), x)","F",0
200,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/(e*sec(d*x+c))^(11/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\left(e \sec\left(d x + c\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/(e*sec(d*x + c))^(11/2), x)","F",0
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249,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(7/2)/(I*a*tan(d*x + c) + a)^3, x)","F",0
250,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/2)/(I*a*tan(d*x + c) + a)^3, x)","F",0
251,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)/(I*a*tan(d*x + c) + a)^3, x)","F",0
252,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{e \sec\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))/(I*a*tan(d*x + c) + a)^3, x)","F",0
253,0,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a)^3), x)","F",0
254,0,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a)^3), x)","F",0
255,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(15/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{15}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(15/2)/(I*a*tan(d*x + c) + a)^4, x)","F",0
256,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(13/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{13}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(13/2)/(I*a*tan(d*x + c) + a)^4, x)","F",0
257,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{11}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(11/2)/(I*a*tan(d*x + c) + a)^4, x)","F",0
258,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(9/2)/(I*a*tan(d*x + c) + a)^4, x)","F",0
259,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(7/2)/(I*a*tan(d*x + c) + a)^4, x)","F",0
260,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/2)/(I*a*tan(d*x + c) + a)^4, x)","F",0
261,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)/(I*a*tan(d*x + c) + a)^4, x)","F",0
262,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\int \frac{\sqrt{e \sec\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))/(I*a*tan(d*x + c) + a)^4, x)","F",0
263,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)*(I*a*tan(f*x + e) + a), x)","F",0
264,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)*(I*a*tan(f*x + e) + a), x)","F",0
265,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)/(d*sec(f*x + e))^(1/3), x)","F",0
266,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)/(d*sec(f*x + e))^(5/3), x)","F",0
267,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)*(I*a*tan(f*x + e) + a)^2, x)","F",0
268,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)*(I*a*tan(f*x + e) + a)^2, x)","F",0
269,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(1/3), x)","F",0
270,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(5/3), x)","F",0
271,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)/(I*a*tan(f*x + e) + a), x)","F",0
272,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)/(I*a*tan(f*x + e) + a), x)","F",0
273,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(1/3)*(I*a*tan(f*x + e) + a)), x)","F",0
274,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/3)*(I*a*tan(f*x + e) + a)), x)","F",0
275,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)/(I*a*tan(f*x + e) + a)^2, x)","F",0
276,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)/(I*a*tan(f*x + e) + a)^2, x)","F",0
277,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(1/3)*(I*a*tan(f*x + e) + a)^2), x)","F",0
278,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/3)*(I*a*tan(f*x + e) + a)^2), x)","F",0
279,0,0,0,0.000000," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sec\left(d x + c\right)^{8}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sec(d*x + c)^8, x)","F",0
280,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sec(d*x + c)^6, x)","F",0
281,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sec(d*x + c)^4, x)","F",0
282,1,55,0,2.137940," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 i \, \left(\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}\right)^{\frac{3}{2}}}{3 \, a d}"," ",0,"-2/3*I*((a*tan(1/2*d*x + 1/2*c)^2 - 2*I*a*tan(1/2*d*x + 1/2*c) - a)/(tan(1/2*d*x + 1/2*c)^2 - 1))^(3/2)/(a*d)","B",0
283,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cos(d*x + c)^2, x)","F",0
284,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cos(d*x + c)^4, x)","F",0
285,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cos(d*x + c)^6, x)","F",0
286,0,0,0,0.000000," ","integrate(sec(d*x+c)^7*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sec\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sec(d*x + c)^7, x)","F",0
287,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sec(d*x + c)^5, x)","F",0
288,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sec(d*x + c)^3, x)","F",0
289,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sec(d*x + c), x)","F",0
290,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cos(d*x + c), x)","F",0
291,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cos(d*x + c)^3, x)","F",0
292,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cos(d*x + c)^5, x)","F",0
293,0,0,0,0.000000," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{8}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sec(d*x + c)^8, x)","F",0
294,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sec(d*x + c)^6, x)","F",0
295,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sec(d*x + c)^4, x)","F",0
296,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sec(d*x + c)^2, x)","F",0
297,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cos(d*x + c)^2, x)","F",0
298,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cos(d*x + c)^4, x)","F",0
299,-1,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sec(d*x + c)^5, x)","F",0
301,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sec(d*x + c)^3, x)","F",0
302,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sec(d*x + c), x)","F",0
303,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cos(d*x + c), x)","F",0
304,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cos(d*x + c)^3, x)","F",0
305,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cos(d*x + c)^5, x)","F",0
306,0,0,0,0.000000," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{8}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*sec(d*x + c)^8, x)","F",0
307,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*sec(d*x + c)^6, x)","F",0
308,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*sec(d*x + c)^4, x)","F",0
309,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*sec(d*x + c)^2, x)","F",0
310,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,-1,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*sec(d*x + c)^3, x)","F",0
314,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*sec(d*x + c), x)","F",0
315,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cos(d*x + c), x)","F",0
316,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cos(d*x + c)^3, x)","F",0
317,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cos(d*x + c)^5, x)","F",0
318,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cos(d*x + c)^7, x)","F",0
319,0,0,0,0.000000," ","integrate(sec(d*x+c)^8*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{8}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*sec(d*x + c)^8, x)","F",0
320,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*sec(d*x + c)^6, x)","F",0
321,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*sec(d*x + c)^4, x)","F",0
322,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*sec(d*x + c)^2, x)","F",0
323,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*sec(d*x + c), x)","F",0
327,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*cos(d*x + c), x)","F",0
328,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*cos(d*x + c)^3, x)","F",0
329,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*cos(d*x + c)^5, x)","F",0
330,-1,0,0,0.000000," ","integrate(cos(d*x+c)^7*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,-1,0,0,0.000000," ","integrate(cos(d*x+c)^9*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(cos(d*x+c)^11*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,0,0,0,0.000000," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{8}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^8/sqrt(I*a*tan(d*x + c) + a), x)","F",0
334,0,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{6}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^6/sqrt(I*a*tan(d*x + c) + a), x)","F",0
335,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/sqrt(I*a*tan(d*x + c) + a), x)","F",0
336,1,55,0,1.997576," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 i \, \sqrt{\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}}{a d}"," ",0,"-2*I*sqrt((a*tan(1/2*d*x + 1/2*c)^2 - 2*I*a*tan(1/2*d*x + 1/2*c) - a)/(tan(1/2*d*x + 1/2*c)^2 - 1))/(a*d)","B",0
337,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/sqrt(I*a*tan(d*x + c) + a), x)","F",0
338,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/sqrt(I*a*tan(d*x + c) + a), x)","F",0
339,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{6}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/sqrt(I*a*tan(d*x + c) + a), x)","F",0
340,0,0,0,0.000000," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{9}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^9/sqrt(I*a*tan(d*x + c) + a), x)","F",0
341,0,0,0,0.000000," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{7}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^7/sqrt(I*a*tan(d*x + c) + a), x)","F",0
342,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/sqrt(I*a*tan(d*x + c) + a), x)","F",0
343,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/sqrt(I*a*tan(d*x + c) + a), x)","F",0
344,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sec(d*x + c)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
345,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
346,0,0,0,0.000000," ","integrate(cos(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{3}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3/sqrt(I*a*tan(d*x + c) + a), x)","F",0
347,0,0,0,0.000000," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{8}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^8/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
348,0,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{6}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^6/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
349,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
350,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
351,0,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
352,0,0,0,0.000000," ","integrate(cos(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
353,0,0,0,0.000000," ","integrate(cos(d*x+c)^6/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(d x + c\right)^{6}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^6/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
354,0,0,0,0.000000," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{11}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^11/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
355,0,0,0,0.000000," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{9}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^9/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
356,0,0,0,0.000000," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{7}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^7/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
357,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
358,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
359,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
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363,0,0,0,0.000000," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{8}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^8/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
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365,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
366,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^2/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
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369,0,0,0,0.000000," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{13}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^13/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
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371,0,0,0,0.000000," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{9}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^9/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
372,0,0,0,0.000000," ","integrate(sec(d*x+c)^7/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{7}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^7/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
373,0,0,0,0.000000," ","integrate(sec(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{5}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^5/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
374,0,0,0,0.000000," ","integrate(sec(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{3}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^3/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
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378,0,0,0,0.000000," ","integrate(sec(d*x+c)^10/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{10}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^10/(I*a*tan(d*x + c) + a)^(7/2), x)","F",0
379,0,0,0,0.000000," ","integrate(sec(d*x+c)^8/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{8}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^8/(I*a*tan(d*x + c) + a)^(7/2), x)","F",0
380,0,0,0,0.000000," ","integrate(sec(d*x+c)^6/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{6}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^6/(I*a*tan(d*x + c) + a)^(7/2), x)","F",0
381,0,0,0,0.000000," ","integrate(sec(d*x+c)^4/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^4/(I*a*tan(d*x + c) + a)^(7/2), x)","F",0
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385,0,0,0,0.000000," ","integrate(sec(d*x+c)^13/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{13}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^13/(I*a*tan(d*x + c) + a)^(7/2), x)","F",0
386,0,0,0,0.000000," ","integrate(sec(d*x+c)^11/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{11}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^11/(I*a*tan(d*x + c) + a)^(7/2), x)","F",0
387,0,0,0,0.000000," ","integrate(sec(d*x+c)^9/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{\sec\left(d x + c\right)^{9}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sec(d*x + c)^9/(I*a*tan(d*x + c) + a)^(7/2), x)","F",0
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394,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} \sqrt{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*sqrt(I*a*tan(d*x + c) + a), x)","F",0
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422,0,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}} \sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*sec(d*x + c))^(7/2)*sqrt(I*a*tan(d*x + c) + a)), x)","F",0
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426,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{e \sec\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
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430,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{9}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(9/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
431,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(7/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
432,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
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437,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(7/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{7}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(7/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
438,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
439,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{2}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(2/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
440,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{\frac{1}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(1/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
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442,0,0,0,0.000000," ","integrate(1/(e*sec(d*x+c))^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \sec\left(d x + c\right)\right)^{\frac{4}{3}} \sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*sec(d*x + c))^(4/3)*sqrt(I*a*tan(d*x + c) + a)), x)","F",0
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446,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(2/3),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2/3)*(I*a*tan(f*x + e) + a)^(2/3), x)","F",0
447,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(5/3),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2/3)*(I*a*tan(f*x + e) + a)^(5/3), x)","F",0
448,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(8/3),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{8}{3}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2/3)*(I*a*tan(f*x + e) + a)^(8/3), x)","F",0
449,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2/3)*(a+I*a*tan(f*x+e))^(11/3),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{2}{3}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{11}{3}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2/3)*(I*a*tan(f*x + e) + a)^(11/3), x)","F",0
450,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^5,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{5} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^5*(e*sec(d*x + c))^m, x)","F",0
451,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3*(e*sec(d*x + c))^m, x)","F",0
452,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2*(e*sec(d*x + c))^m, x)","F",0
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455,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m/(I*a*tan(d*x + c) + a)^2, x)","F",0
456,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m/(I*a*tan(d*x + c) + a)^3, x)","F",0
457,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(7/2)*(e*sec(d*x + c))^m, x)","F",0
458,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*(e*sec(d*x + c))^m, x)","F",0
459,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*(e*sec(d*x + c))^m, x)","F",0
460,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \left(e \sec\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*(e*sec(d*x + c))^m, x)","F",0
461,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{m}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m/sqrt(I*a*tan(d*x + c) + a), x)","F",0
462,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
463,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\left(e \sec\left(d x + c\right)\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
464,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{m} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^m*(I*a*tan(d*x + c) + a)^n, x)","F",0
465,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^6, x)","F",0
466,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^4, x)","F",0
467,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^2, x)","F",0
468,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^2, x)","F",0
469,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^4, x)","F",0
470,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^6, x)","F",0
471,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^5, x)","F",0
472,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c)^3, x)","F",0
473,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sec(d*x + c), x)","F",0
474,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c), x)","F",0
475,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^3, x)","F",0
476,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cos(d*x + c)^5, x)","F",0
477,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(5/2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
478,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
479,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \sqrt{e \sec\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(e*sec(d*x + c))*(I*a*tan(d*x + c) + a)^n, x)","F",0
480,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\sqrt{e \sec\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/sqrt(e*sec(d*x + c)), x)","F",0
481,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\left(e \sec\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/(e*sec(d*x + c))^(3/2), x)","F",0
482,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/(e*sec(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\left(e \sec\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/(e*sec(d*x + c))^(5/2), x)","F",0
483,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-4-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-n - 4} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-n - 4)*(I*a*tan(d*x + c) + a)^n, x)","F",0
484,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-3-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-n - 3} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-n - 3)*(I*a*tan(d*x + c) + a)^n, x)","F",0
485,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-2-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-n - 2} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-n - 2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
486,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-1-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-n - 1} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-n - 1)*(I*a*tan(d*x + c) + a)^n, x)","F",0
487,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^n),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\left(e \sec\left(d x + c\right)\right)^{n}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/(e*sec(d*x + c))^n, x)","F",0
488,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-n + 1} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-n + 1)*(I*a*tan(d*x + c) + a)^n, x)","F",0
489,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-n + 2} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-n + 2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
490,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3-n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-n + 3} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-n + 3)*(I*a*tan(d*x + c) + a)^n, x)","F",0
491,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(6-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 6} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 6)*(I*a*tan(d*x + c) + a)^n, x)","F",0
492,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(5-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 5} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 5)*(I*a*tan(d*x + c) + a)^n, x)","F",0
493,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(4-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 4} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 4)*(I*a*tan(d*x + c) + a)^n, x)","F",0
494,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(3-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 3} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 3)*(I*a*tan(d*x + c) + a)^n, x)","F",0
495,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(2-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 2} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
496,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(1-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n + 1} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n + 1)*(I*a*tan(d*x + c) + a)^n, x)","F",0
497,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/((e*sec(d*x+c))^(2*n)),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\left(e \sec\left(d x + c\right)\right)^{2 \, n}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/(e*sec(d*x + c))^(2*n), x)","F",0
498,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-1-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n - 1} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n - 1)*(I*a*tan(d*x + c) + a)^n, x)","F",0
499,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-2-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n - 2} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n - 2)*(I*a*tan(d*x + c) + a)^n, x)","F",0
500,0,0,0,0.000000," ","integrate((e*sec(d*x+c))^(-3-2*n)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \sec\left(d x + c\right)\right)^{-2 \, n - 3} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*sec(d*x + c))^(-2*n - 3)*(I*a*tan(d*x + c) + a)^n, x)","F",0
501,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-2-n),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{2 \, n} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{-n - 2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2*n)*(I*a*tan(f*x + e) + a)^(-n - 2), x)","F",0
502,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(-1-n),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{2 \, n} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{-n - 1}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2*n)*(I*a*tan(f*x + e) + a)^(-n - 1), x)","F",0
503,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)/((a+I*a*tan(f*x+e))^n),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{2 \, n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{n}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2*n)/(I*a*tan(f*x + e) + a)^n, x)","F",0
504,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(1-n),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{2 \, n} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{-n + 1}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2*n)*(I*a*tan(f*x + e) + a)^(-n + 1), x)","F",0
505,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(2-n),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{2 \, n} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{-n + 2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2*n)*(I*a*tan(f*x + e) + a)^(-n + 2), x)","F",0
506,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(2*n)*(a+I*a*tan(f*x+e))^(3-n),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{2 \, n} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{-n + 3}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(2*n)*(I*a*tan(f*x + e) + a)^(-n + 3), x)","F",0
507,1,70,0,0.324132," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{5 \, b \tan\left(d x + c\right)^{6} + 6 \, a \tan\left(d x + c\right)^{5} + 15 \, b \tan\left(d x + c\right)^{4} + 20 \, a \tan\left(d x + c\right)^{3} + 15 \, b \tan\left(d x + c\right)^{2} + 30 \, a \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(5*b*tan(d*x + c)^6 + 6*a*tan(d*x + c)^5 + 15*b*tan(d*x + c)^4 + 20*a*tan(d*x + c)^3 + 15*b*tan(d*x + c)^2 + 30*a*tan(d*x + c))/d","A",0
508,1,141,0,0.886628," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{15 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 40 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 80 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 10 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 25 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{40 \, d}"," ",0,"1/40*(15*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(25*a*tan(1/2*d*x + 1/2*c)^9 - 40*b*tan(1/2*d*x + 1/2*c)^8 - 10*a*tan(1/2*d*x + 1/2*c)^7 - 80*b*tan(1/2*d*x + 1/2*c)^4 + 10*a*tan(1/2*d*x + 1/2*c)^3 - 25*a*tan(1/2*d*x + 1/2*c) - 8*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
509,1,48,0,0.601917," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{3 \, b \tan\left(d x + c\right)^{4} + 4 \, a \tan\left(d x + c\right)^{3} + 6 \, b \tan\left(d x + c\right)^{2} + 12 \, a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*b*tan(d*x + c)^4 + 4*a*tan(d*x + c)^3 + 6*b*tan(d*x + c)^2 + 12*a*tan(d*x + c))/d","A",0
510,1,99,0,0.576190," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(3*a*tan(1/2*d*x + 1/2*c)^5 - 6*b*tan(1/2*d*x + 1/2*c)^4 - 3*a*tan(1/2*d*x + 1/2*c) - 2*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
511,1,25,0,0.282319," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{b \tan\left(d x + c\right)^{2} + 2 \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b*tan(d*x + c)^2 + 2*a*tan(d*x + c))/d","A",0
512,1,54,0,0.293393," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) - \frac{2 \, b}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"(a*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - a*log(abs(tan(1/2*d*x + 1/2*c) - 1)) - 2*b/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
513,1,129,0,0.211627," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - b \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - b \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, d x\right) - 2 \, a \tan\left(\frac{1}{2} \, c\right) + b}{d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} + d}"," ",0,"-(b*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*tan(1/2*d*x)^2*tan(1/2*c) + 2*a*tan(1/2*d*x)*tan(1/2*c)^2 - b*tan(1/2*d*x)^2 - 4*b*tan(1/2*d*x)*tan(1/2*c) - b*tan(1/2*c)^2 - 2*a*tan(1/2*d*x) - 2*a*tan(1/2*c) + b)/(d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(1/2*d*x)^2 + d*tan(1/2*c)^2 + d)","B",0
514,1,146,0,1.718364," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{2 \, a d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a d x \tan\left(d x\right)^{2} + 2 \, a d x \tan\left(c\right)^{2} - b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, a \tan\left(d x\right)^{2} \tan\left(c\right) - 2 \, a \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, a d x + b \tan\left(d x\right)^{2} + 4 \, b \tan\left(d x\right) \tan\left(c\right) + b \tan\left(c\right)^{2} + 2 \, a \tan\left(d x\right) + 2 \, a \tan\left(c\right) - b}{4 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"1/4*(2*a*d*x*tan(d*x)^2*tan(c)^2 + 2*a*d*x*tan(d*x)^2 + 2*a*d*x*tan(c)^2 - b*tan(d*x)^2*tan(c)^2 - 2*a*tan(d*x)^2*tan(c) - 2*a*tan(d*x)*tan(c)^2 + 2*a*d*x + b*tan(d*x)^2 + 4*b*tan(d*x)*tan(c) + b*tan(c)^2 + 2*a*tan(d*x) + 2*a*tan(c) - b)/(d*tan(d*x)^2*tan(c)^2 + d*tan(d*x)^2 + d*tan(c)^2 + d)","B",0
515,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)(-192*a*tan(c/2)^6*tan(d*x/2)^5-128*a*tan(c/2)^6*tan(d*x/2)^3-192*a*tan(c/2)^6*tan(d*x/2)-192*a*tan(c/2)^5*tan(d*x/2)^6+576*a*tan(c/2)^5*tan(d*x/2)^4-576*a*tan(c/2)^5*tan(d*x/2)^2+192*a*tan(c/2)^5+576*a*tan(c/2)^4*tan(d*x/2)^5-2688*a*tan(c/2)^4*tan(d*x/2)^3+576*a*tan(c/2)^4*tan(d*x/2)-128*a*tan(c/2)^3*tan(d*x/2)^6-2688*a*tan(c/2)^3*tan(d*x/2)^4+2688*a*tan(c/2)^3*tan(d*x/2)^2+128*a*tan(c/2)^3-576*a*tan(c/2)^2*tan(d*x/2)^5+2688*a*tan(c/2)^2*tan(d*x/2)^3-576*a*tan(c/2)^2*tan(d*x/2)-192*a*tan(c/2)*tan(d*x/2)^6+576*a*tan(c/2)*tan(d*x/2)^4-576*a*tan(c/2)*tan(d*x/2)^2+192*a*tan(c/2)+192*a*tan(d*x/2)^5+128*a*tan(d*x/2)^3+192*a*tan(d*x/2)+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)-3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^6-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^4-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^2-3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^6-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^6-27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^4-27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^2-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^4-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^6-27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^4-27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^2-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(c/2)^2-3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(d*x/2)^6-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(d*x/2)^4-9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*tan(d*x/2)^2-3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^6*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^4*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^6+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^4+27*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^2*tan(d*x/2)^2+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(c/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(d*x/2)^6+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(d*x/2)^4+9*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*tan(d*x/2)^2+3*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)-6*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^6-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^4-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^2-6*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^6-54*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^4-54*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^2-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^6-54*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^4-54*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^2-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2-6*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^6-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^4-18*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^2-6*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)+6*b*pi*tan(c/2)^6*tan(d*x/2)^6+18*b*pi*tan(c/2)^6*tan(d*x/2)^4+18*b*pi*tan(c/2)^6*tan(d*x/2)^2+6*b*pi*tan(c/2)^6+18*b*pi*tan(c/2)^4*tan(d*x/2)^6+54*b*pi*tan(c/2)^4*tan(d*x/2)^4+54*b*pi*tan(c/2)^4*tan(d*x/2)^2+18*b*pi*tan(c/2)^4+18*b*pi*tan(c/2)^2*tan(d*x/2)^6+54*b*pi*tan(c/2)^2*tan(d*x/2)^4+54*b*pi*tan(c/2)^2*tan(d*x/2)^2+18*b*pi*tan(c/2)^2+6*b*pi*tan(d*x/2)^6+18*b*pi*tan(d*x/2)^4+18*b*pi*tan(d*x/2)^2+6*b*pi+6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^6+54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4+54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^2+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^6+54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^4+54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^2+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))-6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^6-54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^4-54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^2-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^6-54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^4-54*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^2-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))-6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^6-54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^4-54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^2-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^6-54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^4-54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^2-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^6-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^4-18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^2-6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))+6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^6+54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4+54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^2+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^6+54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^4+54*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^2+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^6+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^4+18*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^2+6*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))-32*b*tan(c/2)^6*tan(d*x/2)^6+96*b*tan(c/2)^6*tan(d*x/2)^4-96*b*tan(c/2)^6*tan(d*x/2)^2+32*b*tan(c/2)^6+384*b*tan(c/2)^5*tan(d*x/2)^5-768*b*tan(c/2)^5*tan(d*x/2)^3+384*b*tan(c/2)^5*tan(d*x/2)+96*b*tan(c/2)^4*tan(d*x/2)^6-1824*b*tan(c/2)^4*tan(d*x/2)^4+1824*b*tan(c/2)^4*tan(d*x/2)^2-96*b*tan(c/2)^4-768*b*tan(c/2)^3*tan(d*x/2)^5+3584*b*tan(c/2)^3*tan(d*x/2)^3-768*b*tan(c/2)^3*tan(d*x/2)-96*b*tan(c/2)^2*tan(d*x/2)^6+1824*b*tan(c/2)^2*tan(d*x/2)^4-1824*b*tan(c/2)^2*tan(d*x/2)^2+96*b*tan(c/2)^2+384*b*tan(c/2)*tan(d*x/2)^5-768*b*tan(c/2)*tan(d*x/2)^3+384*b*tan(c/2)*tan(d*x/2)+32*b*tan(d*x/2)^6-96*b*tan(d*x/2)^4+96*b*tan(d*x/2)^2-32*b)/(96*d*tan(c/2)^6*tan(d*x/2)^6+288*d*tan(c/2)^6*tan(d*x/2)^4+288*d*tan(c/2)^6*tan(d*x/2)^2+96*d*tan(c/2)^6+288*d*tan(c/2)^4*tan(d*x/2)^6+864*d*tan(c/2)^4*tan(d*x/2)^4+864*d*tan(c/2)^4*tan(d*x/2)^2+288*d*tan(c/2)^4+288*d*tan(c/2)^2*tan(d*x/2)^6+864*d*tan(c/2)^2*tan(d*x/2)^4+864*d*tan(c/2)^2*tan(d*x/2)^2+288*d*tan(c/2)^2+96*d*tan(d*x/2)^6+288*d*tan(d*x/2)^4+288*d*tan(d*x/2)^2+96*d)","F(-2)",0
516,1,426,0,0.515997," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{12 \, a d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 24 \, a d x \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 24 \, a d x \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 5 \, b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 20 \, a \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 20 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 12 \, a d x \tan\left(d x\right)^{4} + 48 \, a d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 32 \, b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 12 \, a d x \tan\left(c\right)^{4} + 6 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 12 \, a \tan\left(d x\right)^{4} \tan\left(c\right) + 24 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 24 \, a \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 12 \, a \tan\left(d x\right) \tan\left(c\right)^{4} + 24 \, a d x \tan\left(d x\right)^{2} + 3 \, b \tan\left(d x\right)^{4} + 24 \, a d x \tan\left(c\right)^{2} - 36 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, b \tan\left(c\right)^{4} + 12 \, a \tan\left(d x\right)^{3} - 24 \, a \tan\left(d x\right)^{2} \tan\left(c\right) - 24 \, a \tan\left(d x\right) \tan\left(c\right)^{2} + 12 \, a \tan\left(c\right)^{3} + 12 \, a d x + 6 \, b \tan\left(d x\right)^{2} + 32 \, b \tan\left(d x\right) \tan\left(c\right) + 6 \, b \tan\left(c\right)^{2} + 20 \, a \tan\left(d x\right) + 20 \, a \tan\left(c\right) - 5 \, b}{32 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 2 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 2 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + d \tan\left(d x\right)^{4} + 4 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(c\right)^{4} + 2 \, d \tan\left(d x\right)^{2} + 2 \, d \tan\left(c\right)^{2} + d\right)}}"," ",0,"1/32*(12*a*d*x*tan(d*x)^4*tan(c)^4 + 24*a*d*x*tan(d*x)^4*tan(c)^2 + 24*a*d*x*tan(d*x)^2*tan(c)^4 - 5*b*tan(d*x)^4*tan(c)^4 - 20*a*tan(d*x)^4*tan(c)^3 - 20*a*tan(d*x)^3*tan(c)^4 + 12*a*d*x*tan(d*x)^4 + 48*a*d*x*tan(d*x)^2*tan(c)^2 + 6*b*tan(d*x)^4*tan(c)^2 + 32*b*tan(d*x)^3*tan(c)^3 + 12*a*d*x*tan(c)^4 + 6*b*tan(d*x)^2*tan(c)^4 - 12*a*tan(d*x)^4*tan(c) + 24*a*tan(d*x)^3*tan(c)^2 + 24*a*tan(d*x)^2*tan(c)^3 - 12*a*tan(d*x)*tan(c)^4 + 24*a*d*x*tan(d*x)^2 + 3*b*tan(d*x)^4 + 24*a*d*x*tan(c)^2 - 36*b*tan(d*x)^2*tan(c)^2 + 3*b*tan(c)^4 + 12*a*tan(d*x)^3 - 24*a*tan(d*x)^2*tan(c) - 24*a*tan(d*x)*tan(c)^2 + 12*a*tan(c)^3 + 12*a*d*x + 6*b*tan(d*x)^2 + 32*b*tan(d*x)*tan(c) + 6*b*tan(c)^2 + 20*a*tan(d*x) + 20*a*tan(c) - 5*b)/(d*tan(d*x)^4*tan(c)^4 + 2*d*tan(d*x)^4*tan(c)^2 + 2*d*tan(d*x)^2*tan(c)^4 + d*tan(d*x)^4 + 4*d*tan(d*x)^2*tan(c)^2 + d*tan(c)^4 + 2*d*tan(d*x)^2 + 2*d*tan(c)^2 + d)","B",0
517,1,156,0,0.816376," ","integrate(sec(d*x+c)^8*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{140 \, b^{2} \tan\left(d x + c\right)^{9} + 315 \, a b \tan\left(d x + c\right)^{8} + 180 \, a^{2} \tan\left(d x + c\right)^{7} + 540 \, b^{2} \tan\left(d x + c\right)^{7} + 1260 \, a b \tan\left(d x + c\right)^{6} + 756 \, a^{2} \tan\left(d x + c\right)^{5} + 756 \, b^{2} \tan\left(d x + c\right)^{5} + 1890 \, a b \tan\left(d x + c\right)^{4} + 1260 \, a^{2} \tan\left(d x + c\right)^{3} + 420 \, b^{2} \tan\left(d x + c\right)^{3} + 1260 \, a b \tan\left(d x + c\right)^{2} + 1260 \, a^{2} \tan\left(d x + c\right)}{1260 \, d}"," ",0,"1/1260*(140*b^2*tan(d*x + c)^9 + 315*a*b*tan(d*x + c)^8 + 180*a^2*tan(d*x + c)^7 + 540*b^2*tan(d*x + c)^7 + 1260*a*b*tan(d*x + c)^6 + 756*a^2*tan(d*x + c)^5 + 756*b^2*tan(d*x + c)^5 + 1890*a*b*tan(d*x + c)^4 + 1260*a^2*tan(d*x + c)^3 + 420*b^2*tan(d*x + c)^3 + 1260*a*b*tan(d*x + c)^2 + 1260*a^2*tan(d*x + c))/d","A",0
518,1,118,0,0.532256," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, b^{2} \tan\left(d x + c\right)^{7} + 35 \, a b \tan\left(d x + c\right)^{6} + 21 \, a^{2} \tan\left(d x + c\right)^{5} + 42 \, b^{2} \tan\left(d x + c\right)^{5} + 105 \, a b \tan\left(d x + c\right)^{4} + 70 \, a^{2} \tan\left(d x + c\right)^{3} + 35 \, b^{2} \tan\left(d x + c\right)^{3} + 105 \, a b \tan\left(d x + c\right)^{2} + 105 \, a^{2} \tan\left(d x + c\right)}{105 \, d}"," ",0,"1/105*(15*b^2*tan(d*x + c)^7 + 35*a*b*tan(d*x + c)^6 + 21*a^2*tan(d*x + c)^5 + 42*b^2*tan(d*x + c)^5 + 105*a*b*tan(d*x + c)^4 + 70*a^2*tan(d*x + c)^3 + 35*b^2*tan(d*x + c)^3 + 105*a*b*tan(d*x + c)^2 + 105*a^2*tan(d*x + c))/d","A",0
519,1,80,0,0.496035," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{6 \, b^{2} \tan\left(d x + c\right)^{5} + 15 \, a b \tan\left(d x + c\right)^{4} + 10 \, a^{2} \tan\left(d x + c\right)^{3} + 10 \, b^{2} \tan\left(d x + c\right)^{3} + 30 \, a b \tan\left(d x + c\right)^{2} + 30 \, a^{2} \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(6*b^2*tan(d*x + c)^5 + 15*a*b*tan(d*x + c)^4 + 10*a^2*tan(d*x + c)^3 + 10*b^2*tan(d*x + c)^3 + 30*a*b*tan(d*x + c)^2 + 30*a^2*tan(d*x + c))/d","A",0
520,1,41,0,0.457605," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{b^{2} \tan\left(d x + c\right)^{3} + 3 \, a b \tan\left(d x + c\right)^{2} + 3 \, a^{2} \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(b^2*tan(d*x + c)^3 + 3*a*b*tan(d*x + c)^2 + 3*a^2*tan(d*x + c))/d","B",0
521,1,245,0,2.055749," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + a^{2} d x \tan\left(d x\right)^{2} + b^{2} d x \tan\left(d x\right)^{2} + a^{2} d x \tan\left(c\right)^{2} + b^{2} d x \tan\left(c\right)^{2} - a b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - a^{2} \tan\left(d x\right)^{2} \tan\left(c\right) + b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - a^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + a^{2} d x + b^{2} d x + a b \tan\left(d x\right)^{2} + 4 \, a b \tan\left(d x\right) \tan\left(c\right) + a b \tan\left(c\right)^{2} + a^{2} \tan\left(d x\right) - b^{2} \tan\left(d x\right) + a^{2} \tan\left(c\right) - b^{2} \tan\left(c\right) - a b}{2 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"1/2*(a^2*d*x*tan(d*x)^2*tan(c)^2 + b^2*d*x*tan(d*x)^2*tan(c)^2 + a^2*d*x*tan(d*x)^2 + b^2*d*x*tan(d*x)^2 + a^2*d*x*tan(c)^2 + b^2*d*x*tan(c)^2 - a*b*tan(d*x)^2*tan(c)^2 - a^2*tan(d*x)^2*tan(c) + b^2*tan(d*x)^2*tan(c) - a^2*tan(d*x)*tan(c)^2 + b^2*tan(d*x)*tan(c)^2 + a^2*d*x + b^2*d*x + a*b*tan(d*x)^2 + 4*a*b*tan(d*x)*tan(c) + a*b*tan(c)^2 + a^2*tan(d*x) - b^2*tan(d*x) + a^2*tan(c) - b^2*tan(c) - a*b)/(d*tan(d*x)^2*tan(c)^2 + d*tan(d*x)^2 + d*tan(c)^2 + d)","B",0
522,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)(24*a^2*d*x*tan(c)^4*tan(d*x)^4+48*a^2*d*x*tan(c)^4*tan(d*x)^2+24*a^2*d*x*tan(c)^4+48*a^2*d*x*tan(c)^2*tan(d*x)^4+96*a^2*d*x*tan(c)^2*tan(d*x)^2+48*a^2*d*x*tan(c)^2+24*a^2*d*x*tan(d*x)^4+48*a^2*d*x*tan(d*x)^2+24*a^2*d*x-40*a^2*tan(c)^4*tan(d*x)^3-24*a^2*tan(c)^4*tan(d*x)-40*a^2*tan(c)^3*tan(d*x)^4+48*a^2*tan(c)^3*tan(d*x)^2+24*a^2*tan(c)^3+48*a^2*tan(c)^2*tan(d*x)^3-48*a^2*tan(c)^2*tan(d*x)-24*a^2*tan(c)*tan(d*x)^4-48*a^2*tan(c)*tan(d*x)^2+40*a^2*tan(c)+24*a^2*tan(d*x)^3+40*a^2*tan(d*x)-20*a*b*tan(c)^4*tan(d*x)^4+24*a*b*tan(c)^4*tan(d*x)^2+12*a*b*tan(c)^4+128*a*b*tan(c)^3*tan(d*x)^3+24*a*b*tan(c)^2*tan(d*x)^4-144*a*b*tan(c)^2*tan(d*x)^2+24*a*b*tan(c)^2+128*a*b*tan(c)*tan(d*x)+12*a*b*tan(d*x)^4+24*a*b*tan(d*x)^2-20*a*b+8*b^2*d*x*tan(c)^4*tan(d*x)^4+16*b^2*d*x*tan(c)^4*tan(d*x)^2+8*b^2*d*x*tan(c)^4+16*b^2*d*x*tan(c)^2*tan(d*x)^4+32*b^2*d*x*tan(c)^2*tan(d*x)^2+16*b^2*d*x*tan(c)^2+8*b^2*d*x*tan(d*x)^4+16*b^2*d*x*tan(d*x)^2+8*b^2*d*x+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4*tan(d*x)^4+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4*tan(d*x)^2+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2*tan(d*x)^4+12*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2*tan(d*x)^2+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(d*x)^4+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(d*x)^2+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4*tan(d*x)^4+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4*tan(d*x)^2+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2*tan(d*x)^4+12*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2*tan(d*x)^2+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(d*x)^4+6*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(d*x)^2+3*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))+6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4*tan(d*x)^4+12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4*tan(d*x)^2+6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4+12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2*tan(d*x)^4+24*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2*tan(d*x)^2+12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2+6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(d*x)^4+12*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(d*x)^2+6*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))-6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4*tan(d*x)^4-12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4*tan(d*x)^2-6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4-12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2*tan(d*x)^4-24*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2*tan(d*x)^2-12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2-6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(d*x)^4-12*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(d*x)^2-6*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))+8*b^2*tan(c)^4*tan(d*x)^3-8*b^2*tan(c)^4*tan(d*x)+8*b^2*tan(c)^3*tan(d*x)^4-48*b^2*tan(c)^3*tan(d*x)^2+8*b^2*tan(c)^3-48*b^2*tan(c)^2*tan(d*x)^3+48*b^2*tan(c)^2*tan(d*x)-8*b^2*tan(c)*tan(d*x)^4+48*b^2*tan(c)*tan(d*x)^2-8*b^2*tan(c)+8*b^2*tan(d*x)^3-8*b^2*tan(d*x))/(64*d*tan(c)^4*tan(d*x)^4+128*d*tan(c)^4*tan(d*x)^2+64*d*tan(c)^4+128*d*tan(c)^2*tan(d*x)^4+256*d*tan(c)^2*tan(d*x)^2+128*d*tan(c)^2+64*d*tan(d*x)^4+128*d*tan(d*x)^2+64*d)","F(-2)",0
523,1,437,0,0.597271," ","integrate(sec(d*x+c)^7*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{105 \, {\left(8 \, a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(8 \, a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(1848 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} + 105 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{15} - 5376 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{14} - 3416 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 2779 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 5376 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} + 6328 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 6265 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 26880 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 4760 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 12355 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 26880 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 4760 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 12355 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 16128 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 6328 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6265 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 16128 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 3416 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2779 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 768 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1848 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 105 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 768 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{8}}}{2688 \, d}"," ",0,"1/2688*(105*(8*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(8*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(1848*a^2*tan(1/2*d*x + 1/2*c)^15 + 105*b^2*tan(1/2*d*x + 1/2*c)^15 - 5376*a*b*tan(1/2*d*x + 1/2*c)^14 - 3416*a^2*tan(1/2*d*x + 1/2*c)^13 + 2779*b^2*tan(1/2*d*x + 1/2*c)^13 + 5376*a*b*tan(1/2*d*x + 1/2*c)^12 + 6328*a^2*tan(1/2*d*x + 1/2*c)^11 + 6265*b^2*tan(1/2*d*x + 1/2*c)^11 - 26880*a*b*tan(1/2*d*x + 1/2*c)^10 - 4760*a^2*tan(1/2*d*x + 1/2*c)^9 + 12355*b^2*tan(1/2*d*x + 1/2*c)^9 + 26880*a*b*tan(1/2*d*x + 1/2*c)^8 - 4760*a^2*tan(1/2*d*x + 1/2*c)^7 + 12355*b^2*tan(1/2*d*x + 1/2*c)^7 - 16128*a*b*tan(1/2*d*x + 1/2*c)^6 + 6328*a^2*tan(1/2*d*x + 1/2*c)^5 + 6265*b^2*tan(1/2*d*x + 1/2*c)^5 + 16128*a*b*tan(1/2*d*x + 1/2*c)^4 - 3416*a^2*tan(1/2*d*x + 1/2*c)^3 + 2779*b^2*tan(1/2*d*x + 1/2*c)^3 - 768*a*b*tan(1/2*d*x + 1/2*c)^2 + 1848*a^2*tan(1/2*d*x + 1/2*c) + 105*b^2*tan(1/2*d*x + 1/2*c) + 768*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^8)/d","B",0
524,1,343,0,0.572266," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{15 \, {\left(6 \, a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(6 \, a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} - 480 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 210 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 235 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 480 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 390 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 960 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 390 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 960 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 210 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 235 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 96 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 150 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 96 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{6}}}{240 \, d}"," ",0,"1/240*(15*(6*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(6*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(150*a^2*tan(1/2*d*x + 1/2*c)^11 + 15*b^2*tan(1/2*d*x + 1/2*c)^11 - 480*a*b*tan(1/2*d*x + 1/2*c)^10 - 210*a^2*tan(1/2*d*x + 1/2*c)^9 + 235*b^2*tan(1/2*d*x + 1/2*c)^9 + 480*a*b*tan(1/2*d*x + 1/2*c)^8 + 60*a^2*tan(1/2*d*x + 1/2*c)^7 + 390*b^2*tan(1/2*d*x + 1/2*c)^7 - 960*a*b*tan(1/2*d*x + 1/2*c)^6 + 60*a^2*tan(1/2*d*x + 1/2*c)^5 + 390*b^2*tan(1/2*d*x + 1/2*c)^5 + 960*a*b*tan(1/2*d*x + 1/2*c)^4 - 210*a^2*tan(1/2*d*x + 1/2*c)^3 + 235*b^2*tan(1/2*d*x + 1/2*c)^3 - 96*a*b*tan(1/2*d*x + 1/2*c)^2 + 150*a^2*tan(1/2*d*x + 1/2*c) + 15*b^2*tan(1/2*d*x + 1/2*c) + 96*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^6)/d","B",0
525,1,249,0,0.574122," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, {\left(4 \, a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(4 \, a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 21 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 48 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 21 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4}}}{24 \, d}"," ",0,"1/24*(3*(4*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(4*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(12*a^2*tan(1/2*d*x + 1/2*c)^7 + 3*b^2*tan(1/2*d*x + 1/2*c)^7 - 48*a*b*tan(1/2*d*x + 1/2*c)^6 - 12*a^2*tan(1/2*d*x + 1/2*c)^5 + 21*b^2*tan(1/2*d*x + 1/2*c)^5 + 48*a*b*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*tan(1/2*d*x + 1/2*c)^3 + 21*b^2*tan(1/2*d*x + 1/2*c)^3 - 16*a*b*tan(1/2*d*x + 1/2*c)^2 + 12*a^2*tan(1/2*d*x + 1/2*c) + 3*b^2*tan(1/2*d*x + 1/2*c) + 16*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^4)/d","B",0
526,1,122,0,0.468408," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(2 \, a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - {\left(2 \, a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a b\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*((2*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - (2*a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(b^2*tan(1/2*d*x + 1/2*c)^3 - 4*a*b*tan(1/2*d*x + 1/2*c)^2 + b^2*tan(1/2*d*x + 1/2*c) + 4*a*b)/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","B",0
527,1,1316,0,1.025175," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b \tan\left(\frac{1}{2} \, d x\right)^{2} - 16 \, a b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a b \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) - b^{2} \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, d x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, d x\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) + 1\right)}}{\tan\left(\frac{1}{2} \, c\right)^{2} + 1}\right) - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a b}{2 \, {\left(d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} + d\right)}}"," ",0,"-1/2*(b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*b*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*d*x)^2 + 4*a^2*tan(1/2*d*x)^2*tan(1/2*c) - 4*b^2*tan(1/2*d*x)^2*tan(1/2*c) + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1))*tan(1/2*c)^2 + 4*a^2*tan(1/2*d*x)*tan(1/2*c)^2 - 4*b^2*tan(1/2*d*x)*tan(1/2*c)^2 - 4*a*b*tan(1/2*d*x)^2 - 16*a*b*tan(1/2*d*x)*tan(1/2*c) - 4*a*b*tan(1/2*c)^2 + b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 + 2*tan(1/2*d*x)^4*tan(1/2*c) + 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*tan(1/2*d*x)^3 + 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 - 2*tan(1/2*d*x) - 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) - b^2*log(2*(tan(1/2*d*x)^4*tan(1/2*c)^2 - 2*tan(1/2*d*x)^4*tan(1/2*c) - 2*tan(1/2*d*x)^3*tan(1/2*c)^2 + tan(1/2*d*x)^4 + 2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*tan(1/2*d*x)^3 - 2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*tan(1/2*d*x)^2 + tan(1/2*c)^2 + 2*tan(1/2*d*x) + 2*tan(1/2*c) + 1)/(tan(1/2*c)^2 + 1)) - 4*a^2*tan(1/2*d*x) + 4*b^2*tan(1/2*d*x) - 4*a^2*tan(1/2*c) + 4*b^2*tan(1/2*c) + 4*a*b)/(d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(1/2*d*x)^2 + d*tan(1/2*c)^2 + d)","B",0
528,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)(-96*a^2*tan(c/2)^6*tan(d*x/2)^5-64*a^2*tan(c/2)^6*tan(d*x/2)^3-96*a^2*tan(c/2)^6*tan(d*x/2)-96*a^2*tan(c/2)^5*tan(d*x/2)^6+288*a^2*tan(c/2)^5*tan(d*x/2)^4-288*a^2*tan(c/2)^5*tan(d*x/2)^2+96*a^2*tan(c/2)^5+288*a^2*tan(c/2)^4*tan(d*x/2)^5-1344*a^2*tan(c/2)^4*tan(d*x/2)^3+288*a^2*tan(c/2)^4*tan(d*x/2)-64*a^2*tan(c/2)^3*tan(d*x/2)^6-1344*a^2*tan(c/2)^3*tan(d*x/2)^4+1344*a^2*tan(c/2)^3*tan(d*x/2)^2+64*a^2*tan(c/2)^3-288*a^2*tan(c/2)^2*tan(d*x/2)^5+1344*a^2*tan(c/2)^2*tan(d*x/2)^3-288*a^2*tan(c/2)^2*tan(d*x/2)-96*a^2*tan(c/2)*tan(d*x/2)^6+288*a^2*tan(c/2)*tan(d*x/2)^4-288*a^2*tan(c/2)*tan(d*x/2)^2+96*a^2*tan(c/2)+96*a^2*tan(d*x/2)^5+64*a^2*tan(d*x/2)^3+96*a^2*tan(d*x/2)-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4-27*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4-9*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2-3*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)-6*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^6-18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^4-18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^2-6*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6-18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^6-54*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4-54*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^2-18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4-18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^6-54*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^4-54*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^2-18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2-6*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^6-18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^4-18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^2-6*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))+6*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^6+18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^4+18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^2+6*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6+18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^6+54*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^4+54*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^2+18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4+18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^6+54*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^4+54*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^2+18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2+6*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^6+18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^4+18*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^2+6*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))+6*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^6+18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^4+18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^2+6*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6+18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^6+54*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^4+54*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^2+18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4+18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^6+54*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^4+54*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^2+18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2+6*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^6+18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^4+18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^2+6*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))-6*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^6-18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^4-18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^2-6*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6-18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^6-54*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4-54*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^2-18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4-18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^6-54*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^4-54*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^2-18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2-6*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^6-18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^4-18*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^2-6*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))-32*a*b*tan(c/2)^6*tan(d*x/2)^6+96*a*b*tan(c/2)^6*tan(d*x/2)^4-96*a*b*tan(c/2)^6*tan(d*x/2)^2+32*a*b*tan(c/2)^6+384*a*b*tan(c/2)^5*tan(d*x/2)^5-768*a*b*tan(c/2)^5*tan(d*x/2)^3+384*a*b*tan(c/2)^5*tan(d*x/2)+96*a*b*tan(c/2)^4*tan(d*x/2)^6-1824*a*b*tan(c/2)^4*tan(d*x/2)^4+1824*a*b*tan(c/2)^4*tan(d*x/2)^2-96*a*b*tan(c/2)^4-768*a*b*tan(c/2)^3*tan(d*x/2)^5+3584*a*b*tan(c/2)^3*tan(d*x/2)^3-768*a*b*tan(c/2)^3*tan(d*x/2)-96*a*b*tan(c/2)^2*tan(d*x/2)^6+1824*a*b*tan(c/2)^2*tan(d*x/2)^4-1824*a*b*tan(c/2)^2*tan(d*x/2)^2+96*a*b*tan(c/2)^2+384*a*b*tan(c/2)*tan(d*x/2)^5-768*a*b*tan(c/2)*tan(d*x/2)^3+384*a*b*tan(c/2)*tan(d*x/2)+32*a*b*tan(d*x/2)^6-96*a*b*tan(d*x/2)^4+96*a*b*tan(d*x/2)^2-32*a*b-128*b^2*tan(c/2)^6*tan(d*x/2)^3-384*b^2*tan(c/2)^5*tan(d*x/2)^4+384*b^2*tan(c/2)^5*tan(d*x/2)^2-384*b^2*tan(c/2)^4*tan(d*x/2)^5+1152*b^2*tan(c/2)^4*tan(d*x/2)^3-384*b^2*tan(c/2)^4*tan(d*x/2)-128*b^2*tan(c/2)^3*tan(d*x/2)^6+1152*b^2*tan(c/2)^3*tan(d*x/2)^4-1152*b^2*tan(c/2)^3*tan(d*x/2)^2+128*b^2*tan(c/2)^3+384*b^2*tan(c/2)^2*tan(d*x/2)^5-1152*b^2*tan(c/2)^2*tan(d*x/2)^3+384*b^2*tan(c/2)^2*tan(d*x/2)-384*b^2*tan(c/2)*tan(d*x/2)^4+384*b^2*tan(c/2)*tan(d*x/2)^2+128*b^2*tan(d*x/2)^3)/(48*d*tan(c/2)^6*tan(d*x/2)^6+144*d*tan(c/2)^6*tan(d*x/2)^4+144*d*tan(c/2)^6*tan(d*x/2)^2+48*d*tan(c/2)^6+144*d*tan(c/2)^4*tan(d*x/2)^6+432*d*tan(c/2)^4*tan(d*x/2)^4+432*d*tan(c/2)^4*tan(d*x/2)^2+144*d*tan(c/2)^4+144*d*tan(c/2)^2*tan(d*x/2)^6+432*d*tan(c/2)^2*tan(d*x/2)^4+432*d*tan(c/2)^2*tan(d*x/2)^2+144*d*tan(c/2)^2+48*d*tan(d*x/2)^6+144*d*tan(d*x/2)^4+144*d*tan(d*x/2)^2+48*d)","F(-2)",0
529,-2,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)(-1920*a^2*tan(c/2)^10*tan(d*x/2)^9-2560*a^2*tan(c/2)^10*tan(d*x/2)^7-7424*a^2*tan(c/2)^10*tan(d*x/2)^5-2560*a^2*tan(c/2)^10*tan(d*x/2)^3-1920*a^2*tan(c/2)^10*tan(d*x/2)-1920*a^2*tan(c/2)^9*tan(d*x/2)^10+9600*a^2*tan(c/2)^9*tan(d*x/2)^8-19200*a^2*tan(c/2)^9*tan(d*x/2)^6+19200*a^2*tan(c/2)^9*tan(d*x/2)^4-9600*a^2*tan(c/2)^9*tan(d*x/2)^2+1920*a^2*tan(c/2)^9+9600*a^2*tan(c/2)^8*tan(d*x/2)^9-89600*a^2*tan(c/2)^8*tan(d*x/2)^7+78080*a^2*tan(c/2)^8*tan(d*x/2)^5-89600*a^2*tan(c/2)^8*tan(d*x/2)^3+9600*a^2*tan(c/2)^8*tan(d*x/2)-2560*a^2*tan(c/2)^7*tan(d*x/2)^10-89600*a^2*tan(c/2)^7*tan(d*x/2)^8+281600*a^2*tan(c/2)^7*tan(d*x/2)^6-281600*a^2*tan(c/2)^7*tan(d*x/2)^4+89600*a^2*tan(c/2)^7*tan(d*x/2)^2+2560*a^2*tan(c/2)^7-19200*a^2*tan(c/2)^6*tan(d*x/2)^9+281600*a^2*tan(c/2)^6*tan(d*x/2)^7-688640*a^2*tan(c/2)^6*tan(d*x/2)^5+281600*a^2*tan(c/2)^6*tan(d*x/2)^3-19200*a^2*tan(c/2)^6*tan(d*x/2)-7424*a^2*tan(c/2)^5*tan(d*x/2)^10+78080*a^2*tan(c/2)^5*tan(d*x/2)^8-688640*a^2*tan(c/2)^5*tan(d*x/2)^6+688640*a^2*tan(c/2)^5*tan(d*x/2)^4-78080*a^2*tan(c/2)^5*tan(d*x/2)^2+7424*a^2*tan(c/2)^5+19200*a^2*tan(c/2)^4*tan(d*x/2)^9-281600*a^2*tan(c/2)^4*tan(d*x/2)^7+688640*a^2*tan(c/2)^4*tan(d*x/2)^5-281600*a^2*tan(c/2)^4*tan(d*x/2)^3+19200*a^2*tan(c/2)^4*tan(d*x/2)-2560*a^2*tan(c/2)^3*tan(d*x/2)^10-89600*a^2*tan(c/2)^3*tan(d*x/2)^8+281600*a^2*tan(c/2)^3*tan(d*x/2)^6-281600*a^2*tan(c/2)^3*tan(d*x/2)^4+89600*a^2*tan(c/2)^3*tan(d*x/2)^2+2560*a^2*tan(c/2)^3-9600*a^2*tan(c/2)^2*tan(d*x/2)^9+89600*a^2*tan(c/2)^2*tan(d*x/2)^7-78080*a^2*tan(c/2)^2*tan(d*x/2)^5+89600*a^2*tan(c/2)^2*tan(d*x/2)^3-9600*a^2*tan(c/2)^2*tan(d*x/2)-1920*a^2*tan(c/2)*tan(d*x/2)^10+9600*a^2*tan(c/2)*tan(d*x/2)^8-19200*a^2*tan(c/2)*tan(d*x/2)^6+19200*a^2*tan(c/2)*tan(d*x/2)^4-9600*a^2*tan(c/2)*tan(d*x/2)^2+1920*a^2*tan(c/2)+1920*a^2*tan(d*x/2)^9+2560*a^2*tan(d*x/2)^7+7424*a^2*tan(d*x/2)^5+2560*a^2*tan(d*x/2)^3+1920*a^2*tan(d*x/2)-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^10-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^8-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^6-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^4-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^2-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^10-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^8-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^10-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^8-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^10-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^8-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2+2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2+2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^10-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^8-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^6-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^4-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^2-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^10-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^8-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^10-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^8-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^10-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^8-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-2*tan(c/2)^2*tan(d*x/2)+tan(c/2)^2-tan(d*x/2)^2-2*tan(d*x/2)-1)*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^10-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^8-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^6-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^4-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^2-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^10-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^8-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^10-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^8-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^10-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^8-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2+2*tan(c/2)*tan(d*x/2)^2+2*tan(c/2)+tan(d*x/2)^2-1)-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10*tan(d*x/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^10-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^8-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^6-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^4-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8*tan(d*x/2)^2-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^10-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^8-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^6-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^4-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6*tan(d*x/2)^2-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^10-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^8-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^6-4500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^4-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4*tan(d*x/2)^2-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^10-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^8-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^6-2250*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^4-1125*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2*tan(d*x/2)^2-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(c/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^10-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^8-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^6-450*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^4-225*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)*tan(d*x/2)^2-45*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-2*tan(c/2)*tan(d*x/2)^2-2*tan(c/2)+tan(d*x/2)^2-1)-60*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^10*tan(d*x/2)^10-300*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^10*tan(d*x/2)^8-600*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^10*tan(d*x/2)^6-600*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^10*tan(d*x/2)^4-300*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^10*tan(d*x/2)^2-60*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^10-300*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^8*tan(d*x/2)^10-1500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^8*tan(d*x/2)^8-3000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^8*tan(d*x/2)^6-3000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^8*tan(d*x/2)^4-1500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^8*tan(d*x/2)^2-300*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^8-600*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^10-3000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^8-6000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^6-6000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^4-3000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6*tan(d*x/2)^2-600*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^6-600*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^10-3000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^8-6000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^6-6000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^4-3000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^2-600*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4-300*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^10-1500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^8-3000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^6-3000*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^4-1500*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2*tan(d*x/2)^2-300*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^2-60*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^10-300*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^8-600*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^6-600*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^4-300*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^2-60*a*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)-90*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^10-450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^8-900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^6-900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^4-450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^2-90*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^10-450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^10-2250*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^8-4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^6-4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^4-2250*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^2-450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^8-900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^10-4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^8-9000*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^6-9000*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^4-4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^2-900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^6-900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^10-4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^8-9000*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^6-9000*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4-4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^2-900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4-450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^10-2250*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^8-4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^6-4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^4-2250*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^2-450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^2-90*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^10-450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^8-900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^6-900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^4-450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^2-90*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))+90*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^10+450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^8+900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^6+900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^4+450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^2+90*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^10+450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^10+2250*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^8+4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^6+4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^4+2250*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^2+450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^8+900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^10+4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^8+9000*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^6+9000*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^4+4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^2+900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^6+900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^10+4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^8+9000*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^6+9000*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^4+4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^2+900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^4+450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^10+2250*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^8+4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^6+4500*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^4+2250*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^2+450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(c/2)^2+90*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^10+450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^8+900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^6+900*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^4+450*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))*tan(d*x/2)^2+90*a*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1))+90*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^10+450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^8+900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^6+900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^4+450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^10*tan(d*x/2)^2+90*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^10+450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^10+2250*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^8+4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^6+4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^4+2250*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^8*tan(d*x/2)^2+450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^8+900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^10+4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^8+9000*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^6+9000*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^4+4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6*tan(d*x/2)^2+900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^6+900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^10+4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^8+9000*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^6+9000*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^4+4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4*tan(d*x/2)^2+900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^4+450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^10+2250*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^8+4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^6+4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^4+2250*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2*tan(d*x/2)^2+450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(c/2)^2+90*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^10+450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^8+900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^6+900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^4+450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))*tan(d*x/2)^2+90*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)+tan(d*x/2)+1)/(tan(c/2)*tan(d*x/2)+tan(c/2)-tan(d*x/2)+1))-90*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^10-450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^8-900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^6-900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^4-450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^10*tan(d*x/2)^2-90*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^10-450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^10-2250*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^8-4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^6-4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^4-2250*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^8*tan(d*x/2)^2-450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^8-900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^10-4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^8-9000*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^6-9000*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^4-4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6*tan(d*x/2)^2-900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^6-900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^10-4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^8-9000*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^6-9000*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4-4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^2-900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4-450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^10-2250*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^8-4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^6-4500*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^4-2250*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2*tan(d*x/2)^2-450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^2-90*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^10-450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^8-900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^6-900*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^4-450*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^2-90*a*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))-384*a*b*tan(c/2)^10*tan(d*x/2)^10+1920*a*b*tan(c/2)^10*tan(d*x/2)^8-3840*a*b*tan(c/2)^10*tan(d*x/2)^6+3840*a*b*tan(c/2)^10*tan(d*x/2)^4-1920*a*b*tan(c/2)^10*tan(d*x/2)^2+384*a*b*tan(c/2)^10+7680*a*b*tan(c/2)^9*tan(d*x/2)^9-30720*a*b*tan(c/2)^9*tan(d*x/2)^7+46080*a*b*tan(c/2)^9*tan(d*x/2)^5-30720*a*b*tan(c/2)^9*tan(d*x/2)^3+7680*a*b*tan(c/2)^9*tan(d*x/2)+1920*a*b*tan(c/2)^8*tan(d*x/2)^10-71040*a*b*tan(c/2)^8*tan(d*x/2)^8+203520*a*b*tan(c/2)^8*tan(d*x/2)^6-203520*a*b*tan(c/2)^8*tan(d*x/2)^4+71040*a*b*tan(c/2)^8*tan(d*x/2)^2-1920*a*b*tan(c/2)^8-30720*a*b*tan(c/2)^7*tan(d*x/2)^9+368640*a*b*tan(c/2)^7*tan(d*x/2)^7-675840*a*b*tan(c/2)^7*tan(d*x/2)^5+368640*a*b*tan(c/2)^7*tan(d*x/2)^3-30720*a*b*tan(c/2)^7*tan(d*x/2)-3840*a*b*tan(c/2)^6*tan(d*x/2)^10+203520*a*b*tan(c/2)^6*tan(d*x/2)^8-1082880*a*b*tan(c/2)^6*tan(d*x/2)^6+1082880*a*b*tan(c/2)^6*tan(d*x/2)^4-203520*a*b*tan(c/2)^6*tan(d*x/2)^2+3840*a*b*tan(c/2)^6+46080*a*b*tan(c/2)^5*tan(d*x/2)^9-675840*a*b*tan(c/2)^5*tan(d*x/2)^7+1652736*a*b*tan(c/2)^5*tan(d*x/2)^5-675840*a*b*tan(c/2)^5*tan(d*x/2)^3+46080*a*b*tan(c/2)^5*tan(d*x/2)+3840*a*b*tan(c/2)^4*tan(d*x/2)^10-203520*a*b*tan(c/2)^4*tan(d*x/2)^8+1082880*a*b*tan(c/2)^4*tan(d*x/2)^6-1082880*a*b*tan(c/2)^4*tan(d*x/2)^4+203520*a*b*tan(c/2)^4*tan(d*x/2)^2-3840*a*b*tan(c/2)^4-30720*a*b*tan(c/2)^3*tan(d*x/2)^9+368640*a*b*tan(c/2)^3*tan(d*x/2)^7-675840*a*b*tan(c/2)^3*tan(d*x/2)^5+368640*a*b*tan(c/2)^3*tan(d*x/2)^3-30720*a*b*tan(c/2)^3*tan(d*x/2)-1920*a*b*tan(c/2)^2*tan(d*x/2)^10+71040*a*b*tan(c/2)^2*tan(d*x/2)^8-203520*a*b*tan(c/2)^2*tan(d*x/2)^6+203520*a*b*tan(c/2)^2*tan(d*x/2)^4-71040*a*b*tan(c/2)^2*tan(d*x/2)^2+1920*a*b*tan(c/2)^2+7680*a*b*tan(c/2)*tan(d*x/2)^9-30720*a*b*tan(c/2)*tan(d*x/2)^7+46080*a*b*tan(c/2)*tan(d*x/2)^5-30720*a*b*tan(c/2)*tan(d*x/2)^3+7680*a*b*tan(c/2)*tan(d*x/2)+384*a*b*tan(d*x/2)^10-1920*a*b*tan(d*x/2)^8+3840*a*b*tan(d*x/2)^6-3840*a*b*tan(d*x/2)^4+1920*a*b*tan(d*x/2)^2-384*a*b-2560*b^2*tan(c/2)^10*tan(d*x/2)^7+1024*b^2*tan(c/2)^10*tan(d*x/2)^5-2560*b^2*tan(c/2)^10*tan(d*x/2)^3-7680*b^2*tan(c/2)^9*tan(d*x/2)^8+23040*b^2*tan(c/2)^9*tan(d*x/2)^6-23040*b^2*tan(c/2)^9*tan(d*x/2)^4+7680*b^2*tan(c/2)^9*tan(d*x/2)^2-7680*b^2*tan(c/2)^8*tan(d*x/2)^9+64000*b^2*tan(c/2)^8*tan(d*x/2)^7-133120*b^2*tan(c/2)^8*tan(d*x/2)^5+64000*b^2*tan(c/2)^8*tan(d*x/2)^3-7680*b^2*tan(c/2)^8*tan(d*x/2)-2560*b^2*tan(c/2)^7*tan(d*x/2)^10+64000*b^2*tan(c/2)^7*tan(d*x/2)^8-302080*b^2*tan(c/2)^7*tan(d*x/2)^6+302080*b^2*tan(c/2)^7*tan(d*x/2)^4-64000*b^2*tan(c/2)^7*tan(d*x/2)^2+2560*b^2*tan(c/2)^7+23040*b^2*tan(c/2)^6*tan(d*x/2)^9-302080*b^2*tan(c/2)^6*tan(d*x/2)^7+640000*b^2*tan(c/2)^6*tan(d*x/2)^5-302080*b^2*tan(c/2)^6*tan(d*x/2)^3+23040*b^2*tan(c/2)^6*tan(d*x/2)+1024*b^2*tan(c/2)^5*tan(d*x/2)^10-133120*b^2*tan(c/2)^5*tan(d*x/2)^8+640000*b^2*tan(c/2)^5*tan(d*x/2)^6-640000*b^2*tan(c/2)^5*tan(d*x/2)^4+133120*b^2*tan(c/2)^5*tan(d*x/2)^2-1024*b^2*tan(c/2)^5-23040*b^2*tan(c/2)^4*tan(d*x/2)^9+302080*b^2*tan(c/2)^4*tan(d*x/2)^7-640000*b^2*tan(c/2)^4*tan(d*x/2)^5+302080*b^2*tan(c/2)^4*tan(d*x/2)^3-23040*b^2*tan(c/2)^4*tan(d*x/2)-2560*b^2*tan(c/2)^3*tan(d*x/2)^10+64000*b^2*tan(c/2)^3*tan(d*x/2)^8-302080*b^2*tan(c/2)^3*tan(d*x/2)^6+302080*b^2*tan(c/2)^3*tan(d*x/2)^4-64000*b^2*tan(c/2)^3*tan(d*x/2)^2+2560*b^2*tan(c/2)^3+7680*b^2*tan(c/2)^2*tan(d*x/2)^9-64000*b^2*tan(c/2)^2*tan(d*x/2)^7+133120*b^2*tan(c/2)^2*tan(d*x/2)^5-64000*b^2*tan(c/2)^2*tan(d*x/2)^3+7680*b^2*tan(c/2)^2*tan(d*x/2)-7680*b^2*tan(c/2)*tan(d*x/2)^8+23040*b^2*tan(c/2)*tan(d*x/2)^6-23040*b^2*tan(c/2)*tan(d*x/2)^4+7680*b^2*tan(c/2)*tan(d*x/2)^2+2560*b^2*tan(d*x/2)^7-1024*b^2*tan(d*x/2)^5+2560*b^2*tan(d*x/2)^3)/(960*d*tan(c/2)^10*tan(d*x/2)^10+4800*d*tan(c/2)^10*tan(d*x/2)^8+9600*d*tan(c/2)^10*tan(d*x/2)^6+9600*d*tan(c/2)^10*tan(d*x/2)^4+4800*d*tan(c/2)^10*tan(d*x/2)^2+960*d*tan(c/2)^10+4800*d*tan(c/2)^8*tan(d*x/2)^10+24000*d*tan(c/2)^8*tan(d*x/2)^8+48000*d*tan(c/2)^8*tan(d*x/2)^6+48000*d*tan(c/2)^8*tan(d*x/2)^4+24000*d*tan(c/2)^8*tan(d*x/2)^2+4800*d*tan(c/2)^8+9600*d*tan(c/2)^6*tan(d*x/2)^10+48000*d*tan(c/2)^6*tan(d*x/2)^8+96000*d*tan(c/2)^6*tan(d*x/2)^6+96000*d*tan(c/2)^6*tan(d*x/2)^4+48000*d*tan(c/2)^6*tan(d*x/2)^2+9600*d*tan(c/2)^6+9600*d*tan(c/2)^4*tan(d*x/2)^10+48000*d*tan(c/2)^4*tan(d*x/2)^8+96000*d*tan(c/2)^4*tan(d*x/2)^6+96000*d*tan(c/2)^4*tan(d*x/2)^4+48000*d*tan(c/2)^4*tan(d*x/2)^2+9600*d*tan(c/2)^4+4800*d*tan(c/2)^2*tan(d*x/2)^10+24000*d*tan(c/2)^2*tan(d*x/2)^8+48000*d*tan(c/2)^2*tan(d*x/2)^6+48000*d*tan(c/2)^2*tan(d*x/2)^4+24000*d*tan(c/2)^2*tan(d*x/2)^2+4800*d*tan(c/2)^2+960*d*tan(d*x/2)^10+4800*d*tan(d*x/2)^8+9600*d*tan(d*x/2)^6+9600*d*tan(d*x/2)^4+4800*d*tan(d*x/2)^2+960*d)","F(-2)",0
530,-1,0,0,0.000000," ","integrate(cos(d*x+c)^7*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,1,220,0,1.557576," ","integrate(sec(d*x+c)^8*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{84 \, b^{3} \tan\left(d x + c\right)^{10} + 280 \, a b^{2} \tan\left(d x + c\right)^{9} + 315 \, a^{2} b \tan\left(d x + c\right)^{8} + 315 \, b^{3} \tan\left(d x + c\right)^{8} + 120 \, a^{3} \tan\left(d x + c\right)^{7} + 1080 \, a b^{2} \tan\left(d x + c\right)^{7} + 1260 \, a^{2} b \tan\left(d x + c\right)^{6} + 420 \, b^{3} \tan\left(d x + c\right)^{6} + 504 \, a^{3} \tan\left(d x + c\right)^{5} + 1512 \, a b^{2} \tan\left(d x + c\right)^{5} + 1890 \, a^{2} b \tan\left(d x + c\right)^{4} + 210 \, b^{3} \tan\left(d x + c\right)^{4} + 840 \, a^{3} \tan\left(d x + c\right)^{3} + 840 \, a b^{2} \tan\left(d x + c\right)^{3} + 1260 \, a^{2} b \tan\left(d x + c\right)^{2} + 840 \, a^{3} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(84*b^3*tan(d*x + c)^10 + 280*a*b^2*tan(d*x + c)^9 + 315*a^2*b*tan(d*x + c)^8 + 315*b^3*tan(d*x + c)^8 + 120*a^3*tan(d*x + c)^7 + 1080*a*b^2*tan(d*x + c)^7 + 1260*a^2*b*tan(d*x + c)^6 + 420*b^3*tan(d*x + c)^6 + 504*a^3*tan(d*x + c)^5 + 1512*a*b^2*tan(d*x + c)^5 + 1890*a^2*b*tan(d*x + c)^4 + 210*b^3*tan(d*x + c)^4 + 840*a^3*tan(d*x + c)^3 + 840*a*b^2*tan(d*x + c)^3 + 1260*a^2*b*tan(d*x + c)^2 + 840*a^3*tan(d*x + c))/d","A",0
532,1,166,0,2.715375," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{105 \, b^{3} \tan\left(d x + c\right)^{8} + 360 \, a b^{2} \tan\left(d x + c\right)^{7} + 420 \, a^{2} b \tan\left(d x + c\right)^{6} + 280 \, b^{3} \tan\left(d x + c\right)^{6} + 168 \, a^{3} \tan\left(d x + c\right)^{5} + 1008 \, a b^{2} \tan\left(d x + c\right)^{5} + 1260 \, a^{2} b \tan\left(d x + c\right)^{4} + 210 \, b^{3} \tan\left(d x + c\right)^{4} + 560 \, a^{3} \tan\left(d x + c\right)^{3} + 840 \, a b^{2} \tan\left(d x + c\right)^{3} + 1260 \, a^{2} b \tan\left(d x + c\right)^{2} + 840 \, a^{3} \tan\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*b^3*tan(d*x + c)^8 + 360*a*b^2*tan(d*x + c)^7 + 420*a^2*b*tan(d*x + c)^6 + 280*b^3*tan(d*x + c)^6 + 168*a^3*tan(d*x + c)^5 + 1008*a*b^2*tan(d*x + c)^5 + 1260*a^2*b*tan(d*x + c)^4 + 210*b^3*tan(d*x + c)^4 + 560*a^3*tan(d*x + c)^3 + 840*a*b^2*tan(d*x + c)^3 + 1260*a^2*b*tan(d*x + c)^2 + 840*a^3*tan(d*x + c))/d","A",0
533,1,112,0,1.358781," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{10 \, b^{3} \tan\left(d x + c\right)^{6} + 36 \, a b^{2} \tan\left(d x + c\right)^{5} + 45 \, a^{2} b \tan\left(d x + c\right)^{4} + 15 \, b^{3} \tan\left(d x + c\right)^{4} + 20 \, a^{3} \tan\left(d x + c\right)^{3} + 60 \, a b^{2} \tan\left(d x + c\right)^{3} + 90 \, a^{2} b \tan\left(d x + c\right)^{2} + 60 \, a^{3} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*b^3*tan(d*x + c)^6 + 36*a*b^2*tan(d*x + c)^5 + 45*a^2*b*tan(d*x + c)^4 + 15*b^3*tan(d*x + c)^4 + 20*a^3*tan(d*x + c)^3 + 60*a*b^2*tan(d*x + c)^3 + 90*a^2*b*tan(d*x + c)^2 + 60*a^3*tan(d*x + c))/d","A",0
534,1,57,0,0.962302," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \tan\left(d x + c\right)^{4} + 4 \, a b^{2} \tan\left(d x + c\right)^{3} + 6 \, a^{2} b \tan\left(d x + c\right)^{2} + 4 \, a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(b^3*tan(d*x + c)^4 + 4*a*b^2*tan(d*x + c)^3 + 6*a^2*b*tan(d*x + c)^2 + 4*a^3*tan(d*x + c))/d","B",0
535,1,601,0,3.933688," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, a^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, a b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 2 \, a^{3} d x \tan\left(d x\right)^{2} + 6 \, a b^{2} d x \tan\left(d x\right)^{2} + 2 \, a^{3} d x \tan\left(c\right)^{2} + 6 \, a b^{2} d x \tan\left(c\right)^{2} - 3 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(d x\right)^{2} - 2 \, a^{3} \tan\left(d x\right)^{2} \tan\left(c\right) + 6 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 2 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) \tan\left(c\right)^{2} - 2 \, a^{3} \tan\left(d x\right) \tan\left(c\right)^{2} + 6 \, a b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, a^{3} d x + 6 \, a b^{2} d x + 3 \, a^{2} b \tan\left(d x\right)^{2} - b^{3} \tan\left(d x\right)^{2} + 12 \, a^{2} b \tan\left(d x\right) \tan\left(c\right) - 4 \, b^{3} \tan\left(d x\right) \tan\left(c\right) + 3 \, a^{2} b \tan\left(c\right)^{2} - b^{3} \tan\left(c\right)^{2} - 2 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 2 \, \tan\left(d x\right)^{3} \tan\left(c\right) + \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + \tan\left(d x\right)^{2} - 2 \, \tan\left(d x\right) \tan\left(c\right) + 1\right)}}{\tan\left(c\right)^{2} + 1}\right) + 2 \, a^{3} \tan\left(d x\right) - 6 \, a b^{2} \tan\left(d x\right) + 2 \, a^{3} \tan\left(c\right) - 6 \, a b^{2} \tan\left(c\right) - 3 \, a^{2} b + b^{3}}{4 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + d \tan\left(d x\right)^{2} + d \tan\left(c\right)^{2} + d\right)}}"," ",0,"1/4*(2*a^3*d*x*tan(d*x)^2*tan(c)^2 + 6*a*b^2*d*x*tan(d*x)^2*tan(c)^2 - 2*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2*tan(c)^2 + 2*a^3*d*x*tan(d*x)^2 + 6*a*b^2*d*x*tan(d*x)^2 + 2*a^3*d*x*tan(c)^2 + 6*a*b^2*d*x*tan(c)^2 - 3*a^2*b*tan(d*x)^2*tan(c)^2 + b^3*tan(d*x)^2*tan(c)^2 - 2*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(d*x)^2 - 2*a^3*tan(d*x)^2*tan(c) + 6*a*b^2*tan(d*x)^2*tan(c) - 2*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1))*tan(c)^2 - 2*a^3*tan(d*x)*tan(c)^2 + 6*a*b^2*tan(d*x)*tan(c)^2 + 2*a^3*d*x + 6*a*b^2*d*x + 3*a^2*b*tan(d*x)^2 - b^3*tan(d*x)^2 + 12*a^2*b*tan(d*x)*tan(c) - 4*b^3*tan(d*x)*tan(c) + 3*a^2*b*tan(c)^2 - b^3*tan(c)^2 - 2*b^3*log(4*(tan(d*x)^4*tan(c)^2 - 2*tan(d*x)^3*tan(c) + tan(d*x)^2*tan(c)^2 + tan(d*x)^2 - 2*tan(d*x)*tan(c) + 1)/(tan(c)^2 + 1)) + 2*a^3*tan(d*x) - 6*a*b^2*tan(d*x) + 2*a^3*tan(c) - 6*a*b^2*tan(c) - 3*a^2*b + b^3)/(d*tan(d*x)^2*tan(c)^2 + d*tan(d*x)^2 + d*tan(c)^2 + d)","B",0
536,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)(24*a^3*d*x*tan(c)^4*tan(d*x)^4+48*a^3*d*x*tan(c)^4*tan(d*x)^2+24*a^3*d*x*tan(c)^4+48*a^3*d*x*tan(c)^2*tan(d*x)^4+96*a^3*d*x*tan(c)^2*tan(d*x)^2+48*a^3*d*x*tan(c)^2+24*a^3*d*x*tan(d*x)^4+48*a^3*d*x*tan(d*x)^2+24*a^3*d*x-40*a^3*tan(c)^4*tan(d*x)^3-24*a^3*tan(c)^4*tan(d*x)-40*a^3*tan(c)^3*tan(d*x)^4+48*a^3*tan(c)^3*tan(d*x)^2+24*a^3*tan(c)^3+48*a^3*tan(c)^2*tan(d*x)^3-48*a^3*tan(c)^2*tan(d*x)-24*a^3*tan(c)*tan(d*x)^4-48*a^3*tan(c)*tan(d*x)^2+40*a^3*tan(c)+24*a^3*tan(d*x)^3+40*a^3*tan(d*x)-30*a^2*b*tan(c)^4*tan(d*x)^4+36*a^2*b*tan(c)^4*tan(d*x)^2+18*a^2*b*tan(c)^4+192*a^2*b*tan(c)^3*tan(d*x)^3+36*a^2*b*tan(c)^2*tan(d*x)^4-216*a^2*b*tan(c)^2*tan(d*x)^2+36*a^2*b*tan(c)^2+192*a^2*b*tan(c)*tan(d*x)+18*a^2*b*tan(d*x)^4+36*a^2*b*tan(d*x)^2-30*a^2*b+24*a*b^2*d*x*tan(c)^4*tan(d*x)^4+48*a*b^2*d*x*tan(c)^4*tan(d*x)^2+24*a*b^2*d*x*tan(c)^4+48*a*b^2*d*x*tan(c)^2*tan(d*x)^4+96*a*b^2*d*x*tan(c)^2*tan(d*x)^2+48*a*b^2*d*x*tan(c)^2+24*a*b^2*d*x*tan(d*x)^4+48*a*b^2*d*x*tan(d*x)^2+24*a*b^2*d*x+9*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4*tan(d*x)^4+18*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4*tan(d*x)^2+9*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^4+18*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2*tan(d*x)^4+36*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2*tan(d*x)^2+18*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(c)^2+9*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(d*x)^4+18*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)*tan(d*x)^2+9*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*sign(2*tan(c)^2*tan(d*x)^2-2)+9*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4*tan(d*x)^4+18*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4*tan(d*x)^2+9*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^4+18*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2*tan(d*x)^4+36*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2*tan(d*x)^2+18*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(c)^2+9*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(d*x)^4+18*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))*tan(d*x)^2+9*a*b^2*pi*sign(2*tan(c)^2*tan(d*x)-2*tan(c)*tan(d*x)^2-2*tan(c)+2*tan(d*x))+18*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4*tan(d*x)^4+36*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4*tan(d*x)^2+18*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^4+36*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2*tan(d*x)^4+72*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2*tan(d*x)^2+36*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(c)^2+18*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(d*x)^4+36*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))*tan(d*x)^2+18*a*b^2*atan((tan(c)+tan(d*x))/(tan(c)*tan(d*x)-1))-18*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4*tan(d*x)^4-36*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4*tan(d*x)^2-18*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^4-36*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2*tan(d*x)^4-72*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2*tan(d*x)^2-36*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(c)^2-18*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(d*x)^4-36*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))*tan(d*x)^2-18*a*b^2*atan((tan(c)-tan(d*x))/(tan(c)*tan(d*x)+1))+24*a*b^2*tan(c)^4*tan(d*x)^3-24*a*b^2*tan(c)^4*tan(d*x)+24*a*b^2*tan(c)^3*tan(d*x)^4-144*a*b^2*tan(c)^3*tan(d*x)^2+24*a*b^2*tan(c)^3-144*a*b^2*tan(c)^2*tan(d*x)^3+144*a*b^2*tan(c)^2*tan(d*x)-24*a*b^2*tan(c)*tan(d*x)^4+144*a*b^2*tan(c)*tan(d*x)^2-24*a*b^2*tan(c)+24*a*b^2*tan(d*x)^3-24*a*b^2*tan(d*x)-6*b^3*tan(c)^4*tan(d*x)^4-12*b^3*tan(c)^4*tan(d*x)^2+10*b^3*tan(c)^4+64*b^3*tan(c)^3*tan(d*x)-12*b^3*tan(c)^2*tan(d*x)^4+72*b^3*tan(c)^2*tan(d*x)^2-12*b^3*tan(c)^2+64*b^3*tan(c)*tan(d*x)^3+10*b^3*tan(d*x)^4-12*b^3*tan(d*x)^2-6*b^3)/(64*d*tan(c)^4*tan(d*x)^4+128*d*tan(c)^4*tan(d*x)^2+64*d*tan(c)^4+128*d*tan(c)^2*tan(d*x)^4+256*d*tan(c)^2*tan(d*x)^2+128*d*tan(c)^2+64*d*tan(d*x)^4+128*d*tan(d*x)^2+64*d)","F(-2)",0
537,1,465,0,1.080470," ","integrate(sec(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{105 \, {\left(2 \, a^{3} - a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 105 \, {\left(2 \, a^{3} - a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(350 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} + 105 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{13} - 1680 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{12} - 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 1540 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{11} + 3360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} - 1120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{10} + 630 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 1085 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 5040 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 1120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} + 6720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 2240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 630 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 1085 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3696 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 448 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 840 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 1540 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 672 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 224 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 350 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 105 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 336 \, a^{2} b + 32 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{7}}}{560 \, d}"," ",0,"1/560*(105*(2*a^3 - a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 105*(2*a^3 - a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(350*a^3*tan(1/2*d*x + 1/2*c)^13 + 105*a*b^2*tan(1/2*d*x + 1/2*c)^13 - 1680*a^2*b*tan(1/2*d*x + 1/2*c)^12 - 840*a^3*tan(1/2*d*x + 1/2*c)^11 + 1540*a*b^2*tan(1/2*d*x + 1/2*c)^11 + 3360*a^2*b*tan(1/2*d*x + 1/2*c)^10 - 1120*b^3*tan(1/2*d*x + 1/2*c)^10 + 630*a^3*tan(1/2*d*x + 1/2*c)^9 + 1085*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 5040*a^2*b*tan(1/2*d*x + 1/2*c)^8 - 1120*b^3*tan(1/2*d*x + 1/2*c)^8 + 6720*a^2*b*tan(1/2*d*x + 1/2*c)^6 - 2240*b^3*tan(1/2*d*x + 1/2*c)^6 - 630*a^3*tan(1/2*d*x + 1/2*c)^5 - 1085*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 3696*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 448*b^3*tan(1/2*d*x + 1/2*c)^4 + 840*a^3*tan(1/2*d*x + 1/2*c)^3 - 1540*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 672*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 224*b^3*tan(1/2*d*x + 1/2*c)^2 - 350*a^3*tan(1/2*d*x + 1/2*c) - 105*a*b^2*tan(1/2*d*x + 1/2*c) - 336*a^2*b + 32*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^7)/d","B",0
538,1,333,0,2.614807," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{15 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 15 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} + 45 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{9} - 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{8} - 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 270 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 240 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 480 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 120 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 270 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 80 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 60 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 45 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 120 \, a^{2} b + 16 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{5}}}{120 \, d}"," ",0,"1/120*(15*(4*a^3 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 15*(4*a^3 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(60*a^3*tan(1/2*d*x + 1/2*c)^9 + 45*a*b^2*tan(1/2*d*x + 1/2*c)^9 - 360*a^2*b*tan(1/2*d*x + 1/2*c)^8 - 120*a^3*tan(1/2*d*x + 1/2*c)^7 + 270*a*b^2*tan(1/2*d*x + 1/2*c)^7 + 720*a^2*b*tan(1/2*d*x + 1/2*c)^6 - 240*b^3*tan(1/2*d*x + 1/2*c)^6 - 480*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 80*b^3*tan(1/2*d*x + 1/2*c)^4 + 120*a^3*tan(1/2*d*x + 1/2*c)^3 - 270*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 240*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 80*b^3*tan(1/2*d*x + 1/2*c)^2 - 60*a^3*tan(1/2*d*x + 1/2*c) - 45*a*b^2*tan(1/2*d*x + 1/2*c) - 120*a^2*b + 16*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^5)/d","B",0
539,1,171,0,4.307800," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right) - 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right) + \frac{2 \, {\left(9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 18 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 18 \, a^{2} b + 4 \, b^{3}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3}}}{6 \, d}"," ",0,"1/6*(3*(2*a^3 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1)) - 3*(2*a^3 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1)) + 2*(9*a*b^2*tan(1/2*d*x + 1/2*c)^5 - 18*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 36*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 12*b^3*tan(1/2*d*x + 1/2*c)^2 - 9*a*b^2*tan(1/2*d*x + 1/2*c) - 18*a^2*b + 4*b^3)/(tan(1/2*d*x + 1/2*c)^2 - 1)^3)/d","B",0
540,-2,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)(-8*a^3*tan(c/2)^4*tan(d*x/2)^3+8*a^3*tan(c/2)^4*tan(d*x/2)-8*a^3*tan(c/2)^3*tan(d*x/2)^4+48*a^3*tan(c/2)^3*tan(d*x/2)^2-8*a^3*tan(c/2)^3+48*a^3*tan(c/2)^2*tan(d*x/2)^3-48*a^3*tan(c/2)^2*tan(d*x/2)+8*a^3*tan(c/2)*tan(d*x/2)^4-48*a^3*tan(c/2)*tan(d*x/2)^2+8*a^3*tan(c/2)-8*a^3*tan(d*x/2)^3+8*a^3*tan(d*x/2)-3*a^2*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4*tan(d*x/2)^4+3*a^2*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^4+12*a^2*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^3*tan(d*x/2)^3+12*a^2*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)^3*tan(d*x/2)+12*a^2*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)*tan(d*x/2)^3+12*a^2*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(c/2)*tan(d*x/2)+3*a^2*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)*tan(d*x/2)^4-3*a^2*b*pi*sign(tan(c/2)^2*tan(d*x/2)^2-tan(c/2)^2-4*tan(c/2)*tan(d*x/2)-tan(d*x/2)^2+1)+3*a^2*b*pi*tan(c/2)^4*tan(d*x/2)^4-3*a^2*b*pi*tan(c/2)^4-12*a^2*b*pi*tan(c/2)^3*tan(d*x/2)^3-12*a^2*b*pi*tan(c/2)^3*tan(d*x/2)-12*a^2*b*pi*tan(c/2)*tan(d*x/2)^3-12*a^2*b*pi*tan(c/2)*tan(d*x/2)-3*a^2*b*pi*tan(d*x/2)^4+3*a^2*b*pi+6*a^2*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4-6*a^2*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^4-24*a^2*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^3*tan(d*x/2)^3-24*a^2*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)^3*tan(d*x/2)-24*a^2*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)*tan(d*x/2)^3-24*a^2*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(c/2)*tan(d*x/2)-6*a^2*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))*tan(d*x/2)^4+6*a^2*b*atan((tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1))+6*a^2*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4*tan(d*x/2)^4-6*a^2*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^4-24*a^2*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^3*tan(d*x/2)^3-24*a^2*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)^3*tan(d*x/2)-24*a^2*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)*tan(d*x/2)^3-24*a^2*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(c/2)*tan(d*x/2)-6*a^2*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))*tan(d*x/2)^4+6*a^2*b*atan((tan(c/2)*tan(d*x/2)-tan(c/2)-tan(d*x/2)-1)/(tan(c/2)*tan(d*x/2)+tan(c/2)+tan(d*x/2)-1))-12*a^2*b*tan(c/2)^4*tan(d*x/2)^4+24*a^2*b*tan(c/2)^4*tan(d*x/2)^2-12*a^2*b*tan(c/2)^4+96*a^2*b*tan(c/2)^3*tan(d*x/2)^3-96*a^2*b*tan(c/2)^3*tan(d*x/2)+24*a^2*b*tan(c/2)^2*tan(d*x/2)^4-240*a^2*b*tan(c/2)^2*tan(d*x/2)^2+24*a^2*b*tan(c/2)^2-96*a^2*b*tan(c/2)*tan(d*x/2)^3+96*a^2*b*tan(c/2)*tan(d*x/2)-12*a^2*b*tan(d*x/2)^4+24*a^2*b*tan(d*x/2)^2-12*a^2*b-6*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^4+6*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4+24*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^3*tan(d*x/2)^3+24*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^3*tan(d*x/2)+24*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)^3+24*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)+6*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^4-6*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4+4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2+4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2+4*tan(c/2)*tan(d*x/2)^4-4*tan(c/2)+2*tan(d*x/2)^4-4*tan(d*x/2)^3+4*tan(d*x/2)^2-4*tan(d*x/2)+2)/(tan(c/2)^2+1))+6*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4*tan(d*x/2)^4-6*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^4-24*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^3*tan(d*x/2)^3-24*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)^3*tan(d*x/2)-24*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)^3-24*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(c/2)*tan(d*x/2)-6*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))*tan(d*x/2)^4+6*a*b^2*ln((2*tan(c/2)^2*tan(d*x/2)^4-4*tan(c/2)^2*tan(d*x/2)^3+4*tan(c/2)^2*tan(d*x/2)^2-4*tan(c/2)^2*tan(d*x/2)+2*tan(c/2)^2-4*tan(c/2)*tan(d*x/2)^4+4*tan(c/2)+2*tan(d*x/2)^4+4*tan(d*x/2)^3+4*tan(d*x/2)^2+4*tan(d*x/2)+2)/(tan(c/2)^2+1))+24*a*b^2*tan(c/2)^4*tan(d*x/2)^3-24*a*b^2*tan(c/2)^4*tan(d*x/2)+24*a*b^2*tan(c/2)^3*tan(d*x/2)^4-144*a*b^2*tan(c/2)^3*tan(d*x/2)^2+24*a*b^2*tan(c/2)^3-144*a*b^2*tan(c/2)^2*tan(d*x/2)^3+144*a*b^2*tan(c/2)^2*tan(d*x/2)-24*a*b^2*tan(c/2)*tan(d*x/2)^4+144*a*b^2*tan(c/2)*tan(d*x/2)^2-24*a*b^2*tan(c/2)+24*a*b^2*tan(d*x/2)^3-24*a*b^2*tan(d*x/2)+8*b^3*tan(c/2)^4*tan(d*x/2)^4+8*b^3*tan(c/2)^4-32*b^3*tan(c/2)^3*tan(d*x/2)^3+32*b^3*tan(c/2)^3*tan(d*x/2)+96*b^3*tan(c/2)^2*tan(d*x/2)^2+32*b^3*tan(c/2)*tan(d*x/2)^3-32*b^3*tan(c/2)*tan(d*x/2)+8*b^3*tan(d*x/2)^4+8*b^3)/(4*d*tan(c/2)^4*tan(d*x/2)^4-4*d*tan(c/2)^4-16*d*tan(c/2)^3*tan(d*x/2)^3-16*d*tan(c/2)^3*tan(d*x/2)-16*d*tan(c/2)*tan(d*x/2)^3-16*d*tan(c/2)*tan(d*x/2)-4*d*tan(d*x/2)^4+4*d)","F(-2)",0
541,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate(cos(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,-1,0,0,0.000000," ","integrate(cos(d*x+c)^7*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,1,120,0,0.832253," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, b^{3} \tan\left(d x + c\right)^{4} - 4 \, a b^{2} \tan\left(d x + c\right)^{3} + 6 \, a^{2} b \tan\left(d x + c\right)^{2} + 12 \, b^{3} \tan\left(d x + c\right)^{2} - 12 \, a^{3} \tan\left(d x + c\right) - 24 \, a b^{2} \tan\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{5}}}{12 \, d}"," ",0,"1/12*((3*b^3*tan(d*x + c)^4 - 4*a*b^2*tan(d*x + c)^3 + 6*a^2*b*tan(d*x + c)^2 + 12*b^3*tan(d*x + c)^2 - 12*a^3*tan(d*x + c) - 24*a*b^2*tan(d*x + c))/b^4 + 12*(a^4 + 2*a^2*b^2 + b^4)*log(abs(b*tan(d*x + c) + a))/b^5)/d","A",0
545,1,54,0,0.765853," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{b \tan\left(d x + c\right)^{2} - 2 \, a \tan\left(d x + c\right)}{b^{2}} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{3}}}{2 \, d}"," ",0,"1/2*((b*tan(d*x + c)^2 - 2*a*tan(d*x + c))/b^2 + 2*(a^2 + b^2)*log(abs(b*tan(d*x + c) + a))/b^3)/d","A",0
546,1,19,0,0.705624," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b d}"," ",0,"log(abs(b*tan(d*x + c) + a))/(b*d)","A",0
547,1,182,0,1.109496," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{4} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{3} + 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{b^{3} \tan\left(d x + c\right)^{2} + a^{3} \tan\left(d x + c\right) + a b^{2} \tan\left(d x + c\right) + a^{2} b + 2 \, b^{3}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}}}{2 \, d}"," ",0,"1/2*(2*b^4*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) - b^3*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^3 + 3*a*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + (b^3*tan(d*x + c)^2 + a^3*tan(d*x + c) + a*b^2*tan(d*x + c) + a^2*b + 2*b^3)/((a^4 + 2*a^2*b^2 + b^4)*(tan(d*x + c)^2 + 1)))/d","B",0
548,1,322,0,1.632921," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{8 \, b^{6} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{4 \, b^{5} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{6 \, b^{5} \tan\left(d x + c\right)^{4} + 3 \, a^{5} \tan\left(d x + c\right)^{3} + 10 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} + 7 \, a b^{4} \tan\left(d x + c\right)^{3} + 4 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} + 16 \, b^{5} \tan\left(d x + c\right)^{2} + 5 \, a^{5} \tan\left(d x + c\right) + 14 \, a^{3} b^{2} \tan\left(d x + c\right) + 9 \, a b^{4} \tan\left(d x + c\right) + 2 \, a^{4} b + 8 \, a^{2} b^{3} + 12 \, b^{5}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(8*b^6*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - 4*b^5*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (6*b^5*tan(d*x + c)^4 + 3*a^5*tan(d*x + c)^3 + 10*a^3*b^2*tan(d*x + c)^3 + 7*a*b^4*tan(d*x + c)^3 + 4*a^2*b^3*tan(d*x + c)^2 + 16*b^5*tan(d*x + c)^2 + 5*a^5*tan(d*x + c) + 14*a^3*b^2*tan(d*x + c) + 9*a*b^4*tan(d*x + c) + 2*a^4*b + 8*a^2*b^3 + 12*b^5)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(d*x + c)^2 + 1)^2))/d","B",0
549,1,278,0,0.807911," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} + \frac{6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}} + \frac{2 \, {\left(3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 12 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{2} + 8 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{3}}}{6 \, d}"," ",0,"-1/6*(3*(2*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*(2*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 + 6*(a^4 + 2*a^2*b^2 + b^4)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4) + 2*(3*a*b*tan(1/2*d*x + 1/2*c)^5 + 6*a^2*tan(1/2*d*x + 1/2*c)^4 + 12*b^2*tan(1/2*d*x + 1/2*c)^4 - 12*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 3*a*b*tan(1/2*d*x + 1/2*c) + 6*a^2 + 8*b^2)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^3))/d","B",0
550,1,136,0,1.529174," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{\sqrt{a^{2} + b^{2}} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{b^{2}} + \frac{2}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b}}{d}"," ",0,"-(a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + sqrt(a^2 + b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/b^2 + 2/((tan(1/2*d*x + 1/2*c)^2 - 1)*b))/d","A",0
551,1,74,0,0.613256," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} d}"," ",0,"-log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*d)","A",0
552,1,118,0,1.196236," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{b^{2} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b\right)}}{{\left(a^{2} + b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}}}{d}"," ",0,"-(b^2*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(a*tan(1/2*d*x + 1/2*c) + b)/((a^2 + b^2)*(tan(1/2*d*x + 1/2*c)^2 + 1)))/d","A",0
553,1,286,0,2.797815," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, b^{4} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 6 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2} b + 4 \, b^{3}\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*b^4*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(3*a^3*tan(1/2*d*x + 1/2*c)^5 + 6*a*b^2*tan(1/2*d*x + 1/2*c)^5 + 3*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 6*b^3*tan(1/2*d*x + 1/2*c)^4 + 2*a^3*tan(1/2*d*x + 1/2*c)^3 + 8*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 6*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^3*tan(1/2*d*x + 1/2*c) + 6*a*b^2*tan(1/2*d*x + 1/2*c) + a^2*b + 4*b^3)/((a^4 + 2*a^2*b^2 + b^4)*(tan(1/2*d*x + 1/2*c)^2 + 1)^3))/d","A",0
554,1,253,0,4.956809," ","integrate(sec(d*x+c)^8/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{60 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{7}} - \frac{10 \, {\left(6 \, a^{5} b \tan\left(d x + c\right) + 12 \, a^{3} b^{3} \tan\left(d x + c\right) + 6 \, a b^{5} \tan\left(d x + c\right) + 5 \, a^{6} + 9 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)} b^{7}} - \frac{2 \, b^{8} \tan\left(d x + c\right)^{5} - 5 \, a b^{7} \tan\left(d x + c\right)^{4} + 10 \, a^{2} b^{6} \tan\left(d x + c\right)^{3} + 10 \, b^{8} \tan\left(d x + c\right)^{3} - 20 \, a^{3} b^{5} \tan\left(d x + c\right)^{2} - 30 \, a b^{7} \tan\left(d x + c\right)^{2} + 50 \, a^{4} b^{4} \tan\left(d x + c\right) + 90 \, a^{2} b^{6} \tan\left(d x + c\right) + 30 \, b^{8} \tan\left(d x + c\right)}{b^{10}}}{10 \, d}"," ",0,"-1/10*(60*(a^5 + 2*a^3*b^2 + a*b^4)*log(abs(b*tan(d*x + c) + a))/b^7 - 10*(6*a^5*b*tan(d*x + c) + 12*a^3*b^3*tan(d*x + c) + 6*a*b^5*tan(d*x + c) + 5*a^6 + 9*a^4*b^2 + 3*a^2*b^4 - b^6)/((b*tan(d*x + c) + a)*b^7) - (2*b^8*tan(d*x + c)^5 - 5*a*b^7*tan(d*x + c)^4 + 10*a^2*b^6*tan(d*x + c)^3 + 10*b^8*tan(d*x + c)^3 - 20*a^3*b^5*tan(d*x + c)^2 - 30*a*b^7*tan(d*x + c)^2 + 50*a^4*b^4*tan(d*x + c) + 90*a^2*b^6*tan(d*x + c) + 30*b^8*tan(d*x + c))/b^10)/d","A",0
555,1,149,0,1.582219," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{12 \, {\left(a^{3} + a b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{5}} - \frac{b^{4} \tan\left(d x + c\right)^{3} - 3 \, a b^{3} \tan\left(d x + c\right)^{2} + 9 \, a^{2} b^{2} \tan\left(d x + c\right) + 6 \, b^{4} \tan\left(d x + c\right)}{b^{6}} - \frac{3 \, {\left(4 \, a^{3} b \tan\left(d x + c\right) + 4 \, a b^{3} \tan\left(d x + c\right) + 3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)} b^{5}}}{3 \, d}"," ",0,"-1/3*(12*(a^3 + a*b^2)*log(abs(b*tan(d*x + c) + a))/b^5 - (b^4*tan(d*x + c)^3 - 3*a*b^3*tan(d*x + c)^2 + 9*a^2*b^2*tan(d*x + c) + 6*b^4*tan(d*x + c))/b^6 - 3*(4*a^3*b*tan(d*x + c) + 4*a*b^3*tan(d*x + c) + 3*a^4 + 2*a^2*b^2 - b^4)/((b*tan(d*x + c) + a)*b^5))/d","A",0
556,1,71,0,5.249263," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, a \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{3}} - \frac{\tan\left(d x + c\right)}{b^{2}} - \frac{2 \, a b \tan\left(d x + c\right) + a^{2} - b^{2}}{{\left(b \tan\left(d x + c\right) + a\right)} b^{3}}}{d}"," ",0,"-(2*a*log(abs(b*tan(d*x + c) + a))/b^3 - tan(d*x + c)/b^2 - (2*a*b*tan(d*x + c) + a^2 - b^2)/((b*tan(d*x + c) + a)*b^3))/d","A",0
557,1,20,0,4.898880," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} b d}"," ",0,"-1/((b*tan(d*x + c) + a)*b*d)","A",0
558,1,250,0,1.268786," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{8 \, a b^{4} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{4 \, a b^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{4} + 6 \, a^{2} b^{2} - 3 \, b^{4}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{a^{2} b \tan\left(d x + c\right)^{2} - 3 \, b^{3} \tan\left(d x + c\right)^{2} + a^{3} \tan\left(d x + c\right) + a b^{2} \tan\left(d x + c\right) + 2 \, a^{2} b - 2 \, b^{3}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(d x + c\right)^{3} + a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*(8*a*b^4*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - 4*a*b^3*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^4 + 6*a^2*b^2 - 3*b^4)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^2*b*tan(d*x + c)^2 - 3*b^3*tan(d*x + c)^2 + a^3*tan(d*x + c) + a*b^2*tan(d*x + c) + 2*a^2*b - 2*b^3)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(d*x + c)^3 + a*tan(d*x + c)^2 + b*tan(d*x + c) + a)))/d","A",0
559,1,464,0,2.633240," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{48 \, a b^{6} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}} - \frac{24 \, a b^{5} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{3 \, {\left(a^{6} + 5 \, a^{4} b^{2} + 15 \, a^{2} b^{4} - 5 \, b^{6}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{8 \, {\left(6 \, a b^{6} \tan\left(d x + c\right) + 7 \, a^{2} b^{5} + b^{7}\right)}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}} + \frac{36 \, a b^{5} \tan\left(d x + c\right)^{4} + 3 \, a^{6} \tan\left(d x + c\right)^{3} + 15 \, a^{4} b^{2} \tan\left(d x + c\right)^{3} + 5 \, a^{2} b^{4} \tan\left(d x + c\right)^{3} - 7 \, b^{6} \tan\left(d x + c\right)^{3} + 16 \, a^{3} b^{3} \tan\left(d x + c\right)^{2} + 88 \, a b^{5} \tan\left(d x + c\right)^{2} + 5 \, a^{6} \tan\left(d x + c\right) + 17 \, a^{4} b^{2} \tan\left(d x + c\right) + 3 \, a^{2} b^{4} \tan\left(d x + c\right) - 9 \, b^{6} \tan\left(d x + c\right) + 4 \, a^{5} b + 24 \, a^{3} b^{3} + 56 \, a b^{5}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}^{2}}}{8 \, d}"," ",0,"1/8*(48*a*b^6*log(abs(b*tan(d*x + c) + a))/(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9) - 24*a*b^5*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3*(a^6 + 5*a^4*b^2 + 15*a^2*b^4 - 5*b^6)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 8*(6*a*b^6*tan(d*x + c) + 7*a^2*b^5 + b^7)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)) + (36*a*b^5*tan(d*x + c)^4 + 3*a^6*tan(d*x + c)^3 + 15*a^4*b^2*tan(d*x + c)^3 + 5*a^2*b^4*tan(d*x + c)^3 - 7*b^6*tan(d*x + c)^3 + 16*a^3*b^3*tan(d*x + c)^2 + 88*a*b^5*tan(d*x + c)^2 + 5*a^6*tan(d*x + c) + 17*a^4*b^2*tan(d*x + c) + 3*a^2*b^4*tan(d*x + c) - 9*b^6*tan(d*x + c) + 4*a^5*b + 24*a^3*b^3 + 56*a*b^5)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(tan(d*x + c)^2 + 1)^2))/d","B",0
560,1,530,0,5.884548," ","integrate(sec(d*x+c)^7/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(8 \, a^{4} + 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{6}} - \frac{15 \, {\left(8 \, a^{4} + 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{6}} + \frac{120 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}} + \frac{48 \, {\left(a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} a b^{5}} + \frac{2 \, {\left(36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 27 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 96 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 144 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 288 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 336 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 288 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 304 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 36 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 27 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, a^{3} - 112 \, a b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{4} b^{5}}}{24 \, d}"," ",0,"1/24*(15*(8*a^4 + 12*a^2*b^2 + 3*b^4)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^6 - 15*(8*a^4 + 12*a^2*b^2 + 3*b^4)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^6 + 120*(a^5 + 2*a^3*b^2 + a*b^4)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6) + 48*(a^4*b*tan(1/2*d*x + 1/2*c) + 2*a^2*b^3*tan(1/2*d*x + 1/2*c) + b^5*tan(1/2*d*x + 1/2*c) + a^5 + 2*a^3*b^2 + a*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)*a*b^5) + 2*(36*a^2*b*tan(1/2*d*x + 1/2*c)^7 + 27*b^3*tan(1/2*d*x + 1/2*c)^7 + 96*a^3*tan(1/2*d*x + 1/2*c)^6 + 144*a*b^2*tan(1/2*d*x + 1/2*c)^6 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 3*b^3*tan(1/2*d*x + 1/2*c)^5 - 288*a^3*tan(1/2*d*x + 1/2*c)^4 - 336*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 36*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 3*b^3*tan(1/2*d*x + 1/2*c)^3 + 288*a^3*tan(1/2*d*x + 1/2*c)^2 + 304*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 36*a^2*b*tan(1/2*d*x + 1/2*c) + 27*b^3*tan(1/2*d*x + 1/2*c) - 96*a^3 - 112*a*b^2)/((tan(1/2*d*x + 1/2*c)^2 - 1)^4*b^5))/d","B",0
561,1,280,0,2.926253," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} + \frac{6 \, {\left(a^{3} + a b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2} b^{3}} + \frac{4 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3} + a b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} a b^{3}}}{2 \, d}"," ",0,"1/2*(3*(2*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 3*(2*a^2 + b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 + 6*(a^3 + a*b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4) + 2*(b*tan(1/2*d*x + 1/2*c)^3 + 4*a*tan(1/2*d*x + 1/2*c)^2 + b*tan(1/2*d*x + 1/2*c) - 4*a)/((tan(1/2*d*x + 1/2*c)^2 - 1)^2*b^3) + 4*(a^2*b*tan(1/2*d*x + 1/2*c) + b^3*tan(1/2*d*x + 1/2*c) + a^3 + a*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)*a*b^3))/d","A",0
562,1,166,0,1.927719," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{a \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{2}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{2}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{2}} + \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)} a b}}{d}"," ",0,"(a*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^2) + log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^2 - log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^2 + 2*(b*tan(1/2*d*x + 1/2*c) + a)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)*a*b))/d","A",0
563,1,138,0,2.937762," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{a \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b\right)}}{{\left(a^{3} + a b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}}{d}"," ",0,"-(a*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(b^2*tan(1/2*d*x + 1/2*c) + a*b)/((a^3 + a*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)))/d","A",0
564,1,286,0,3.730521," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{3 \, a b^{2} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 3 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} b + a b^{3}\right)}}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}}}{d}"," ",0,"-(3*a*b^2*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(a^4*tan(1/2*d*x + 1/2*c)^3 - a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + b^4*tan(1/2*d*x + 1/2*c)^3 + 3*a*b^3*tan(1/2*d*x + 1/2*c)^2 - a^4*tan(1/2*d*x + 1/2*c) - 3*a^2*b^2*tan(1/2*d*x + 1/2*c) + b^4*tan(1/2*d*x + 1/2*c) - 2*a^3*b + a*b^3)/((a^5 + 2*a^3*b^2 + a*b^4)*(a*tan(1/2*d*x + 1/2*c)^4 - 2*b*tan(1/2*d*x + 1/2*c)^3 - 2*b*tan(1/2*d*x + 1/2*c) - a)))/d","A",0
565,1,438,0,7.026483," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{15 \, a b^{4} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{6 \, {\left(b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a b^{5}\right)}}{{\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}} - \frac{2 \, {\left(3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 6 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 6 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 8 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a^{3} b + 14 \, a b^{3}\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(15*a*b^4*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 6*(b^6*tan(1/2*d*x + 1/2*c) + a*b^5)/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)) - 2*(3*a^4*tan(1/2*d*x + 1/2*c)^5 + 9*a^2*b^2*tan(1/2*d*x + 1/2*c)^5 - 6*b^4*tan(1/2*d*x + 1/2*c)^5 + 6*a^3*b*tan(1/2*d*x + 1/2*c)^4 + 18*a*b^3*tan(1/2*d*x + 1/2*c)^4 + 2*a^4*tan(1/2*d*x + 1/2*c)^3 + 18*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 - 8*b^4*tan(1/2*d*x + 1/2*c)^3 + 24*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*a^4*tan(1/2*d*x + 1/2*c) + 9*a^2*b^2*tan(1/2*d*x + 1/2*c) - 6*b^4*tan(1/2*d*x + 1/2*c) + 2*a^3*b + 14*a*b^3)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(1/2*d*x + 1/2*c)^2 + 1)^3))/d","A",0
566,1,243,0,1.618025," ","integrate(sec(d*x+c)^8/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{12 \, {\left(5 \, a^{4} + 6 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{7}} - \frac{2 \, {\left(45 \, a^{4} b^{2} \tan\left(d x + c\right)^{2} + 54 \, a^{2} b^{4} \tan\left(d x + c\right)^{2} + 9 \, b^{6} \tan\left(d x + c\right)^{2} + 78 \, a^{5} b \tan\left(d x + c\right) + 84 \, a^{3} b^{3} \tan\left(d x + c\right) + 6 \, a b^{5} \tan\left(d x + c\right) + 34 \, a^{6} + 33 \, a^{4} b^{2} + b^{6}\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} b^{7}} + \frac{b^{9} \tan\left(d x + c\right)^{4} - 4 \, a b^{8} \tan\left(d x + c\right)^{3} + 12 \, a^{2} b^{7} \tan\left(d x + c\right)^{2} + 6 \, b^{9} \tan\left(d x + c\right)^{2} - 40 \, a^{3} b^{6} \tan\left(d x + c\right) - 36 \, a b^{8} \tan\left(d x + c\right)}{b^{12}}}{4 \, d}"," ",0,"1/4*(12*(5*a^4 + 6*a^2*b^2 + b^4)*log(abs(b*tan(d*x + c) + a))/b^7 - 2*(45*a^4*b^2*tan(d*x + c)^2 + 54*a^2*b^4*tan(d*x + c)^2 + 9*b^6*tan(d*x + c)^2 + 78*a^5*b*tan(d*x + c) + 84*a^3*b^3*tan(d*x + c) + 6*a*b^5*tan(d*x + c) + 34*a^6 + 33*a^4*b^2 + b^6)/((b*tan(d*x + c) + a)^2*b^7) + (b^9*tan(d*x + c)^4 - 4*a*b^8*tan(d*x + c)^3 + 12*a^2*b^7*tan(d*x + c)^2 + 6*b^9*tan(d*x + c)^2 - 40*a^3*b^6*tan(d*x + c) - 36*a*b^8*tan(d*x + c))/b^12)/d","A",0
567,1,140,0,2.035985," ","integrate(sec(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(3 \, a^{2} + b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{5}} + \frac{b^{3} \tan\left(d x + c\right)^{2} - 6 \, a b^{2} \tan\left(d x + c\right)}{b^{6}} - \frac{18 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} + 6 \, b^{4} \tan\left(d x + c\right)^{2} + 28 \, a^{3} b \tan\left(d x + c\right) + 4 \, a b^{3} \tan\left(d x + c\right) + 11 \, a^{4} + b^{4}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} b^{5}}}{2 \, d}"," ",0,"1/2*(4*(3*a^2 + b^2)*log(abs(b*tan(d*x + c) + a))/b^5 + (b^3*tan(d*x + c)^2 - 6*a*b^2*tan(d*x + c))/b^6 - (18*a^2*b^2*tan(d*x + c)^2 + 6*b^4*tan(d*x + c)^2 + 28*a^3*b*tan(d*x + c) + 4*a*b^3*tan(d*x + c) + 11*a^4 + b^4)/((b*tan(d*x + c) + a)^2*b^5))/d","A",0
568,1,62,0,2.846368," ","integrate(sec(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{b^{3}} - \frac{3 \, b \tan\left(d x + c\right)^{2} + 2 \, a \tan\left(d x + c\right) + b}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} b^{2}}}{2 \, d}"," ",0,"1/2*(2*log(abs(b*tan(d*x + c) + a))/b^3 - (3*b*tan(d*x + c)^2 + 2*a*tan(d*x + c) + b)/((b*tan(d*x + c) + a)^2*b^2))/d","A",0
569,1,20,0,0.886625," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(b \tan\left(d x + c\right) + a\right)}^{2} b d}"," ",0,"-1/2/((b*tan(d*x + c) + a)^2*b*d)","A",0
570,1,439,0,1.144013," ","integrate(cos(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{{\left(a^{5} + 10 \, a^{3} b^{2} - 15 \, a b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{2 \, {\left(5 \, a^{2} b^{3} - b^{5}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{4 \, {\left(5 \, a^{2} b^{4} - b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}} + \frac{10 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} - 2 \, b^{5} \tan\left(d x + c\right)^{2} + a^{5} \tan\left(d x + c\right) - 2 \, a^{3} b^{2} \tan\left(d x + c\right) - 3 \, a b^{4} \tan\left(d x + c\right) + 3 \, a^{4} b + 12 \, a^{2} b^{3} - 3 \, b^{5}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\tan\left(d x + c\right)^{2} + 1\right)}} - \frac{30 \, a^{2} b^{5} \tan\left(d x + c\right)^{2} - 6 \, b^{7} \tan\left(d x + c\right)^{2} + 68 \, a^{3} b^{4} \tan\left(d x + c\right) - 4 \, a b^{6} \tan\left(d x + c\right) + 39 \, a^{4} b^{3} + 4 \, a^{2} b^{5} + b^{7}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*((a^5 + 10*a^3*b^2 - 15*a*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 2*(5*a^2*b^3 - b^5)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 4*(5*a^2*b^4 - b^6)*log(abs(b*tan(d*x + c) + a))/(a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9) + (10*a^2*b^3*tan(d*x + c)^2 - 2*b^5*tan(d*x + c)^2 + a^5*tan(d*x + c) - 2*a^3*b^2*tan(d*x + c) - 3*a*b^4*tan(d*x + c) + 3*a^4*b + 12*a^2*b^3 - 3*b^5)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(tan(d*x + c)^2 + 1)) - (30*a^2*b^5*tan(d*x + c)^2 - 6*b^7*tan(d*x + c)^2 + 68*a^3*b^4*tan(d*x + c) - 4*a*b^6*tan(d*x + c) + 39*a^4*b^3 + 4*a^2*b^5 + b^7)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)^2))/d","B",0
571,1,587,0,1.325974," ","integrate(cos(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{7} + 7 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 35 \, a b^{6}\right)} {\left(d x + c\right)}}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} - \frac{12 \, {\left(7 \, a^{2} b^{5} - b^{7}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{10} + 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} + 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} + b^{10}} + \frac{24 \, {\left(7 \, a^{2} b^{6} - b^{8}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{10} b + 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} + 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} + b^{11}} + \frac{3 \, a^{5} b^{2} \tan\left(d x + c\right)^{5} + 18 \, a^{3} b^{4} \tan\left(d x + c\right)^{5} - 81 \, a b^{6} \tan\left(d x + c\right)^{5} + 6 \, a^{6} b \tan\left(d x + c\right)^{4} + 36 \, a^{4} b^{3} \tan\left(d x + c\right)^{4} - 78 \, a^{2} b^{5} \tan\left(d x + c\right)^{4} - 12 \, b^{7} \tan\left(d x + c\right)^{4} + 3 \, a^{7} \tan\left(d x + c\right)^{3} + 23 \, a^{5} b^{2} \tan\left(d x + c\right)^{3} + 61 \, a^{3} b^{4} \tan\left(d x + c\right)^{3} - 151 \, a b^{6} \tan\left(d x + c\right)^{3} + 10 \, a^{6} b \tan\left(d x + c\right)^{2} + 74 \, a^{4} b^{3} \tan\left(d x + c\right)^{2} - 146 \, a^{2} b^{5} \tan\left(d x + c\right)^{2} - 18 \, b^{7} \tan\left(d x + c\right)^{2} + 5 \, a^{7} \tan\left(d x + c\right) + 26 \, a^{5} b^{2} \tan\left(d x + c\right) + 49 \, a^{3} b^{4} \tan\left(d x + c\right) - 68 \, a b^{6} \tan\left(d x + c\right) + 6 \, a^{6} b + 44 \, a^{4} b^{3} - 62 \, a^{2} b^{5} - 4 \, b^{7}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right)^{3} + a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right) + a\right)}^{2}}}{8 \, d}"," ",0,"1/8*(3*(a^7 + 7*a^5*b^2 + 35*a^3*b^4 - 35*a*b^6)*(d*x + c)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) - 12*(7*a^2*b^5 - b^7)*log(tan(d*x + c)^2 + 1)/(a^10 + 5*a^8*b^2 + 10*a^6*b^4 + 10*a^4*b^6 + 5*a^2*b^8 + b^10) + 24*(7*a^2*b^6 - b^8)*log(abs(b*tan(d*x + c) + a))/(a^10*b + 5*a^8*b^3 + 10*a^6*b^5 + 10*a^4*b^7 + 5*a^2*b^9 + b^11) + (3*a^5*b^2*tan(d*x + c)^5 + 18*a^3*b^4*tan(d*x + c)^5 - 81*a*b^6*tan(d*x + c)^5 + 6*a^6*b*tan(d*x + c)^4 + 36*a^4*b^3*tan(d*x + c)^4 - 78*a^2*b^5*tan(d*x + c)^4 - 12*b^7*tan(d*x + c)^4 + 3*a^7*tan(d*x + c)^3 + 23*a^5*b^2*tan(d*x + c)^3 + 61*a^3*b^4*tan(d*x + c)^3 - 151*a*b^6*tan(d*x + c)^3 + 10*a^6*b*tan(d*x + c)^2 + 74*a^4*b^3*tan(d*x + c)^2 - 146*a^2*b^5*tan(d*x + c)^2 - 18*b^7*tan(d*x + c)^2 + 5*a^7*tan(d*x + c) + 26*a^5*b^2*tan(d*x + c) + 49*a^3*b^4*tan(d*x + c) - 68*a*b^6*tan(d*x + c) + 6*a^6*b + 44*a^4*b^3 - 62*a^2*b^5 - 4*b^7)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(b*tan(d*x + c)^3 + a*tan(d*x + c)^2 + b*tan(d*x + c) + a)^2))/d","B",0
572,1,510,0,1.602618," ","integrate(sec(d*x+c)^7/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{6}} - \frac{15 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{6}} + \frac{15 \, {\left(4 \, a^{4} + 5 \, a^{2} b^{2} + b^{4}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{6}} + \frac{2 \, {\left(9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 36 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 18 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 72 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 36 \, a^{2} + 14 \, b^{2}\right)}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{3} b^{5}} + \frac{6 \, {\left(7 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 5 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 25 \, a^{5} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 23 \, a^{3} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{6} - 7 \, a^{4} b^{2} + a^{2} b^{4}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2} a^{2} b^{5}}}{6 \, d}"," ",0,"-1/6*(15*(4*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^6 - 15*(4*a^3 + 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^6 + 15*(4*a^4 + 5*a^2*b^2 + b^4)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^6) + 2*(9*a*b*tan(1/2*d*x + 1/2*c)^5 + 36*a^2*tan(1/2*d*x + 1/2*c)^4 + 18*b^2*tan(1/2*d*x + 1/2*c)^4 - 72*a^2*tan(1/2*d*x + 1/2*c)^2 - 24*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a*b*tan(1/2*d*x + 1/2*c) + 36*a^2 + 14*b^2)/((tan(1/2*d*x + 1/2*c)^2 - 1)^3*b^5) + 6*(7*a^5*b*tan(1/2*d*x + 1/2*c)^3 + 5*a^3*b^3*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^5*tan(1/2*d*x + 1/2*c)^3 + 8*a^6*tan(1/2*d*x + 1/2*c)^2 - 9*a^4*b^2*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*b^4*tan(1/2*d*x + 1/2*c)^2 + 2*b^6*tan(1/2*d*x + 1/2*c)^2 - 25*a^5*b*tan(1/2*d*x + 1/2*c) - 23*a^3*b^3*tan(1/2*d*x + 1/2*c) + 2*a*b^5*tan(1/2*d*x + 1/2*c) - 8*a^6 - 7*a^4*b^2 + a^2*b^4)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2*a^2*b^5))/d","B",0
573,1,314,0,3.694303," ","integrate(sec(d*x+c)^5/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{b^{4}} - \frac{6 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{b^{4}} + \frac{3 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} b^{4}} + \frac{4}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)} b^{3}} + \frac{2 \, {\left(3 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 2 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 13 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{4} + a^{2} b^{2}\right)}}{{\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2} a^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(6*a*log(abs(tan(1/2*d*x + 1/2*c) + 1))/b^4 - 6*a*log(abs(tan(1/2*d*x + 1/2*c) - 1))/b^4 + 3*(2*a^2 + b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*b^4) + 4/((tan(1/2*d*x + 1/2*c)^2 - 1)*b^3) + 2*(3*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 2*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 2*b^4*tan(1/2*d*x + 1/2*c)^2 - 13*a^3*b*tan(1/2*d*x + 1/2*c) + 2*a*b^3*tan(1/2*d*x + 1/2*c) - 4*a^4 + a^2*b^2)/((a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2*a^2*b^3))/d","B",0
574,1,221,0,1.738523," ","integrate(sec(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{\log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b\right)}}{{\left(a^{4} + a^{2} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(a^3*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^2*tan(1/2*d*x + 1/2*c)^3 + a^2*b*tan(1/2*d*x + 1/2*c)^2 - 2*b^3*tan(1/2*d*x + 1/2*c)^2 + a^3*tan(1/2*d*x + 1/2*c) - 2*a*b^2*tan(1/2*d*x + 1/2*c) - a^2*b)/((a^4 + a^2*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2))/d","B",0
575,1,293,0,3.189784," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, a^{2} - b^{2}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, a^{4} b - a^{2} b^{3}\right)}}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*((2*a^2 - b^2)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(5*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 4*a^4*b*tan(1/2*d*x + 1/2*c)^2 - 7*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 2*b^5*tan(1/2*d*x + 1/2*c)^2 - 11*a^3*b^2*tan(1/2*d*x + 1/2*c) - 2*a*b^4*tan(1/2*d*x + 1/2*c) - 4*a^4*b - a^2*b^3)/((a^6 + 2*a^4*b^2 + a^2*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2))/d","B",0
576,1,399,0,2.751795," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(4 \, a^{2} b^{2} - b^{4}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a^{2} + b^{2}}} - \frac{4 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2} b - b^{3}\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}} - \frac{2 \, {\left(9 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 8 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 23 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{4} b^{3} - a^{2} b^{5}\right)}}{{\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(3*(4*a^2*b^2 - b^4)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a^2 + b^2)) - 4*(a^3*tan(1/2*d*x + 1/2*c) - 3*a*b^2*tan(1/2*d*x + 1/2*c) + 3*a^2*b - b^3)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(tan(1/2*d*x + 1/2*c)^2 + 1)) - 2*(9*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 8*a^4*b^3*tan(1/2*d*x + 1/2*c)^2 - 15*a^2*b^5*tan(1/2*d*x + 1/2*c)^2 - 2*b^7*tan(1/2*d*x + 1/2*c)^2 - 23*a^3*b^4*tan(1/2*d*x + 1/2*c) - 2*a*b^6*tan(1/2*d*x + 1/2*c) - 8*a^4*b^3 - a^2*b^5)/((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2))/d","A",0
577,1,640,0,4.344730," ","integrate(cos(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(6 \, a^{2} b^{4} - b^{6}\right)} \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} + b^{2}}} - \frac{6 \, {\left(13 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 12 \, a^{4} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 23 \, a^{2} b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{9} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 35 \, a^{3} b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{8} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, a^{4} b^{5} - a^{2} b^{7}\right)}}{{\left(a^{10} + 4 \, a^{8} b^{2} + 6 \, a^{6} b^{4} + 4 \, a^{4} b^{6} + a^{2} b^{8}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2}} - \frac{4 \, {\left(3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 27 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 9 \, a^{4} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 36 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 9 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 32 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 42 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, a^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 27 \, a b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4} b + 32 \, a^{2} b^{3} - 7 \, b^{5}\right)}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(15*(6*a^2*b^4 - b^6)*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*sqrt(a^2 + b^2)) - 6*(13*a^3*b^6*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^8*tan(1/2*d*x + 1/2*c)^3 + 12*a^4*b^5*tan(1/2*d*x + 1/2*c)^2 - 23*a^2*b^7*tan(1/2*d*x + 1/2*c)^2 - 2*b^9*tan(1/2*d*x + 1/2*c)^2 - 35*a^3*b^6*tan(1/2*d*x + 1/2*c) - 2*a*b^8*tan(1/2*d*x + 1/2*c) - 12*a^4*b^5 - a^2*b^7)/((a^10 + 4*a^8*b^2 + 6*a^6*b^4 + 4*a^4*b^6 + a^2*b^8)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2) - 4*(3*a^5*tan(1/2*d*x + 1/2*c)^5 + 12*a^3*b^2*tan(1/2*d*x + 1/2*c)^5 - 27*a*b^4*tan(1/2*d*x + 1/2*c)^5 + 9*a^4*b*tan(1/2*d*x + 1/2*c)^4 + 36*a^2*b^3*tan(1/2*d*x + 1/2*c)^4 - 9*b^5*tan(1/2*d*x + 1/2*c)^4 + 2*a^5*tan(1/2*d*x + 1/2*c)^3 + 32*a^3*b^2*tan(1/2*d*x + 1/2*c)^3 - 42*a*b^4*tan(1/2*d*x + 1/2*c)^3 + 60*a^2*b^3*tan(1/2*d*x + 1/2*c)^2 - 12*b^5*tan(1/2*d*x + 1/2*c)^2 + 3*a^5*tan(1/2*d*x + 1/2*c) + 12*a^3*b^2*tan(1/2*d*x + 1/2*c) - 27*a*b^4*tan(1/2*d*x + 1/2*c) + 3*a^4*b + 32*a^2*b^3 - 7*b^5)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(tan(1/2*d*x + 1/2*c)^2 + 1)^3))/d","B",0
578,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(7/2)*(b*tan(f*x + e) + a), x)","F",0
579,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a), x)","F",0
580,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a), x)","F",0
581,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a), x)","F",0
582,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{b \tan\left(f x + e\right) + a}{\sqrt{d \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/sqrt(d*sec(f*x + e)), x)","F",0
583,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(3/2), x)","F",0
584,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(5/2), x)","F",0
585,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(7/2), x)","F",0
586,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a)^2, x)","F",0
587,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a)^2, x)","F",0
588,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)^2, x)","F",0
589,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\sqrt{d \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/sqrt(d*sec(f*x + e)), x)","F",0
590,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(3/2), x)","F",0
591,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(5/2), x)","F",0
592,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(7/2), x)","F",0
593,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(9/2), x)","F",0
594,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a)^3, x)","F",0
595,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a)^3, x)","F",0
596,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{3}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)^3, x)","F",0
597,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\sqrt{d \sec\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/sqrt(d*sec(f*x + e)), x)","F",0
598,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/(d*sec(f*x + e))^(3/2), x)","F",0
599,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/(d*sec(f*x + e))^(5/2), x)","F",0
600,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/(d*sec(f*x + e))^(7/2), x)","F",0
601,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\left(d \sec\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/(d*sec(f*x + e))^(9/2), x)","F",0
602,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(d*sec(f*x+e))^(11/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}{\left(d \sec\left(f x + e\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3/(d*sec(f*x + e))^(11/2), x)","F",0
603,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(7/2)/(b*tan(f*x + e) + a), x)","F",0
604,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/2)/(b*tan(f*x + e) + a), x)","F",0
605,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)/(b*tan(f*x + e) + a), x)","F",0
606,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{d \sec\left(f x + e\right)}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))/(b*tan(f*x + e) + a), x)","F",0
607,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)), x)","F",0
608,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a)), x)","F",0
609,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a)), x)","F",0
610,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(7/2)/(b*tan(f*x + e) + a)^2, x)","F",0
611,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/2)/(b*tan(f*x + e) + a)^2, x)","F",0
612,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)/(b*tan(f*x + e) + a)^2, x)","F",0
613,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\sqrt{d \sec\left(f x + e\right)}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))/(b*tan(f*x + e) + a)^2, x)","F",0
614,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)^2), x)","F",0
615,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a)^2), x)","F",0
616,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a)^2), x)","F",0
617,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(7/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{7}{2}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(7/2)/(b*tan(f*x + e) + a)^3, x)","F",0
618,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/2)/(b*tan(f*x + e) + a)^3, x)","F",0
619,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(3/2)/(b*tan(f*x + e) + a)^3, x)","F",0
620,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\sqrt{d \sec\left(f x + e\right)}}{{\left(b \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e))/(b*tan(f*x + e) + a)^3, x)","F",0
621,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{1}{\sqrt{d \sec\left(f x + e\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(d*sec(f*x + e))*(b*tan(f*x + e) + a)^3), x)","F",0
622,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(3/2)*(b*tan(f*x + e) + a)^3), x)","F",0
623,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/2)*(b*tan(f*x + e) + a)^3), x)","F",0
624,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)*(b*tan(f*x + e) + a), x)","F",0
625,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a), x)","F",0
626,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(1/3), x)","F",0
627,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(d*sec(f*x+e))^(5/3),x, algorithm=""giac"")","\int \frac{b \tan\left(f x + e\right) + a}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)/(d*sec(f*x + e))^(5/3), x)","F",0
628,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)*(b*tan(f*x + e) + a)^2, x)","F",0
629,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a)^2, x)","F",0
630,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(1/3),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(1/3), x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(d*sec(f*x+e))^(5/3),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/(d*sec(f*x + e))^(5/3), x)","F",0
632,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)/(b*tan(f*x + e) + a), x)","F",0
633,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)/(b*tan(f*x + e) + a), x)","F",0
634,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a)), x)","F",0
635,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(b \tan\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/3)*(b*tan(f*x + e) + a)), x)","F",0
636,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(5/3)/(b*tan(f*x + e) + a)^2, x)","F",0
637,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^(1/3)/(b*tan(f*x + e) + a)^2, x)","F",0
638,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(1/3)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{1}{3}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(1/3)*(b*tan(f*x + e) + a)^2), x)","F",0
639,0,0,0,0.000000," ","integrate(1/(d*sec(f*x+e))^(5/3)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{\left(d \sec\left(f x + e\right)\right)^{\frac{5}{3}} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*sec(f*x + e))^(5/3)*(b*tan(f*x + e) + a)^2), x)","F",0
640,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{3} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3*(d*sec(f*x + e))^m, x)","F",0
641,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*(d*sec(f*x + e))^m, x)","F",0
642,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)} \left(d \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)*(d*sec(f*x + e))^m, x)","F",0
643,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{m}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^m/(b*tan(f*x + e) + a), x)","F",0
644,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \sec\left(f x + e\right)\right)^{m}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^m/(b*tan(f*x + e) + a)^2, x)","F",0
645,0,0,0,0.000000," ","integrate((d*sec(f*x+e))^m*(a+b*tan(f*x+e))^n,x, algorithm=""giac"")","\int \left(d \sec\left(f x + e\right)\right)^{m} {\left(b \tan\left(f x + e\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((d*sec(f*x + e))^m*(b*tan(f*x + e) + a)^n, x)","F",0
646,0,0,0,0.000000," ","integrate(sec(d*x+c)^6*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sec(d*x + c)^6, x)","F",0
647,0,0,0,0.000000," ","integrate(sec(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sec(d*x + c)^4, x)","F",0
648,0,0,0,0.000000," ","integrate(sec(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sec(d*x + c)^2, x)","F",0
649,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cos(d*x + c)^2, x)","F",0
650,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.45Unable to divide, perhaps due to rounding error%%%{1048576,[2,0,10,17,20,20]%%%}+%%%{-10485760,[2,0,10,17,20,18]%%%}+%%%{47185920,[2,0,10,17,20,16]%%%}+%%%{-125829120,[2,0,10,17,20,14]%%%}+%%%{220200960,[2,0,10,17,20,12]%%%}+%%%{-264241152,[2,0,10,17,20,10]%%%}+%%%{220200960,[2,0,10,17,20,8]%%%}+%%%{-125829120,[2,0,10,17,20,6]%%%}+%%%{47185920,[2,0,10,17,20,4]%%%}+%%%{-10485760,[2,0,10,17,20,2]%%%}+%%%{1048576,[2,0,10,17,20,0]%%%}+%%%{3145728*i,[2,0,10,16,21,20]%%%}+%%%{-31457280*i,[2,0,10,16,21,18]%%%}+%%%{141557760*i,[2,0,10,16,21,16]%%%}+%%%{-377487360*i,[2,0,10,16,21,14]%%%}+%%%{660602880*i,[2,0,10,16,21,12]%%%}+%%%{-792723456*i,[2,0,10,16,21,10]%%%}+%%%{660602880*i,[2,0,10,16,21,8]%%%}+%%%{-377487360*i,[2,0,10,16,21,6]%%%}+%%%{141557760*i,[2,0,10,16,21,4]%%%}+%%%{-31457280*i,[2,0,10,16,21,2]%%%}+%%%{3145728*i,[2,0,10,16,21,0]%%%}+%%%{4194304,[2,0,10,15,22,20]%%%}+%%%{-41943040,[2,0,10,15,22,18]%%%}+%%%{188743680,[2,0,10,15,22,16]%%%}+%%%{-503316480,[2,0,10,15,22,14]%%%}+%%%{880803840,[2,0,10,15,22,12]%%%}+%%%{-1056964608,[2,0,10,15,22,10]%%%}+%%%{880803840,[2,0,10,15,22,8]%%%}+%%%{-503316480,[2,0,10,15,22,6]%%%}+%%%{188743680,[2,0,10,15,22,4]%%%}+%%%{-41943040,[2,0,10,15,22,2]%%%}+%%%{4194304,[2,0,10,15,22,0]%%%}+%%%{20971520*i,[2,0,10,14,23,20]%%%}+%%%{-209715200*i,[2,0,10,14,23,18]%%%}+%%%{943718400*i,[2,0,10,14,23,16]%%%}+%%%{-2516582400*i,[2,0,10,14,23,14]%%%}+%%%{4404019200*i,[2,0,10,14,23,12]%%%}+%%%{-5284823040*i,[2,0,10,14,23,10]%%%}+%%%{4404019200*i,[2,0,10,14,23,8]%%%}+%%%{-2516582400*i,[2,0,10,14,23,6]%%%}+%%%{943718400*i,[2,0,10,14,23,4]%%%}+%%%{-209715200*i,[2,0,10,14,23,2]%%%}+%%%{20971520*i,[2,0,10,14,23,0]%%%}+%%%{58720256*i,[2,0,10,12,25,20]%%%}+%%%{-587202560*i,[2,0,10,12,25,18]%%%}+%%%{2642411520*i,[2,0,10,12,25,16]%%%}+%%%{-7046430720*i,[2,0,10,12,25,14]%%%}+%%%{12331253760*i,[2,0,10,12,25,12]%%%}+%%%{-14797504512*i,[2,0,10,12,25,10]%%%}+%%%{12331253760*i,[2,0,10,12,25,8]%%%}+%%%{-7046430720*i,[2,0,10,12,25,6]%%%}+%%%{2642411520*i,[2,0,10,12,25,4]%%%}+%%%{-587202560*i,[2,0,10,12,25,2]%%%}+%%%{58720256*i,[2,0,10,12,25,0]%%%}+%%%{-29360128,[2,0,10,11,26,20]%%%}+%%%{293601280,[2,0,10,11,26,18]%%%}+%%%{-1321205760,[2,0,10,11,26,16]%%%}+%%%{3523215360,[2,0,10,11,26,14]%%%}+%%%{-6165626880,[2,0,10,11,26,12]%%%}+%%%{7398752256,[2,0,10,11,26,10]%%%}+%%%{-6165626880,[2,0,10,11,26,8]%%%}+%%%{3523215360,[2,0,10,11,26,6]%%%}+%%%{-1321205760,[2,0,10,11,26,4]%%%}+%%%{293601280,[2,0,10,11,26,2]%%%}+%%%{-29360128,[2,0,10,11,26,0]%%%}+%%%{88080384*i,[2,0,10,10,27,20]%%%}+%%%{-880803840*i,[2,0,10,10,27,18]%%%}+%%%{3963617280*i,[2,0,10,10,27,16]%%%}+%%%{-10569646080*i,[2,0,10,10,27,14]%%%}+%%%{18496880640*i,[2,0,10,10,27,12]%%%}+%%%{-22196256768*i,[2,0,10,10,27,10]%%%}+%%%{18496880640*i,[2,0,10,10,27,8]%%%}+%%%{-10569646080*i,[2,0,10,10,27,6]%%%}+%%%{3963617280*i,[2,0,10,10,27,4]%%%}+%%%{-880803840*i,[2,0,10,10,27,2]%%%}+%%%{88080384*i,[2,0,10,10,27,0]%%%}+%%%{-73400320,[2,0,10,9,28,20]%%%}+%%%{734003200,[2,0,10,9,28,18]%%%}+%%%{-3303014400,[2,0,10,9,28,16]%%%}+%%%{8808038400,[2,0,10,9,28,14]%%%}+%%%{-15414067200,[2,0,10,9,28,12]%%%}+%%%{18496880640,[2,0,10,9,28,10]%%%}+%%%{-15414067200,[2,0,10,9,28,8]%%%}+%%%{8808038400,[2,0,10,9,28,6]%%%}+%%%{-3303014400,[2,0,10,9,28,4]%%%}+%%%{734003200,[2,0,10,9,28,2]%%%}+%%%{-73400320,[2,0,10,9,28,0]%%%}+%%%{73400320*i,[2,0,10,8,29,20]%%%}+%%%{-734003200*i,[2,0,10,8,29,18]%%%}+%%%{3303014400*i,[2,0,10,8,29,16]%%%}+%%%{-8808038400*i,[2,0,10,8,29,14]%%%}+%%%{15414067200*i,[2,0,10,8,29,12]%%%}+%%%{-18496880640*i,[2,0,10,8,29,10]%%%}+%%%{15414067200*i,[2,0,10,8,29,8]%%%}+%%%{-8808038400*i,[2,0,10,8,29,6]%%%}+%%%{3303014400*i,[2,0,10,8,29,4]%%%}+%%%{-734003200*i,[2,0,10,8,29,2]%%%}+%%%{73400320*i,[2,0,10,8,29,0]%%%}+%%%{-88080384,[2,0,10,7,30,20]%%%}+%%%{880803840,[2,0,10,7,30,18]%%%}+%%%{-3963617280,[2,0,10,7,30,16]%%%}+%%%{10569646080,[2,0,10,7,30,14]%%%}+%%%{-18496880640,[2,0,10,7,30,12]%%%}+%%%{22196256768,[2,0,10,7,30,10]%%%}+%%%{-18496880640,[2,0,10,7,30,8]%%%}+%%%{10569646080,[2,0,10,7,30,6]%%%}+%%%{-3963617280,[2,0,10,7,30,4]%%%}+%%%{880803840,[2,0,10,7,30,2]%%%}+%%%{-88080384,[2,0,10,7,30,0]%%%}+%%%{29360128*i,[2,0,10,6,31,20]%%%}+%%%{-293601280*i,[2,0,10,6,31,18]%%%}+%%%{1321205760*i,[2,0,10,6,31,16]%%%}+%%%{-3523215360*i,[2,0,10,6,31,14]%%%}+%%%{6165626880*i,[2,0,10,6,31,12]%%%}+%%%{-7398752256*i,[2,0,10,6,31,10]%%%}+%%%{6165626880*i,[2,0,10,6,31,8]%%%}+%%%{-3523215360*i,[2,0,10,6,31,6]%%%}+%%%{1321205760*i,[2,0,10,6,31,4]%%%}+%%%{-293601280*i,[2,0,10,6,31,2]%%%}+%%%{29360128*i,[2,0,10,6,31,0]%%%}+%%%{-58720256,[2,0,10,5,32,20]%%%}+%%%{587202560,[2,0,10,5,32,18]%%%}+%%%{-2642411520,[2,0,10,5,32,16]%%%}+%%%{7046430720,[2,0,10,5,32,14]%%%}+%%%{-12331253760,[2,0,10,5,32,12]%%%}+%%%{14797504512,[2,0,10,5,32,10]%%%}+%%%{-12331253760,[2,0,10,5,32,8]%%%}+%%%{7046430720,[2,0,10,5,32,6]%%%}+%%%{-2642411520,[2,0,10,5,32,4]%%%}+%%%{587202560,[2,0,10,5,32,2]%%%}+%%%{-58720256,[2,0,10,5,32,0]%%%}+%%%{-20971520,[2,0,10,3,34,20]%%%}+%%%{209715200,[2,0,10,3,34,18]%%%}+%%%{-943718400,[2,0,10,3,34,16]%%%}+%%%{2516582400,[2,0,10,3,34,14]%%%}+%%%{-4404019200,[2,0,10,3,34,12]%%%}+%%%{5284823040,[2,0,10,3,34,10]%%%}+%%%{-4404019200,[2,0,10,3,34,8]%%%}+%%%{2516582400,[2,0,10,3,34,6]%%%}+%%%{-943718400,[2,0,10,3,34,4]%%%}+%%%{209715200,[2,0,10,3,34,2]%%%}+%%%{-20971520,[2,0,10,3,34,0]%%%}+%%%{-4194304*i,[2,0,10,2,35,20]%%%}+%%%{41943040*i,[2,0,10,2,35,18]%%%}+%%%{-188743680*i,[2,0,10,2,35,16]%%%}+%%%{503316480*i,[2,0,10,2,35,14]%%%}+%%%{-880803840*i,[2,0,10,2,35,12]%%%}+%%%{1056964608*i,[2,0,10,2,35,10]%%%}+%%%{-880803840*i,[2,0,10,2,35,8]%%%}+%%%{503316480*i,[2,0,10,2,35,6]%%%}+%%%{-188743680*i,[2,0,10,2,35,4]%%%}+%%%{41943040*i,[2,0,10,2,35,2]%%%}+%%%{-4194304*i,[2,0,10,2,35,0]%%%}+%%%{-3145728,[2,0,10,1,36,20]%%%}+%%%{31457280,[2,0,10,1,36,18]%%%}+%%%{-141557760,[2,0,10,1,36,16]%%%}+%%%{377487360,[2,0,10,1,36,14]%%%}+%%%{-660602880,[2,0,10,1,36,12]%%%}+%%%{792723456,[2,0,10,1,36,10]%%%}+%%%{-660602880,[2,0,10,1,36,8]%%%}+%%%{377487360,[2,0,10,1,36,6]%%%}+%%%{-141557760,[2,0,10,1,36,4]%%%}+%%%{31457280,[2,0,10,1,36,2]%%%}+%%%{-3145728,[2,0,10,1,36,0]%%%}+%%%{-1048576*i,[2,0,10,0,37,20]%%%}+%%%{10485760*i,[2,0,10,0,37,18]%%%}+%%%{-47185920*i,[2,0,10,0,37,16]%%%}+%%%{125829120*i,[2,0,10,0,37,14]%%%}+%%%{-220200960*i,[2,0,10,0,37,12]%%%}+%%%{264241152*i,[2,0,10,0,37,10]%%%}+%%%{-220200960*i,[2,0,10,0,37,8]%%%}+%%%{125829120*i,[2,0,10,0,37,6]%%%}+%%%{-47185920*i,[2,0,10,0,37,4]%%%}+%%%{10485760*i,[2,0,10,0,37,2]%%%}+%%%{-1048576*i,[2,0,10,0,37,0]%%%}+%%%{2097152,[1,0,10,17,20,20]%%%}+%%%{-20971520,[1,0,10,17,20,18]%%%}+%%%{94371840,[1,0,10,17,20,16]%%%}+%%%{-251658240,[1,0,10,17,20,14]%%%}+%%%{440401920,[1,0,10,17,20,12]%%%}+%%%{-528482304,[1,0,10,17,20,10]%%%}+%%%{440401920,[1,0,10,17,20,8]%%%}+%%%{-251658240,[1,0,10,17,20,6]%%%}+%%%{94371840,[1,0,10,17,20,4]%%%}+%%%{-20971520,[1,0,10,17,20,2]%%%}+%%%{2097152,[1,0,10,17,20,0]%%%}+%%%{4194304*i,[1,0,10,16,21,20]%%%}+%%%{-41943040*i,[1,0,10,16,21,18]%%%}+%%%{188743680*i,[1,0,10,16,21,16]%%%}+%%%{-503316480*i,[1,0,10,16,21,14]%%%}+%%%{880803840*i,[1,0,10,16,21,12]%%%}+%%%{-1056964608*i,[1,0,10,16,21,10]%%%}+%%%{880803840*i,[1,0,10,16,21,8]%%%}+%%%{-503316480*i,[1,0,10,16,21,6]%%%}+%%%{188743680*i,[1,0,10,16,21,4]%%%}+%%%{-41943040*i,[1,0,10,16,21,2]%%%}+%%%{4194304*i,[1,0,10,16,21,0]%%%}+%%%{16777216,[1,0,10,15,22,20]%%%}+%%%{-167772160,[1,0,10,15,22,18]%%%}+%%%{754974720,[1,0,10,15,22,16]%%%}+%%%{-2013265920,[1,0,10,15,22,14]%%%}+%%%{3523215360,[1,0,10,15,22,12]%%%}+%%%{-4227858432,[1,0,10,15,22,10]%%%}+%%%{3523215360,[1,0,10,15,22,8]%%%}+%%%{-2013265920,[1,0,10,15,22,6]%%%}+%%%{754974720,[1,0,10,15,22,4]%%%}+%%%{-167772160,[1,0,10,15,22,2]%%%}+%%%{16777216,[1,0,10,15,22,0]%%%}+%%%{41943040*i,[1,0,10,14,23,20]%%%}+%%%{-419430400*i,[1,0,10,14,23,18]%%%}+%%%{1887436800*i,[1,0,10,14,23,16]%%%}+%%%{-5033164800*i,[1,0,10,14,23,14]%%%}+%%%{8808038400*i,[1,0,10,14,23,12]%%%}+%%%{-10569646080*i,[1,0,10,14,23,10]%%%}+%%%{8808038400*i,[1,0,10,14,23,8]%%%}+%%%{-5033164800*i,[1,0,10,14,23,6]%%%}+%%%{1887436800*i,[1,0,10,14,23,4]%%%}+%%%{-419430400*i,[1,0,10,14,23,2]%%%}+%%%{41943040*i,[1,0,10,14,23,0]%%%}+%%%{41943040,[1,0,10,13,24,20]%%%}+%%%{-419430400,[1,0,10,13,24,18]%%%}+%%%{1887436800,[1,0,10,13,24,16]%%%}+%%%{-5033164800,[1,0,10,13,24,14]%%%}+%%%{8808038400,[1,0,10,13,24,12]%%%}+%%%{-10569646080,[1,0,10,13,24,10]%%%}+%%%{8808038400,[1,0,10,13,24,8]%%%}+%%%{-5033164800,[1,0,10,13,24,6]%%%}+%%%{1887436800,[1,0,10,13,24,4]%%%}+%%%{-419430400,[1,0,10,13,24,2]%%%}+%%%{41943040,[1,0,10,13,24,0]%%%}+%%%{159383552*i,[1,0,10,12,25,20]%%%}+%%%{-1593835520*i,[1,0,10,12,25,18]%%%}+%%%{7172259840*i,[1,0,10,12,25,16]%%%}+%%%{-19126026240*i,[1,0,10,12,25,14]%%%}+%%%{33470545920*i,[1,0,10,12,25,12]%%%}+%%%{-40164655104*i,[1,0,10,12,25,10]%%%}+%%%{33470545920*i,[1,0,10,12,25,8]%%%}+%%%{-19126026240*i,[1,0,10,12,25,6]%%%}+%%%{7172259840*i,[1,0,10,12,25,4]%%%}+%%%{-1593835520*i,[1,0,10,12,25,2]%%%}+%%%{159383552*i,[1,0,10,12,25,0]%%%}+%%%{16777216,[1,0,10,11,26,20]%%%}+%%%{-167772160,[1,0,10,11,26,18]%%%}+%%%{754974720,[1,0,10,11,26,16]%%%}+%%%{-2013265920,[1,0,10,11,26,14]%%%}+%%%{3523215360,[1,0,10,11,26,12]%%%}+%%%{-4227858432,[1,0,10,11,26,10]%%%}+%%%{3523215360,[1,0,10,11,26,8]%%%}+%%%{-2013265920,[1,0,10,11,26,6]%%%}+%%%{754974720,[1,0,10,11,26,4]%%%}+%%%{-167772160,[1,0,10,11,26,2]%%%}+%%%{16777216,[1,0,10,11,26,0]%%%}+%%%{310378496*i,[1,0,10,10,27,20]%%%}+%%%{-3103784960*i,[1,0,10,10,27,18]%%%}+%%%{13967032320*i,[1,0,10,10,27,16]%%%}+%%%{-37245419520*i,[1,0,10,10,27,14]%%%}+%%%{65179484160*i,[1,0,10,10,27,12]%%%}+%%%{-78215380992*i,[1,0,10,10,27,10]%%%}+%%%{65179484160*i,[1,0,10,10,27,8]%%%}+%%%{-37245419520*i,[1,0,10,10,27,6]%%%}+%%%{13967032320*i,[1,0,10,10,27,4]%%%}+%%%{-3103784960*i,[1,0,10,10,27,2]%%%}+%%%{310378496*i,[1,0,10,10,27,0]%%%}+%%%{-104857600,[1,0,10,9,28,20]%%%}+%%%{1048576000,[1,0,10,9,28,18]%%%}+%%%{-4718592000,[1,0,10,9,28,16]%%%}+%%%{12582912000,[1,0,10,9,28,14]%%%}+%%%{-22020096000,[1,0,10,9,28,12]%%%}+%%%{26424115200,[1,0,10,9,28,10]%%%}+%%%{-22020096000,[1,0,10,9,28,8]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35,14]%%%}+%%%{2113929216*i,[0,0,10,2,35,13]%%%}+%%%{-352321536*i,[0,0,10,2,35,12]%%%}+%%%{-3170893824*i,[0,0,10,2,35,11]%%%}+%%%{1056964608*i,[0,0,10,2,35,10]%%%}+%%%{3170893824*i,[0,0,10,2,35,9]%%%}+%%%{-1409286144*i,[0,0,10,2,35,8]%%%}+%%%{-2113929216*i,[0,0,10,2,35,7]%%%}+%%%{1107296256*i,[0,0,10,2,35,6]%%%}+%%%{905969664*i,[0,0,10,2,35,5]%%%}+%%%{-528482304*i,[0,0,10,2,35,4]%%%}+%%%{-226492416*i,[0,0,10,2,35,3]%%%}+%%%{142606336*i,[0,0,10,2,35,2]%%%}+%%%{25165824*i,[0,0,10,2,35,1]%%%}+%%%{-16777216*i,[0,0,10,2,35,0]%%%}+%%%{1048576,[0,0,10,1,36,20]%%%}+%%%{-25165824,[0,0,10,1,36,19]%%%}+%%%{14680064,[0,0,10,1,36,18]%%%}+%%%{226492416,[0,0,10,1,36,17]%%%}+%%%{-179306496,[0,0,10,1,36,16]%%%}+%%%{-905969664,[0,0,10,1,36,15]%%%}+%%%{780140544,[0,0,10,1,36,14]%%%}+%%%{2113929216,[0,0,10,1,36,13]%%%}+%%%{-1893728256,[0,0,10,1,36,12]%%%}+%%%{-3170893824,[0,0,10,1,36,11]%%%}+%%%{2906652672,[0,0,10,1,36,10]%%%}+%%%{3170893824,[0,0,10,1,36,9]%%%}+%%%{-2950692864,[0,0,10,1,36,8]%%%}+%%%{-2113929216,[0,0,10,1,36,7]%%%}+%%%{1988100096,[0,0,10,1,36,6]%%%}+%%%{905969664,[0,0,10,1,36,5]%%%}+%%%{-858783744,[0,0,10,1,36,4]%%%}+%%%{-226492416,[0,0,10,1,36,3]%%%}+%%%{216006656,[0,0,10,1,36,2]%%%}+%%%{25165824,[0,0,10,1,36,1]%%%}+%%%{-24117248,[0,0,10,1,36,0]%%%}+%%%{1048576*i,[0,0,10,0,37,20]%%%}+%%%{-8388608*i,[0,0,10,0,37,19]%%%}+%%%{-2097152*i,[0,0,10,0,37,18]%%%}+%%%{75497472*i,[0,0,10,0,37,17]%%%}+%%%{-28311552*i,[0,0,10,0,37,16]%%%}+%%%{-301989888*i,[0,0,10,0,37,15]%%%}+%%%{176160768*i,[0,0,10,0,37,14]%%%}+%%%{704643072*i,[0,0,10,0,37,13]%%%}+%%%{-484442112*i,[0,0,10,0,37,12]%%%}+%%%{-1056964608*i,[0,0,10,0,37,11]%%%}+%%%{792723456*i,[0,0,10,0,37,10]%%%}+%%%{1056964608*i,[0,0,10,0,37,9]%%%}+%%%{-836763648*i,[0,0,10,0,37,8]%%%}+%%%{-704643072*i,[0,0,10,0,37,7]%%%}+%%%{578813952*i,[0,0,10,0,37,6]%%%}+%%%{301989888*i,[0,0,10,0,37,5]%%%}+%%%{-254803968*i,[0,0,10,0,37,4]%%%}+%%%{-75497472*i,[0,0,10,0,37,3]%%%}+%%%{65011712*i,[0,0,10,0,37,2]%%%}+%%%{8388608*i,[0,0,10,0,37,1]%%%}+%%%{-7340032*i,[0,0,10,0,37,0]%%%} / %%%{1024,[0,0,5,9,10,10]%%%}+%%%{-5120,[0,0,5,9,10,8]%%%}+%%%{10240,[0,0,5,9,10,6]%%%}+%%%{-10240,[0,0,5,9,10,4]%%%}+%%%{5120,[0,0,5,9,10,2]%%%}+%%%{-1024,[0,0,5,9,10,0]%%%}+%%%{1024*i,[0,0,5,8,11,10]%%%}+%%%{-5120*i,[0,0,5,8,11,8]%%%}+%%%{10240*i,[0,0,5,8,11,6]%%%}+%%%{-10240*i,[0,0,5,8,11,4]%%%}+%%%{5120*i,[0,0,5,8,11,2]%%%}+%%%{-1024*i,[0,0,5,8,11,0]%%%}+%%%{4096,[0,0,5,7,12,10]%%%}+%%%{-20480,[0,0,5,7,12,8]%%%}+%%%{40960,[0,0,5,7,12,6]%%%}+%%%{-40960,[0,0,5,7,12,4]%%%}+%%%{20480,[0,0,5,7,12,2]%%%}+%%%{-4096,[0,0,5,7,12,0]%%%}+%%%{4096*i,[0,0,5,6,13,10]%%%}+%%%{-20480*i,[0,0,5,6,13,8]%%%}+%%%{40960*i,[0,0,5,6,13,6]%%%}+%%%{-40960*i,[0,0,5,6,13,4]%%%}+%%%{20480*i,[0,0,5,6,13,2]%%%}+%%%{-4096*i,[0,0,5,6,13,0]%%%}+%%%{6144,[0,0,5,5,14,10]%%%}+%%%{-30720,[0,0,5,5,14,8]%%%}+%%%{61440,[0,0,5,5,14,6]%%%}+%%%{-61440,[0,0,5,5,14,4]%%%}+%%%{30720,[0,0,5,5,14,2]%%%}+%%%{-6144,[0,0,5,5,14,0]%%%}+%%%{6144*i,[0,0,5,4,15,10]%%%}+%%%{-30720*i,[0,0,5,4,15,8]%%%}+%%%{61440*i,[0,0,5,4,15,6]%%%}+%%%{-61440*i,[0,0,5,4,15,4]%%%}+%%%{30720*i,[0,0,5,4,15,2]%%%}+%%%{-6144*i,[0,0,5,4,15,0]%%%}+%%%{4096,[0,0,5,3,16,10]%%%}+%%%{-20480,[0,0,5,3,16,8]%%%}+%%%{40960,[0,0,5,3,16,6]%%%}+%%%{-40960,[0,0,5,3,16,4]%%%}+%%%{20480,[0,0,5,3,16,2]%%%}+%%%{-4096,[0,0,5,3,16,0]%%%}+%%%{4096*i,[0,0,5,2,17,10]%%%}+%%%{-20480*i,[0,0,5,2,17,8]%%%}+%%%{40960*i,[0,0,5,2,17,6]%%%}+%%%{-40960*i,[0,0,5,2,17,4]%%%}+%%%{20480*i,[0,0,5,2,17,2]%%%}+%%%{-4096*i,[0,0,5,2,17,0]%%%}+%%%{1024,[0,0,5,1,18,10]%%%}+%%%{-5120,[0,0,5,1,18,8]%%%}+%%%{10240,[0,0,5,1,18,6]%%%}+%%%{-10240,[0,0,5,1,18,4]%%%}+%%%{5120,[0,0,5,1,18,2]%%%}+%%%{-1024,[0,0,5,1,18,0]%%%}+%%%{1024*i,[0,0,5,0,19,10]%%%}+%%%{-5120*i,[0,0,5,0,19,8]%%%}+%%%{10240*i,[0,0,5,0,19,6]%%%}+%%%{-10240*i,[0,0,5,0,19,4]%%%}+%%%{5120*i,[0,0,5,0,19,2]%%%}+%%%{-1024*i,[0,0,5,0,19,0]%%%} Error: Bad Argument Value","F(-2)",0
651,0,0,0,0.000000," ","integrate(sec(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sec(d*x + c)^3, x)","F",0
652,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sec\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sec(d*x + c), x)","F",0
653,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cos(d*x + c), x)","F",0
654,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cos\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cos(d*x + c)^3, x)","F",0
655,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)*(I*a*tan(d*x + c) + a), x)","F",0
656,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)*(I*a*tan(d*x + c) + a), x)","F",0
657,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
658,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \sqrt{e \cos\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))*(I*a*tan(d*x + c) + a), x)","F",0
659,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
660,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(3/2), x)","F",0
661,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(5/2), x)","F",0
662,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(7/2), x)","F",0
663,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(7/2)/(I*a*tan(d*x + c) + a)^2, x)","F",0
664,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/(I*a*tan(d*x + c) + a)^2, x)","F",0
665,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/(I*a*tan(d*x + c) + a)^2, x)","F",0
666,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/(I*a*tan(d*x + c) + a)^2, x)","F",0
667,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*(I*a*tan(d*x + c) + a)^2), x)","F",0
668,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*(I*a*tan(d*x + c) + a)^2), x)","F",0
669,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*(I*a*tan(d*x + c) + a)^2), x)","F",0
670,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*(I*a*tan(d*x + c) + a)^2), x)","F",0
671,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(9/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{9}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(9/2)*(I*a*tan(d*x + c) + a)^2), x)","F",0
672,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(11/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{11}{2}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(11/2)*(I*a*tan(d*x + c) + a)^2), x)","F",0
673,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))^(7/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
674,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [7]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-27]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [26]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-89]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [63]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-49]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-86]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-64]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-30]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [70]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [22]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [42]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [56]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-9]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-13]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [46]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [24]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [49]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-6]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [81]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [18]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-49]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-33]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-70]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [8]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [63]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-64]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [2]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [62]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-37]Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-80]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-23]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [65]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-85]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [28]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-44]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-22]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [93]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [91]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [31]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-21]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [88]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [76]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-66]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [66]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [5]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-23]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [79]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-88]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [9]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [6]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-69]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-8]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [31]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [89]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [2]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [97]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-92]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [80]Warning, choosing root of [1,0,0,0,%%%{-1,[1]%%%}] at parameters values [-24]Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 5.13Done","F(-2)",0
675,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueSimplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.49Done","F(-2)",0
676,-2,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Simplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueSimplification assuming c near 0Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Simplification assuming a near 0Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.46Done","F(-2)",0
677,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{e \cos\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/sqrt(e*cos(d*x + c)), x)","F",0
678,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(3/2), x)","F",0
679,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(5/2), x)","F",0
680,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/(e*cos(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/(e*cos(d*x + c))^(7/2), x)","F",0
681,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(5/2)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
682,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^(3/2)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
683,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e \cos\left(d x + c\right)}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(e*cos(d*x + c))/sqrt(I*a*tan(d*x + c) + a), x)","F",0
684,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e \cos\left(d x + c\right)} \sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/(sqrt(e*cos(d*x + c))*sqrt(I*a*tan(d*x + c) + a)), x)","F",0
685,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{3}{2}} \sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(3/2)*sqrt(I*a*tan(d*x + c) + a)), x)","F",0
686,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{5}{2}} \sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(5/2)*sqrt(I*a*tan(d*x + c) + a)), x)","F",0
687,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\left(e \cos\left(d x + c\right)\right)^{\frac{7}{2}} \sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/((e*cos(d*x + c))^(7/2)*sqrt(I*a*tan(d*x + c) + a)), x)","F",0
688,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int \left(e \cos\left(d x + c\right)\right)^{m} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^m*(I*a*tan(d*x + c) + a)^n, x)","F",0
689,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \left(e \cos\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2*(e*cos(d*x + c))^m, x)","F",0
690,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)} \left(e \cos\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)*(e*cos(d*x + c))^m, x)","F",0
691,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{m}}{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^m/(I*a*tan(d*x + c) + a), x)","F",0
692,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^m/(I*a*tan(d*x + c) + a)^2, x)","F",0
693,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \left(e \cos\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*(e*cos(d*x + c))^m, x)","F",0
694,0,0,0,0.000000," ","integrate((e*cos(d*x+c))^m/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\left(e \cos\left(d x + c\right)\right)^{m}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((e*cos(d*x + c))^m/sqrt(I*a*tan(d*x + c) + a), x)","F",0
695,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{3} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3*(d*cos(f*x + e))^m, x)","F",0
696,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*(d*cos(f*x + e))^m, x)","F",0
697,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)} \left(d \cos\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)*(d*cos(f*x + e))^m, x)","F",0
698,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{m}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^m/(b*tan(f*x + e) + a), x)","F",0
699,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \cos\left(f x + e\right)\right)^{m}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^m/(b*tan(f*x + e) + a)^2, x)","F",0
700,0,0,0,0.000000," ","integrate((d*cos(f*x+e))^m*(a+b*tan(f*x+e))^n,x, algorithm=""giac"")","\int \left(d \cos\left(f x + e\right)\right)^{m} {\left(b \tan\left(f x + e\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((d*cos(f*x + e))^m*(b*tan(f*x + e) + a)^n, x)","F",0
